Numerical analysis of heat treatment of TiCN coated AA7075 aluminium alloy

NASA Astrophysics Data System (ADS)

Srinath, M. K.; Prasad, M. S. Ganesha

2018-04-01

The Numerical analysis of heat treatments of TiCN coated AA7075 aluminium alloys is presented in this paper. The Convection-Diffusion-Reaction (CDR) equation with solutions in the Streamlined-Upward Petrov-Galerkin (SUPG) method for different parameters is provided for the understanding of the process. An experimental process to improve the surface properties of AA-7075 aluminium alloy was attempted through the coatings of TiCN and subsequent heat treatments. From the experimental process, optimized temperature and time was obtained which gave the maximum surface hardness and corrosion resistance. The paper gives an understanding and use of the CDR equation for application of the process. Expression to determine convection, diffusion and reaction parameters are provided which is used to obtain the overall expression of the heat treatment process. With the substitution of the optimized temperature and time, the governing equation may be obtained. Additionally, the total energy consumed during the heat treatment process is also developed to give a mathematical formulation of the energy consumed.

Heat Diffusion in Gases, Including Effects of Chemical Reaction

NASA Technical Reports Server (NTRS)

Hansen, C. Frederick

1960-01-01

The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

Generalized thermoelastic diffusive waves in heat conducting materials

NASA Astrophysics Data System (ADS)

Sharma, J. N.

2007-04-01

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.

Heat transfer, diffusion, and evaporation

NASA Technical Reports Server (NTRS)

Nusselt, Wilhelm

1954-01-01

Although it has long been known that the differential equations of the heat-transfer and diffusion processes are identical, application to technical problems has only recently been made. In 1916 it was shown that the speed of oxidation of the carbon in iron ore depends upon the speed with which the oxygen of the combustion air diffuses through the core of gas surrounding the carbon surface. The identity previously referred to was then used to calculate the amount of oxygen diffusing to the carbon surface on the basis of the heat transfer between the gas stream and the carbon surface. Then in 1921, H. Thoma reversed that procedure; he used diffusion experiments to determine heat-transfer coefficients. Recently Lohrisch has extended this work by experiment. A technically very important application of the identity of heat transfer and diffusion is that of the cooling tower, since in this case both processes occur simultaneously.

Investigating the use of a rational Runge Kutta method for transport modelling

NASA Astrophysics Data System (ADS)

Dougherty, David E.

An unconditionally stable explicit time integrator has recently been developed for parabolic systems of equations. This rational Runge Kutta (RRK) method, proposed by Wambecq 1 and Hairer 2, has been applied by Liu et al.3 to linear heat conduction problems in a time-partitioned solution context. An important practical question is whether the method has application for the solution of (nearly) hyperbolic equations as well. In this paper the RRK method is applied to a nonlinear heat conduction problem, the advection-diffusion equation, and the hyperbolic Buckley-Leverett problem. The method is, indeed, found to be unconditionally stable for the linear heat conduction problem and performs satisfactorily for the nonlinear heat flow case. A heuristic limitation on the utility of RRK for the advection-diffusion equation arises in the Courant number; for the second-order accurate one-step two-stage RRK method, a limiting Courant number of 2 applies. First order upwinding is not as effective when used with RRK as with Euler one-step methods. The method is found to perform poorly for the Buckley-Leverett problem.

The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation

NASA Astrophysics Data System (ADS)

Oliveira, F. De; Franco, S. R.; Pinto, M. A. Villela

2018-02-01

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

Simultaneous Heat and Mass Transfer Model for Convective Drying of Building Material

NASA Astrophysics Data System (ADS)

Upadhyay, Ashwani; Chandramohan, V. P.

2018-04-01

A mathematical model of simultaneous heat and moisture transfer is developed for convective drying of building material. A rectangular brick is considered for sample object. Finite-difference method with semi-implicit scheme is used for solving the transient governing heat and mass transfer equation. Convective boundary condition is used, as the product is exposed in hot air. The heat and mass transfer equations are coupled through diffusion coefficient which is assumed as the function of temperature of the product. Set of algebraic equations are generated through space and time discretization. The discretized algebraic equations are solved by Gauss-Siedel method via iteration. Grid and time independent studies are performed for finding the optimum number of nodal points and time steps respectively. A MATLAB computer code is developed to solve the heat and mass transfer equations simultaneously. Transient heat and mass transfer simulations are performed to find the temperature and moisture distribution inside the brick.

Finite-volume scheme for anisotropic diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

An approximate analysis of the diffusing flow in a self-controlled heat pipe.

NASA Technical Reports Server (NTRS)

Somogyi, D.; Yen, H. H.

1973-01-01

Constant-density two-dimensional axisymmetric equations are presented for the diffusing flow of a class of self-controlled heat pipes. The analysis is restricted to the vapor space. Condensation of the vapor is related to its mass fraction at the wall by the gas kinetic formula. The Karman-Pohlhausen integral method is applied to obtain approximate solutions. Solutions are presented for a water heat pipe with neon control gas.

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Jungpyo; Wright, John; Bertelli, Nicola

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

DOE PAGES

Lee, Jungpyo; Wright, John; Bertelli, Nicola; ...

2017-04-24

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Fem Formulation for Heat and Mass Transfer in Porous Medium

NASA Astrophysics Data System (ADS)

Azeem; Soudagar, Manzoor Elahi M.; Salman Ahmed, N. J.; Anjum Badruddin, Irfan

2017-08-01

Heat and mass transfer in porous medium can be modelled using three partial differential equations namely, momentum equation, energy equation and mass diffusion. These three equations are coupled to each other by some common terms that turn the whole phenomenon into a complex problem with inter-dependable variables. The current article describes the finite element formulation of heat and mass transfer in porous medium with respect to Cartesian coordinates. The problem under study is formulated into algebraic form of equations by using Galerkin's method with the help of two-node linear triangular element having three nodes. The domain is meshed with smaller sized elements near the wall region and bigger size away from walls.

Theory of a time-dependent heat diffusion determination of thermal diffusivities with a single temperature measurement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perez, R. B.; Carroll, R. M.; Sisman, O.

1971-02-01

A method to measure the thermal diffusivity of reactor fuels during irradiation is developed, based on a time-dependent heat diffusion equation. With this technique the temperature is measured at only one point in the fuel specimen. This method has the advantage that it is not necessary to know the heat generation (a difficult evaluation during irradiation). The theory includes realistic boundary conditions, applicable to actual experimental systems. The parameters are the time constants associated with the first two time modes in the temperature-vs-time curve resulting from a step change in heat input to the specimen. With the time constants andmore » the necessary material properties and dimensions of the specimen and specimen holder, the thermal diffusivity of the specimen can be calculated.« less

Heat and Mass Transfer in an L Shaped Porous Medium

NASA Astrophysics Data System (ADS)

Salman Ahmed, N. J.; Azeem; Yunus Khan, T. M.

2017-08-01

This article is an extension to the heat transfer in L-shaped porous medium by including the mass diffusion. The heat and mass transfer in the porous domain is represented by three coupled partial differential equations representing the fluid movement, energy transport and mass transport. The equations are converted into algebraic form of equations by the application of finite element method that can be conveniently solved by matrix method. An iterative approach is adopted to solve the coupled equations by setting suitable convergence criterion. The results are discussed in terms of heat transfer characteristics influenced by physical parameters such as buoyancy ratio, Lewis number, Rayleigh number etc. It is found that these physical parameters have significant effect on heat and mass transfer behavior of L-shaped porous medium.

Fem Simulation of Triple Diffusive Natural Convection Along Inclined Plate in Porous Medium: Prescribed Surface Heat, Solute and Nanoparticles Flux

NASA Astrophysics Data System (ADS)

Goyal, M.; Goyal, R.; Bhargava, R.

2017-12-01

In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

Transient in-plane thermal transport in nanofilms with internal heating

PubMed Central

Cao, Bing-Yang

2016-01-01

Wide applications of nanofilms in electronics necessitate an in-depth understanding of nanoscale thermal transport, which significantly deviates from Fourier's law. Great efforts have focused on the effective thermal conductivity under temperature difference, while it is still ambiguous whether the diffusion equation with an effective thermal conductivity can accurately characterize the nanoscale thermal transport with internal heating. In this work, transient in-plane thermal transport in nanofilms with internal heating is studied via Monte Carlo (MC) simulations in comparison to the heat diffusion model and mechanism analyses using Fourier transform. Phonon-boundary scattering leads to larger temperature rise and slower thermal response rate when compared with the heat diffusion model based on Fourier's law. The MC simulations are also compared with the diffusion model with effective thermal conductivity. In the first case of continuous internal heating, the diffusion model with effective thermal conductivity under-predicts the temperature rise by the MC simulations at the initial heating stage, while the deviation between them gradually decreases and vanishes with time. By contrast, for the one-pulse internal heating case, the diffusion model with effective thermal conductivity under-predicts both the peak temperature rise and the cooling rate, so the deviation can always exist. PMID:27118903

Transient in-plane thermal transport in nanofilms with internal heating.

PubMed

Hua, Yu-Chao; Cao, Bing-Yang

2016-02-01

Wide applications of nanofilms in electronics necessitate an in-depth understanding of nanoscale thermal transport, which significantly deviates from Fourier's law. Great efforts have focused on the effective thermal conductivity under temperature difference, while it is still ambiguous whether the diffusion equation with an effective thermal conductivity can accurately characterize the nanoscale thermal transport with internal heating. In this work, transient in-plane thermal transport in nanofilms with internal heating is studied via Monte Carlo (MC) simulations in comparison to the heat diffusion model and mechanism analyses using Fourier transform. Phonon-boundary scattering leads to larger temperature rise and slower thermal response rate when compared with the heat diffusion model based on Fourier's law. The MC simulations are also compared with the diffusion model with effective thermal conductivity. In the first case of continuous internal heating, the diffusion model with effective thermal conductivity under-predicts the temperature rise by the MC simulations at the initial heating stage, while the deviation between them gradually decreases and vanishes with time. By contrast, for the one-pulse internal heating case, the diffusion model with effective thermal conductivity under-predicts both the peak temperature rise and the cooling rate, so the deviation can always exist.

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Shi, E-mail: sjin@wisc.edu; Institute of Natural Sciences, Department of Mathematics, MOE-LSEC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240; Lu, Hanqing, E-mail: hanqing@math.wisc.edu

2017-04-01

In this paper, we develop an Asymptotic-Preserving (AP) stochastic Galerkin scheme for the radiative heat transfer equations with random inputs and diffusive scalings. In this problem the random inputs arise due to uncertainties in cross section, initial data or boundary data. We use the generalized polynomial chaos based stochastic Galerkin (gPC-SG) method, which is combined with the micro–macro decomposition based deterministic AP framework in order to handle efficiently the diffusive regime. For linearized problem we prove the regularity of the solution in the random space and consequently the spectral accuracy of the gPC-SG method. We also prove the uniform (inmore » the mean free path) linear stability for the space-time discretizations. Several numerical tests are presented to show the efficiency and accuracy of proposed scheme, especially in the diffusive regime.« less

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

PubMed Central

Chung, Moo K.; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K.

2014-01-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface. PMID:25791435

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Peridynamic thermal diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oterkus, Selda; Madenci, Erdogan, E-mail: madenci@email.arizona.edu; Agwai, Abigail

This study presents the derivation of ordinary state-based peridynamic heat conduction equation based on the Lagrangian formalism. The peridynamic heat conduction parameters are related to those of the classical theory. An explicit time stepping scheme is adopted for numerical solution of various benchmark problems with known solutions. It paves the way for applying the peridynamic theory to other physical fields such as neutronic diffusion and electrical potential distribution.

Cattaneo-Christov double-diffusion theory for three-dimensional flow of viscoelastic nanofluid with the effect of heat generation/absorption

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sajid; Shehzad, Sabir Ali; Alsaedi, Ahmed

2018-03-01

The present research article focuses on three-dimensional flow of viscoelastic(second grade) nanofluid in the presence of Cattaneo-Christov double-diffusion theory. Flow caused is due to stretching sheet. Characteristics of heat transfer are interpreted by considering the heat generation/absorption. Nanofluid theory comprises of Brownian motion and thermophoresis. Cattaneo-Christov double-diffusion theory is introduced in the energy and concentration expressions. Such diffusions are developed as a part of formulating the thermal and solutal relaxation times framework. Suitable variables are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been explored through homotopic algorithm. Behavior of sundry variables on the velocities, temperature and concentration are scrutinized graphically. Numerical values of skin friction coefficients are also calculated and examined. Here thermal field enhances for heat generation parameter while reverse situation is noticed for heat absorption parameter.

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

NASA Technical Reports Server (NTRS)

Salamon, N. J. (Principal Investigator); Sullivan, Roy M.; Lee, Sunpyo

1995-01-01

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Cattaneo-Christov heat flux effect on hydromagnetic radiative Oldroyd-B liquid flow across a cone/wedge in the presence of cross-diffusion

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, M.

2018-01-01

The present article scrutinizes the prominent characteristics of the Cattaneo-Christov heat flux on magnetohydrodynamic Oldroyd-B radiative liquid flow over two different geometries. The effects of cross-diffusion are considered in the modeling of species and energy equations. Similarity transformations are employed to transmute the governing flow, species and energy equations into a set of nonlinear ordinary differential equations (ODEs) with the appropriate boundary conditions. The final system of dimensionless equations is resolved numerically by utilizing the R-K-Fehlberg numerical approach. The behaviors of all physical pertinent flow controlling variables on the three flow distributions are analyzed through plots. The obtained numerical results have been compared with earlier published work and reveal good agreement. The Deborah numbers γ1 and γ2 have quite opposite effects on velocity and energy fields. The increase in thermal relaxation parameter β corresponds to a decrease in the fluid temperature. This study has salient applications in heat and mass transfer manufacturing system processing for energy conversion.

Theory of transformation thermal convection for creeping flow in porous media: Cloaking, concentrating, and camouflage

NASA Astrophysics Data System (ADS)

Dai, Gaole; Shang, Jin; Huang, Jiping

2018-02-01

Heat can transfer via thermal conduction, thermal radiation, and thermal convection. All the existing theories of transformation thermotics and optics can treat thermal conduction and thermal radiation, respectively. Unfortunately, thermal convection has seldom been touched in transformation theories due to the lack of a suitable theory, thus limiting applications associated with heat transfer through fluids (liquid or gas). Here, we develop a theory of transformation thermal convection by considering the convection-diffusion equation, the equation of continuity, and the Darcy law. By introducing porous media, we get a set of equations keeping their forms under coordinate transformation. As model applications, the theory helps to show the effects of cloaking, concentrating, and camouflage. Our finite-element simulations confirm the theoretical findings. This work offers a transformation theory for thermal convection, thus revealing novel behaviors associated with potential applications; it not only provides different hints on how to control heat transfer by combining thermal conduction, thermal convection, and thermal radiation, but also benefits mass diffusion and other related fields that contain a set of equations and need to transform velocities at the same time.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less

Numerical Calculation and Exergy Equations of Spray Heat Exchanger Attached to a Main Fan Diffuser

NASA Astrophysics Data System (ADS)

Cui, H.; Wang, H.; Chen, S.

2015-04-01

In the present study, the energy depreciation rule of spray heat exchanger, which is attached to a main fan diffuser, is analyzed based on the second law of thermodynamics. Firstly, the exergy equations of the exchanger are deduced. The equations are numerically calculated by the fourth-order Runge-Kutta method, and the exergy destruction is quantitatively effected by the exchanger structure parameters, working fluid (polluted air, i.e., PA; sprayed water, i.e., SW) initial state parameters and the ambient reference parameters. The results are showed: (1) heat transfer is given priority to latent transfer at the bottom of the exchanger, and heat transfer of convection and is equivalent to that of condensation in the upper. (2) With the decrease of initial temperature of SW droplet, the decrease of PA velocity or the ambient reference temperature, and with the increase of a SW droplet size or initial PA temperature, exergy destruction both increase. (3) The exergy efficiency of the exchanger is 72.1 %. An approach to analyze the energy potential of the exchanger may be provided for engineering designs.

Homotopic solutions for unsteady second grade liquid utilizing non-Fourier double diffusion concept

NASA Astrophysics Data System (ADS)

Sohail, A.; Khan, W. A.; Khan, M.; Shah, S. I. A.

Main purpose of the current work is to investigate the features of unsteady Cattaneo-Christov heat and mass flux models on the second grade fluid over a stretching surface. The characteristics of unsteady Cattaneo-Christov heat and mass flux models are incorporated in the energy and concentration equations. The unsteady Cattaneo-Christov heat and mass flux models are the generalization of Fourier's and Fick's laws in which the time space upper-convected derivative are utilized to describe the heat conduction and mass diffusion phenomena. The suitable transformations are used to alter the governing partial differential equations into the ordinary differential equations. The resulting problem under consideration is solved analytically by using the homotopy analysis method (HAM). The effect of non-dimensional pertinent parameters on the temperature and concentration distribution are deliberated by using graphs and tables. Results show that the temperature and concentration profiles diminish for augmented values of the thermal and concentration relaxation parameters. Additionally, it is perceived that the temperature and concentration profiles are higher in case of classical Fourier's and Fick's laws as compared to non-Fourier's and non-Fick's laws.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Marangoni Convection during Free Electron Laser Nitriding of Titanium

NASA Astrophysics Data System (ADS)

Höche, Daniel; Müller, Sven; Rapin, Gerd; Shinn, Michelle; Remdt, Elvira; Gubisch, Maik; Schaaf, Peter

2009-08-01

Pure titanium was treated by free electron laser (FEL) radiation in a nitrogen atmosphere. As a result, nitrogen diffusion occurs and a TiN coating was synthesized. Local gradients of interfacial tension due to the local heating lead to a Marangoni convection, which determines the track properties. Because of the experimental inaccessibility of time-dependent occurrences, finite element calculations were performed, to determine the physical processes such as heat transfer, melt flow, and mass transport. In order to calculate the surface deformation of the gas-liquid interface, the level set approach was used. The equations were modified and coupled with heat-transfer and diffusion equations. The process was characterized by dimensionless numbers such as the Reynolds, Peclet, and capillary numbers, to obtain more information about the acting forces and the coating development. Moreover, the nitrogen distribution was calculated using the corresponding transport equation. The simulations were compared with cross-sectional micrographs of the treated titanium sheets and checked for their validity. Finally, the process presented is discussed and compared with similar laser treatments.

Heat capacities and thermal diffusivities of n-alkane acid ethyl esters—biodiesel fuel components

NASA Astrophysics Data System (ADS)

Bogatishcheva, N. S.; Faizullin, M. Z.; Nikitin, E. D.

2017-09-01

The heat capacities and thermal diffusivities of ethyl esters of liquid n-alkane acids C n H2 n-1O2C2H5 with the number of carbon atoms in the parent acid n = 10, 11, 12, 14, and 16 are measured. The heat capacities are measured using a DSC 204 F1 Phoenix heat flux differential scanning calorimeter (Netzsch, Germany) in the temperature range of 305-375 K. Thermal diffusivities are measured by means of laser flash method on an LFA-457 instrument (Netzsch, Germany) at temperatures of 305-400 K. An equation is derived for the dependence of the molar heat capacities of the investigated esters on temperature. It is shown that the dependence of molar heat capacity C p,m (298.15 K) on n ( n = 1-6) is close to linear. The dependence of thermal diffusivity on temperature in the investigated temperature range is described by a first-degree polynomial, but thermal diffusivity a (298.15 K) as a function of n has a minimum at n = 5.

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

Development of an Advanced Flameless Combustion Heat Source Utilizing Heavy Fuels

DTIC Science & Technology

2010-07-01

Flow Uniformity Test Cell .............................................................................51 Figure 37. Relationship Between Thermal...equations that influence both transient and steady state thermal behavior. Equation 1 describes the relationship between thermal diffusivity and the...intrinsic properties of any material. Equation 2 describes the Wiedemann-Franz law. P. Grootenhuis, et al reported on the relationship between

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

Heat transfer in suspensions of rigid particles

NASA Astrophysics Data System (ADS)

Brandt, Luca; Niazi Ardekani, Mehdi; Abouali, Omid

2016-11-01

We study the heat transfer in laminar Couette flow of suspensions of rigid neutrally buoyant particles by means of numerical simulations. An Immersed Boundary Method is coupled with a VOF approach to simulate the heat transfer in the fluid and solid phase, enabling us to fully resolve the heat diffusion. First, we consider spherical particles and show that the proposed algorithm is able to reproduce the correlations between heat flux across the channel, the particle volume fraction and the heat diffusivity obtained in laboratory experiments and recently proposed in the literature, results valid in the limit of vanishing inertia. We then investigate the role of inertia on the heat transfer and show an increase of the suspension diffusivity at finite particle Reynolds numbers. Finally, we vary the relativity diffusivity of the fluid and solid phase and investigate its effect on the effective heat flux across the channel. The data are analyzed by considering the ensemble averaged energy equation and decomposing the heat flux in 4 different contributions, related to diffusion in the solid and fluid phase, and the correlations between wall-normal velocity and temperature fluctuations. Results for non-spherical particles will be examined before the meeting. Supported by the European Research Council Grant No. ERC-2013- CoG-616186, TRITOS. The authors acknowledge computer time provided by SNIC (Swedish National Infrastructure for Computing).

Laser induced heat source distribution in bio-tissues

NASA Astrophysics Data System (ADS)

Li, Xiaoxia; Fan, Shifu; Zhao, Youquan

2006-09-01

During numerical simulation of laser and tissue thermal interaction, the light fluence rate distribution should be formularized and constituted to the source term in the heat transfer equation. Usually the solution of light irradiative transport equation is given in extreme conditions such as full absorption (Lambert-Beer Law), full scattering (Lubelka-Munk theory), most scattering (Diffusion Approximation) et al. But in specific conditions, these solutions will induce different errors. The usually used Monte Carlo simulation (MCS) is more universal and exact but has difficulty to deal with dynamic parameter and fast simulation. Its area partition pattern has limits when applying FEM (finite element method) to solve the bio-heat transfer partial differential coefficient equation. Laser heat source plots of above methods showed much difference with MCS. In order to solve this problem, through analyzing different optical actions such as reflection, scattering and absorption on the laser induced heat generation in bio-tissue, a new attempt was made out which combined the modified beam broaden model and the diffusion approximation model. First the scattering coefficient was replaced by reduced scattering coefficient in the beam broaden model, which is more reasonable when scattering was treated as anisotropic scattering. Secondly the attenuation coefficient was replaced by effective attenuation coefficient in scattering dominating turbid bio-tissue. The computation results of the modified method were compared with Monte Carlo simulation and showed the model provided reasonable predictions of heat source term distribution than past methods. Such a research is useful for explaining the physical characteristics of heat source in the heat transfer equation, establishing effective photo-thermal model, and providing theory contrast for related laser medicine experiments.

An AMR capable finite element diffusion solver for ALE hydrocodes [An AMR capable diffusion solver for ALE-AMR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fisher, A. C.; Bailey, D. S.; Kaiser, T. B.

2015-02-01

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L 2 norm.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

PubMed

Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

2008-02-01

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald ripening (only one hole survives at the end), and we report a particular regime where the "hole ripening" statistics exhibits a simple dynamic scaling behavior.

Automated software to determine thermal diffusivity of oilgas mixture

NASA Astrophysics Data System (ADS)

Khismatullin, A. S.

2018-05-01

The paper presents automated software to determine thermal diffusivity of oil-gas mixture. A series of laboratory testscovering transformer oil cooling in a power transformer tank was conducted. The paper also describes diagrams of temperature-timedependence of bubbling. Thermal diffusivity coefficients are experimentally defined. The paper considers a mathematical task of heat flowdistribution in a rectangular parallelepiped, alongside with the solution of heat a conduction equation in a power transformer tank, which represents a rectangular parallelepiped. A device for temperature monitoring in the tank is described in detail. The relay control diagram, which ensures temperature monitoring againsttransformer overheating is described.

Nanofluid flow and heat transfer in boundary layers: the influence of the concentration diffusion layer on heat transfer enhancement

NASA Astrophysics Data System (ADS)

Liu, Joseph T. C.; Barbosa Decastilho, Cintia Juliana; Fuller, Mark E.; Sane, Aakash

2017-11-01

The present work uses a perturbation procedure to deduce the small nanoparticle volume concentration conservation equations for momentum, heat and concentration diffusion. Thermal physical variables are obtained from conventional means (mixture and field theories) for alumina-water and gold-water nanofluids. In the case of gold-water nano fluid molecular dynamics results are used to estimate such properties, including transport coefficients. The very thin diffusion layer at large Schmidt numbers is found to have a great impact on the velocity and temperature profiles owing to their dependency on transport properties. This has a profound effect on the conduction surface heat transfer rate enhancement and skin friction suppression for the case of nano fluid concentration withdrawal at the wall, while the diffusional surface heat transfer rate is negligible due to large Schmidt numbers. Possible experimental directed at this interesting phenomenon is suggested.

Boundary Waves on the Ice Surface Created by Currents

NASA Astrophysics Data System (ADS)

Naito, K.; Izumi, N.; Yokokawa, M.; Yamada, T.; de Lima, A. C.

2013-12-01

The formation of periodic boundary waves, e.g. antidunes and cyclic steps (Parker & Izumi 2000) has been known to be caused by instabilities between flow and bed (e.g. Engelund 1970), and are observed not only on river beds or ocean floors but also on ice surfaces, such as the surface of glaciers and underside of river ice (Carey 1966). In addition, owing to recent advancements of remote sensing technology, it has been found that the surfaces of the polar ice caps on Mars as well as on the Earth have step-like formations (Smith & Holt 2010) which are assumed to be boundary waves, because they are generated perpendicularly to the direction of the currents. These currents acting on the polar ice caps are density airflow, i.e. katabatic wind (Howard et al 2000). The comprehension of the formation process of the Martian polar ice caps may reveal climate changes which have occurred on Mars. Although the formation of boundary waves on river beds or ocean floors has been studied by a number of researchers, there are few works on their formation on ice surfaces. Yokokawa et al (2013) suggested that the temperature distribution of the ambient air, fluid and ice is a factor which determines the direction of migration of boundary waves formed on ice surfaces through their experiments. In this study, we propose a mathematical model in order to describe the formation process of the boundary waves and the direction of their migration. We consider that a liquid is flowing through a flume filled with a flat ice layer on the bottom. The flow is assumed to be turbulent and its temperature is assumed to merge with the ambient temperature at the flow surface and with the melting point of ice at the bottom (ice surface). The ice surface evolution is dependent on the unbalance between the interfacial heat flux of the liquid and ice, and we employ the Reynolds-averaged Navier-Stokes equation, the continuity equation, heat transfer equations for the liquid and ice, and a heat balance equation at the flow-ice interface. It is assumed that the interfacial heat fluxes of the liquid and ice are determined by the temperature profile, and the Reynolds stress and the turbulent heat flux are expressed by the eddy diffusivity of momentum and the eddy diffusivity of heat, respectively. In addition, the liquid can be divided into two layers; viscous sublayer and turbulent layer. In order to determine the velocity and temperature profile in the liquid, we employ the Prandtl-Taylor analogy which assumes that the velocity profile follows a linear law in the viscous sublayer and a logarithmic law in the turbulent layer, and the eddy diffusivity of heat is described by the eddy diffusivity of momentum and Prandtl number of the liquid. Finally, we obtain the temperature profiles (because the heat transfer equation for the ice reduces to the Laplace equation, the temperature profile in the ice can be easily estimated) and interfacial heat fluxes.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

Thermal transport at the nanoscale: A Fourier's law vs. phonon Boltzmann equation study

NASA Astrophysics Data System (ADS)

Kaiser, J.; Feng, T.; Maassen, J.; Wang, X.; Ruan, X.; Lundstrom, M.

2017-01-01

Steady-state thermal transport in nanostructures with dimensions comparable to the phonon mean-free-path is examined. Both the case of contacts at different temperatures with no internal heat generation and contacts at the same temperature with internal heat generation are considered. Fourier's law results are compared to finite volume method solutions of the phonon Boltzmann equation in the gray approximation. When the boundary conditions are properly specified, results obtained using Fourier's law without modifying the bulk thermal conductivity are in essentially exact quantitative agreement with the phonon Boltzmann equation in the ballistic and diffusive limits. The errors between these two limits are examined in this paper. For the four cases examined, the error in the apparent thermal conductivity as deduced from a correct application of Fourier's law is less than 6%. We also find that the Fourier's law results presented here are nearly identical to those obtained from a widely used ballistic-diffusive approach but analytically much simpler. Although limited to steady-state conditions with spatial variations in one dimension and to a gray model of phonon transport, the results show that Fourier's law can be used for linear transport from the diffusive to the ballistic limit. The results also contribute to an understanding of how heat transport at the nanoscale can be understood in terms of the conceptual framework that has been established for electron transport at the nanoscale.

Fourier's law of heat conduction: quantum mechanical master equation analysis.

PubMed

Wu, Lian-Ao; Segal, Dvira

2008-06-01

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting of an exchange effect. The pure exchange model directly leads to energy diffusion in a weakly coupled spin- 12 chain.

Simulations of surface winds at the Viking Lander sites using a one-level model

NASA Technical Reports Server (NTRS)

Bridger, Alison F. C.; Haberle, Robert M.

1992-01-01

The one-level model developed by Mass and Dempsey for use in predicting surface flows in regions of complex terrain was adapted to simulate surface flows at the Viking lander sites on Mars. In the one-level model, prediction equations for surface winds and temperatures are formulated and solved. Surface temperatures change with time in response to diabatic heating, horizontal advection, adiabatic heating and cooling effects, and horizontal diffusion. Surface winds can change in response to horizontal advection, pressure gradient forces, Coriolis forces, surface drag, and horizontal diffusion. Surface pressures are determined by integration of the hydrostatic equation from the surface to some reference level. The model has successfully simulated surface flows under a variety of conditions in complex-terrain regions on Earth.

Estimation of Phonon and Carrier Thermal Conductivities for Bulk Thermoelectric Materials Using Transport Properties

NASA Astrophysics Data System (ADS)

Otsuka, Mioko; Homma, Ryoei; Hasegawa, Yasuhiro

2017-05-01

The phonon and carrier thermal conductivities of thermoelectric materials were calculated using the Wiedemann-Franz law, Boltzmann equation, and a method we propose in this study called the Debye specific heat method. We prepared polycrystalline n-type doped bismuth telluride (BiTe) and bismuth antimony (BiSb) bulk alloy samples and measured six parameters (Seebeck coefficient, resistivity, thermal conductivity, thermal diffusivity, magneto-resistivity, and Hall coefficient). The carrier density and mobility were estimated for calculating the carrier thermal conductivity by using the Boltzmann equation. In the Debye specific heat method, the phonon thermal diffusivity, and thermal conductivity were calculated from the temperature dependence of the effective specific heat by using not only the measured thermal conductivity and Debye model, but also the measured thermal diffusivity. The carrier thermal conductivity was also evaluated from the phonon thermal conductivity by using the specific heat. The ratio of carrier thermal conductivity to thermal conductivity was evaluated for the BiTe and BiSb samples, and the values obtained using the Debye specific heat method at 300 K were 52% for BiTe and <5.5% for BiSb. These values are either considerably larger or smaller than those obtained using other methods. The Dulong-Petit law was applied to validate the Debye specific heat method at 300 K, which is significantly greater than the Debye temperature of the BiTe and BiSb samples, and it was confirmed that the phonon specific heat at 300 K has been accurately reproduced using our proposed method.

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Magnetic flux and heat losses by diffusive, advective, and Nernst effects in MagLIF-like plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velikovich, A. L., E-mail: sasha.velikovich@nrl.navy.mil; Giuliani, J. L., E-mail: sasha.velikovich@nrl.navy.mil; Zalesak, S. T.

2014-12-15

The MagLIF approach to inertial confinement fusion involves subsonic/isobaric compression and heating of a DT plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstrates that the heat loss from the hot plasma to the cold liner is dominated by the transverse heat conduction and advection, andmore » the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter ω{sub e}τ{sub e} effective diffusion coefficients determining the losses of heat and magnetic flux are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient, which is commonly associated with low collisionality and two-dimensional transport. This family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.« less

Diffusion of Chromium in Alpha Cobalt-Chromium Solid Solutions

NASA Technical Reports Server (NTRS)

Weeton, John W

1951-01-01

Diffusion of chromium in cobalt-chromium solid solutions was investigated in the range 0 to 40 atomic percent at temperatures of 1360 degrees, 1300 degrees, 1150 degrees, and 10000 degrees c. The diffusion coefficients were found to be relatively constant within the composition range covered by each specimen. The activation heat of diffusion was determined to be 63,000 calories per mole. This value agrees closely with the value of 63,400 calories per mole calculated by means of the Dushman-Langmuir equation.

Prediction of heat release effects on a mixing layer

NASA Technical Reports Server (NTRS)

Farshchi, M.

1986-01-01

A fully second-order closure model for turbulent reacting flows is suggested based on Favre statistics. For diffusion flames the local thermodynamic state is related to single conserved scalar. The properties of pressure fluctuations are analyzed for turbulent flows with fluctuating density. Closure models for pressure correlations are discussed and modeled transport equations for Reynolds stresses, turbulent kinetic energy dissipation, density-velocity correlations, scalar moments and dissipation are presented and solved, together with the mean equations for momentum and mixture fraction. Solutions of these equations are compared with the experimental data for high heat release free mixing layers of fluorine and hydrogen in a nitrogen diluent.

Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions

NASA Astrophysics Data System (ADS)

Chebotarev, Alexander Yu.; Grenkin, Gleb V.; Kovtanyuk, Andrey E.; Botkin, Nikolai D.; Hoffmann, Karl-Heinz

2018-04-01

The paper is concerned with a problem of diffraction type. The study starts with equations of complex (radiative and conductive) heat transfer in a multicomponent domain with Fresnel matching conditions at the interfaces. Applying the diffusion, P1, approximation yields a pair of coupled nonlinear PDEs describing the radiation intensity and temperature for each component of the domain. Matching conditions for these PDEs, imposed at the interfaces between the domain components, are derived. The unique solvability of the obtained problem is proven, and numerical experiments are conducted.

Computation of Turbulent Heat Transfer on the Walls of a 180 Degree Turn Channel With a Low Reynolds Number Reynolds Stress Model

NASA Technical Reports Server (NTRS)

Ameri, A. A.; Rigby, D. L.; Steinthorsson, E.; Gaugler, Raymond (Technical Monitor)

2002-01-01

The Low Reynolds number version of the Stress-omega model and the two equation k-omega model of Wilcox were used for the calculation of turbulent heat transfer in a 180 degree turn simulating an internal coolant passage. The Stress-omega model was chosen for its robustness. The turbulent thermal fluxes were calculated by modifying and using the Generalized Gradient Diffusion Hypothesis. The results showed that using this Reynolds Stress model allowed better prediction of heat transfer compared to the k-omega two equation model. This improvement however required a finer grid and commensurately more CPU time.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Transition and separation process in brine channels formation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berti, Alessia, E-mail: alessia.berti@unibs.it; Bochicchio, Ivana, E-mail: ibochicchio@unisa.it; Fabrizio, Mauro, E-mail: mauro.fabrizio@unibo.it

2016-02-15

In this paper, we discuss the formation of brine channels in sea ice. The model includes a time-dependent Ginzburg-Landau equation for the solid-liquid phase change, a diffusion equation of the Cahn-Hilliard kind for the solute dynamics, and the heat equation for the temperature change. The macroscopic motion of the fluid is also considered, so the resulting differential system couples with the Navier-Stokes equation. The compatibility of this system with the thermodynamic laws and a maximum theorem is proved.

Applications of an exponential finite difference technique

DOE Office of Scientific and Technical Information (OSTI.GOV)

Handschuh, R.F.; Keith, T.G. Jr.

1988-07-01

An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Soret and Dufour effects on MHD peristaltic flow of Prandtl fluid in a rotating channel

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Zahir, Hina; Tanveer, Anum; Alsaedi, Ahmed

2018-03-01

An analysis has been arranged to study the magnetohydrodynamics (MHD) peristaltic flow of Prandtl fluid in a channel with flexible walls. Both fluid and channel are in a state of solid body rotation. Simultaneous effects of heat and mass transfer with thermal-diffusion (Soret) and diffusion-thermo (Dufour) effects are considered. Convective conditions for heat and mass transfer in the formulation are adopted. Ordinary differential systems using low Reynolds number and long wavelength approximation are obtained. Resulting equations have been solved numerically. The discussion of axial and secondary velocities, temperature, concentration and heat transfer coefficient with respect to emerging parameters embedded in the flow model is presented after sketching plots.

Is the kinetic equation for turbulent gas-particle flows ill posed?

PubMed

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Axi-symmetric generalized thermoelastic diffusion problem with two-temperature and initial stress under fractional order heat conduction

NASA Astrophysics Data System (ADS)

Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh

2016-09-01

A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.

Influence of a Simple Heat Loss Profile on a Pure Diffusion Flame

NASA Technical Reports Server (NTRS)

Ray, Anjan; Wichman, Indrek S.

1996-01-01

The presence of soot on the fuel side of a diffusion flame results in significant radiative heat losses. The influence of a fuel side heat loss zone on a pure diffusion flame established between a fuel and an oxidizer wall is investigated by assuming a hypothetical sech(sup 2) heat loss profile. The intensity and width of the loss zone are parametrically varied. The loss zone is placed at different distances from the Burke-Schumann flame location. The migration of the temperature and reactivity peaks are examined for a variety of situations. For certain cases the reaction zone breaks through the loss zone and relocates itself on the fuel side of the loss zone. In all cases the temperature and reactivity peaks move toward the fuel side with increased heat losses. The flame structure reveals that the primary balance for the energy equation is between the reaction term and the diffusion term. Extinction plots are generated for a variety of situations. The heat transfer from the flame to the walls and the radiative fraction is also investigated, and an analytical correlation formula, derived in a previous study, is shown to produce excellent predictions of our numerical results when an O(l) numerical multiplicative constant is employed.

CFD simulation of simultaneous monotonic cooling and surface heat transfer coefficient

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mihálka, Peter, E-mail: usarmipe@savba.sk; Matiašovský, Peter, E-mail: usarmat@savba.sk

The monotonic heating regime method for determination of thermal diffusivity is based on the analysis of an unsteady-state (stabilised) thermal process characterised by an independence of the space-time temperature distribution on initial conditions. At the first kind of the monotonic regime a sample of simple geometry is heated / cooled at constant ambient temperature. The determination of thermal diffusivity requires the determination rate of a temperature change and simultaneous determination of the first eigenvalue. According to a characteristic equation the first eigenvalue is a function of the Biot number defined by a surface heat transfer coefficient and thermal conductivity ofmore » an analysed material. Knowing the surface heat transfer coefficient and the first eigenvalue the thermal conductivity can be determined. The surface heat transport coefficient during the monotonic regime can be determined by the continuous measurement of long-wave radiation heat flow and the photoelectric measurement of the air refractive index gradient in a boundary layer. CFD simulation of the cooling process was carried out to analyse local convective and radiative heat transfer coefficients more in detail. Influence of ambient air flow was analysed. The obtained eigenvalues and corresponding surface heat transfer coefficient values enable to determine thermal conductivity of the analysed specimen together with its thermal diffusivity during a monotonic heating regime.« less

A simple Boltzmann transport equation for ballistic to diffusive transient heat transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maassen, Jesse, E-mail: jmaassen@purdue.edu; Lundstrom, Mark

2015-04-07

Developing simplified, but accurate, theoretical approaches to treat heat transport on all length and time scales is needed to further enable scientific insight and technology innovation. Using a simplified form of the Boltzmann transport equation (BTE), originally developed for electron transport, we demonstrate how ballistic phonon effects and finite-velocity propagation are easily and naturally captured. We show how this approach compares well to the phonon BTE, and readily handles a full phonon dispersion and energy-dependent mean-free-path. This study of transient heat transport shows (i) how fundamental temperature jumps at the contacts depend simply on the ballistic thermal resistance, (ii) thatmore » phonon transport at early times approach the ballistic limit in samples of any length, and (iii) perceived reductions in heat conduction, when ballistic effects are present, originate from reductions in temperature gradient. Importantly, this framework can be recast exactly as the Cattaneo and hyperbolic heat equations, and we discuss how the key to capturing ballistic heat effects is to use the correct physical boundary conditions.« less

The contributions of Lewis Fry Richardson to drainage theory, soil physics, and the soil-plant-atmosphere continuum

NASA Astrophysics Data System (ADS)

Knight, John; Raats, Peter

2016-04-01

The EGU Division on Nonlinear Processes in Geophysics awards the Lewis Fry Richardson Medal. Richardson's significance is highlighted in http://www.egu.eu/awards-medals/portrait-lewis-fry-richardson/, but his contributions to soil physics and to numerical solutions of heat and diffusion equations are not mentioned. We would like to draw attention to those little known contributions. Lewis Fry Richardson (1881-1953) made important contributions to many fields including numerical weather prediction, finite difference solutions of partial differential equations, turbulent flow and diffusion, fractals, quantitative psychology and studies of conflict. He invented numerical weather prediction during World War I, although his methods were not successfully applied until 1950, after the invention of fast digital computers. In 1922 he published the book `Numerical weather prediction', of which few copies were sold and even fewer were read until the 1950s. To model heat and mass transfer in the atmosphere, he did much original work on turbulent flow and defined what is now known as the Richardson number. His technique for improving the convergence of a finite difference calculation is known as Richardson extrapolation, and was used by John Philip in his 1957 semi-analytical solution of the Richards equation for water movement in unsaturated soil. Richardson's first papers in 1908 concerned the numerical solution of the free surface problem of unconfined flow of water in saturated soil, arising in the design of drain spacing in peat. Later, for the lower boundary of his atmospheric model he needed to understand the movement of heat, liquid water and water vapor in what is now called the vadose zone and the soil plant atmosphere system, and to model coupled transfer of heat and flow of water in unsaturated soil. Finding little previous work, he formulated partial differential equations for transient, vertical flow of liquid water and for transfer of heat and water vapor. He paid considerable attention to the balances of water and energy at the soil-atmosphere and plant-atmosphere interfaces, making use of the concept of transfer resistance introduced by Brown and Escombe (1900) for leaf-atmosphere interfaces. He incorporated finite difference versions of all equations into his numerical weather forecasting model. From 1916, Richardson drove an ambulance in France in World War I, did weather computations in his spare time, and wrote a draft of his book. Later researchers such as L.A. Richards, D.A. de Vries and J.R. Philip from the 1930s to the 1950s were unaware that Richardson had anticipated many of their ideas on soil liquid water, heat, water vapor, and the soil-plant-atmosphere system. The Richards (1931) equation could rightly be called the Richardson (1922) equation! Richardson (1910) developed what we now call the Crank Nicolson implicit method for the heat or diffusion equation. To save effort, he used an explicit three level method after the first time step. Crank and Nicolson (1947) pointed out the instability in the explicit method, and used his implicit method for all time steps. Hanks and Bowers (1962) adapted the Crank Nicolson method to solve the Richards equation. So we could say that Hanks and Bowers used the Richardson finite difference method to solve the Richardson equation for soil water flow!

Refractive Index Effects on Radiation in an Absorbing, Emitting, and Scattering Laminated Layer

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1993-01-01

A simple set of equations is derived for predicting temperature radiative energy flow in a two-region semitransparent laminated layer in the limit of zero heat conduction. The composite is heated on its two sides by unequal amounts of incident radiation. The two layers of the composite have different refractive indices, and each material absorbs, emits, and isotropically scatters radiation. The interfaces are diffuse, and all interface reflections are included. To illustrate the thermal behavior that is readily calculated from the equations, typical results an given for various optical thicknesses and refractive indices of the layers. Internal reflections have a substantial effect on the temperature distribution and radiative heat flow.

Flow Distribution Control Characteristics in Marine Gas Turbine Waste-Heat Recovery Systems. Phase I. Flow Distribution Characteristics and Control in Diffusers.

DTIC Science & Technology

1981-08-01

provide the lowest rate of momentum outflow and thus yield maximum diffuser efficiency. In their study, Wolf and Johnston (Ref. 1.12) used screens made...other words, the uniform velocity at the diffuser exit implies the lowest exit velocity attainable for a given flow rate and lowest rate of momentum ... momentum , and energy and the equation of state. The procedures of manipulating these partial differential iations into an analytical model for analyzing

Modelling of convective processes during the Bridgman growth of poly-silicon

NASA Astrophysics Data System (ADS)

Popov, V. N.

2009-09-01

An original 3D model was used to numerically examine convective heat-and-mass transfer processes in the melt during the growth of polycrystalline silicon in vertical Bridgman configuration. The flow in the liquid was modelled using the Navier — Stokes equations in the Boussinesq approximation. The distribution of dissolved impurities was determined by solving the convective diffusion equation. The effects due to non-uniform heating of the lateral wall of the vessel and due to the shape of the crystallization front on the structure of melt flows and on the distribution of dissolved impurities in the liquid are examined.

Solutal separation in a binary nanofluid due to thermodiffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saghir, M.Z.; Yousefi, T.; Farahbakhsh, B.

2015-03-10

Transport phenomena in porous media have received considerable attention due to an increasing interest in geothermal processes, chemical catalytic reactors, waste storage (especially geological or ocean storage of carbon dioxide), etc. Among others, oil industry has shown an increasing interest in studying diffusion phenomenon. Nanofluid is a term used to describe the suspension of low concentration of metallic and non-metallic nanoparticles in a base fluid. The size of a nanoparticle ranges from 10 to 100nm, and the conventional fluids used are water, ethylene glycol (C{sub 2}H{sub 6}O{sub 2}) or engine oil. Various studies have proven that nanoparticles improve the heatmore » transfer of a base fluid. However, using various nanofluids it has been shown that the results could vary depending on different initial concentrations. The main objective of this paper is to study the diffusion and the thermodiffusion effect in a nanofluid for different fluid/porous media configurations. In this configuration, a liquid layer surrounds a porous layer. The full Brinkman equation coupled with the heat and mass transfer equations have been solved numerically for the porous layer using the finite element technique. The full Navier stokes equation coupled with heat and mass transfer equations have been solved for the liquid layer using the finite element method. A constraint between the liquid and porous layer has been applied to ensure heat flow and mass transfer continuity is maintained. A square cavity filled with hydrocarbon nanofluid of a mixture of fullerene-toluene with varying concentration of fullerene has been subject to different heating conditions. The entire cavity has been considered to be fully wetted with nanofluid. Results have confirmed that in the presence of a nanofluid a heat transfer enhancement is present up to certain initial concentration of the fullerene. The heat convection coefficient has been found to be 16% higher when a nanofluid is used as the working fluid.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novascone, Stephen Rhead; Peterson, John William

Abstract This report documents the progress of simulating pore migration in ceramic (UO 2 and mixed oxide or MOX) fuel using BISON. The porosity field is treated as a function of space and time whose evolution is governed by a custom convection-diffusion-reaction equation (described here) which is coupled to the heat transfer equation via the temperature field. The porosity is initialized to a constant value at every point in the domain, and as the temperature (and its gradient) are increased by application of a heat source, the pores move up the thermal gradient and accumulate at the center of themore » fuel in a time-frame that is consistent with observations from experiments. There is an inverse dependence of the fuel’s thermal conductivity on porosity (increasing porosity decreases thermal conductivity, and vice-versa) which is also accounted for, allowing the porosity equation to couple back into the heat transfer equation. Results from an example simulation are shown to demonstrate the new capability.« less

Marangoni convection in Casson liquid flow due to an infinite disk with exponential space dependent heat source and cross-diffusion effects

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.; Shashikumar, N. S.; Hayat, T.; Alsaedi, A.

2018-06-01

Present work aims to investigate the features of the exponential space dependent heat source (ESHS) and cross-diffusion effects in Marangoni convective heat mass transfer flow due to an infinite disk. Flow analysis is comprised with magnetohydrodynamics (MHD). The effects of Joule heating, viscous dissipation and solar radiation are also utilized. The thermal and solute field on the disk surface varies in a quadratic manner. The ordinary differential equations have been obtained by utilizing Von Kármán transformations. The resulting problem under consideration is solved numerically via Runge-Kutta-Fehlberg based shooting scheme. The effects of involved pertinent flow parameters are explored by graphical illustrations. Results point out that the ESHS effect dominates thermal dependent heat source effect on thermal boundary layer growth. The concentration and temperature distributions and their associated layer thicknesses are enhanced by Marangoni effect.

Heating of solid targets with laser pulses

NASA Technical Reports Server (NTRS)

Bechtel, J. H.

1975-01-01

Analytical and numerical solutions to the heat-conduction equation are obtained for the heating of absorbing media with pulsed lasers. The spatial and temporal form of the temperature is determined using several different models of the laser irradiance. Both surface and volume generation of heat are discussed. It is found that if the depth of thermal diffusion for the laser-pulse duration is large compared to the optical-attenuation depth, the surface- and volume-generation models give nearly identical results. However, if the thermal-diffusion depth for the laser-pulse duration is comparable to or less than the optical-attenuation depth, the surface-generation model can give significantly different results compared to the volume-generation model. Specific numerical results are given for a tungsten target irradiated by pulses of different temporal durations and the implications of the results are discussed with respect to the heating of metals by picosecond laser pulses.

Macroscopic modeling for heat and water vapor transfer in dry snow by homogenization.

PubMed

Calonne, Neige; Geindreau, Christian; Flin, Frédéric

2014-11-26

Dry snow metamorphism, involved in several topics related to cryospheric sciences, is mainly linked to heat and water vapor transfers through snow including sublimation and deposition at the ice-pore interface. In this paper, the macroscopic equivalent modeling of heat and water vapor transfers through a snow layer was derived from the physics at the pore scale using the homogenization of multiple scale expansions. The microscopic phenomena under consideration are heat conduction, vapor diffusion, sublimation, and deposition. The obtained macroscopic equivalent model is described by two coupled transient diffusion equations including a source term arising from phase change at the pore scale. By dimensional analysis, it was shown that the influence of such source terms on the overall transfers can generally not be neglected, except typically under small temperature gradients. The precision and the robustness of the proposed macroscopic modeling were illustrated through 2D numerical simulations. Finally, the effective vapor diffusion tensor arising in the macroscopic modeling was computed on 3D images of snow. The self-consistent formula offers a good estimate of the effective diffusion coefficient with respect to the snow density, within an average relative error of 10%. Our results confirm recent work that the effective vapor diffusion is not enhanced in snow.

Estimation of Turbulent Heat Fluxes by Assimilation of Land Surface Temperature Observations From GOES Satellites Into an Ensemble Kalman Smoother Framework

NASA Astrophysics Data System (ADS)

Xu, Tongren; Bateni, S. M.; Neale, C. M. U.; Auligne, T.; Liu, Shaomin

2018-03-01

In different studies, land surface temperature (LST) observations have been assimilated into the variational data assimilation (VDA) approaches to estimate turbulent heat fluxes. The VDA methods yield accurate turbulent heat fluxes, but they need an adjoint model, which is difficult to derive and code. They also cannot directly calculate the uncertainty of their estimates. To overcome the abovementioned drawbacks, this study assimilates LST data from Geostationary Operational Environmental Satellite into the ensemble Kalman smoother (EnKS) data assimilation system to estimate turbulent heat fluxes. EnKS does not need to derive the adjoint term and directly generates statistical information on the accuracy of its predictions. It uses the heat diffusion equation to simulate LST. EnKS with the state augmentation approach finds the optimal values for the unknown parameters (i.e., evaporative fraction and neutral bulk heat transfer coefficient, CHN) by minimizing the misfit between LST observations from Geostationary Operational Environmental Satellite and LST estimations from the heat diffusion equation. The augmented EnKS scheme is tested over six Ameriflux sites with a wide range of hydrological and vegetative conditions. The results show that EnKS can predict not only the model parameters and turbulent heat fluxes but also their uncertainties over a variety of land surface conditions. Compared to the variational method, EnKS yields suboptimal turbulent heat fluxes. However, suboptimality of EnKS is small, and its results are comparable to those of the VDA method. Overall, EnKS is a feasible and reliable method for estimation of turbulent heat fluxes.

Numerical simulation of life cycles of advection warm fog

NASA Technical Reports Server (NTRS)

Hung, R. J.; Vaughan, O. H.

1977-01-01

The formation, development and dissipation of advection warm fog is investigated. The equations employed in the model include the equation of continuity, momentum and energy for the descriptions of density, wind component and potential temperature, respectively, together with two diffusion equations for the modification of water-vapor mixing ratio and liquid-water mixing ratios. A description of the vertical turbulent transfer of heat, moisture and momentum has been taken into consideration. The turbulent exchange coefficients adopted in the model are based on empirical flux-gradient relations.

Synthesis of Refractory Compounds with Gasless Combustion Reactions.

DTIC Science & Technology

1983-09-01

either Al or Mg as the reducing agent. With Al as the reductant, the stoichiometric equation is 2Mo03 + B203 + 6 Al 2MoB + 3 A120 3 Using the methods...r. rr. . . ;. ., .s . , . . o. . - •-~~- ~- . . . .4 calculated to be 267.3 kcal/mole. With Mg as the reductant, the stoichio- metric equation for the...reaction conditions also are assumed for each model. Conservation of energy and heat diffusion equations are applied to a characteristic control volume

Calculation of two-dimension radial electric field in boundary plasmas by using BOUT++

NASA Astrophysics Data System (ADS)

Li, N. M.; Xu, X. Q.; Rognlien, T. D.; Gui, B.; Sun, J. Z.; Wang, D. Z.

2018-07-01

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tel'nikhin, A. A.; Kronberg, T. K.

2007-01-01

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Study of cerium diffusion in undoped lithium-6 enriched glass with Rutherford backscattering spectrometry

NASA Astrophysics Data System (ADS)

Zhang, Xiaodong; Moore, Michael E.; Lee, Kyung-Min; Lukosi, Eric D.; Hayward, Jason P.

2016-07-01

Undoped lithium-6 enriched glasses coated with pure cerium (99.9%) with a gold protection layer on top were heated at three different temperatures (500, 550, and 600 °C) for varied durations (1, 2, and 4 h). Diffusion profiles of cerium in such glasses were obtained with the conventional Rutherford backscattering technique. Through fitting the diffusion profiles with the thin-film solution of Fick's second law, diffusion coefficients of cerium with different annealing temperatures and durations were solved. Then, the activation energy of cerium for the diffusion process in the studied glasses was found to be 114 kJ/mol with the Arrhenius equation.

Double diffusive conjugate heat transfer: Part I

NASA Astrophysics Data System (ADS)

Azeem, Soudagar, Manzoor Elahi M.

2018-05-01

The present work is undertaken to investigate the effect of solid wall being placed at left of square cavity filled with porous medium. The presence of a solid wall in the porous medium turns the situation into a conjugate heat transfer problem. The boundary conditions are such that the left vertical surface is maintained at highest temperature and concentration whereas right vertical surface at lowest temperature and concentration in the medium. The top and bottom surfaces are adiabatic. The additional conduction equation along with the regular momentum and energy equations of porous medium are solved in an iterative manner with the help of finite element method. It is seen that the heat and mass transfer rate is lesser due to smaller thermal and concentration gradients.

Diffusion of external magnetic fields into the cone-in-shell target in the fast ignition

NASA Astrophysics Data System (ADS)

Sunahara, Atsushi; Morita, Hiroki; Johzaki, Tomoyuki; Nagatomo, Hideo; Fujioka, Shinsuke; Hassanein, Ahmed; Firex Project Team

2017-10-01

We simulated the diffusion of externally applied magnetic fields into cone-in-shell target in the fast ignition. Recently, in the fast ignition scheme, the externally magnetic fields up to kilo-Tesla is used to guide fast electrons to the high-dense imploded core. In order to study the profile of the magnetic field, we have developed 2D cylindrical Maxwell equation solver with Ohm's law, and carried out simulations of diffusion of externally applied magnetic fields into a cone-in-shell target. We estimated the conductivity of the cone and shell target based on the assumption of Saha-ionization equilibrium. Also, we calculated the temporal evolution of the target temperature heated by the eddy current driven by temporal variation of magnetic fields, based on the accurate equation of state. Both, the diffusion of magnetic field and the increase of target temperature interact with each other. We present our results of temporal evolution of the magnetic field and its diffusion into the cone and shell target.

Cross diffusion effect on MHD mixed convection flow of nonlinear radiative heat and mass transfer of Casson fluid over a vertical plate

NASA Astrophysics Data System (ADS)

Ganesh Kumar, K.; Archana, M.; Gireesha, B. J.; Krishanamurthy, M. R.; Rudraswamy, N. G.

2018-03-01

A study on magnetohydrodynamic mixed convection flow of Casson fluid over a vertical plate has been modelled in the presence of Cross diffusion effect and nonlinear thermal radiation. The governing partial differential equations are remodelled into ordinary differential equations by using similarity transformation. The accompanied differential equations are resolved numerically by using Runge-Kutta-Fehlberg forth-fifth order along with shooting method (RKF45 Method). The results of various physical parameters on velocity and temperature profiles are given diagrammatically. The numerical values of the local skin friction coefficient, local Nusselt number and local Sherwood number also are shown in a tabular form. It is found that, effect of Dufour and Soret parameter increases the temperature and concentration component correspondingly.

Effects of unsteady free stream velocity and free stream turbulence on stagnation point heat transfer

NASA Technical Reports Server (NTRS)

Gorla, R. S. R.

1984-01-01

The combined effects of transient free stream velocity and free stream turbulence on heat transfer at a stagnation point over a cylinder situated in a crossflow are studied. An eddy diffusivity model was formulated and the governing momentum and energy equations are integrated by means of the steepest descent method. The numerical results for the wall shear stress and heat transfer rate are correlated by a turbulence parameter. The wall friction and heat transfer rate increase with increasing free stream turbulence intensity.

Effect of particle- and specimen-level transport on product state in compacted-powder combustion synthesis and thermal debinding of polymers from molded powders

NASA Astrophysics Data System (ADS)

Oliveira, Amir Antonio Martins

The existence of large gradients within particles and fast temporal variations in the temperature and species concentration prevents the use of asymptotic approximations for the closure of the volume-averaged, specimen-level formulations. In this case a solution of the particle-level transport problem is needed to complement the specimen-level volume-averaged equations. Here, the use of combined specimen-level and particle-level models for transport in reactive porous media is demonstrated with two examples. For the gasless compacted-powder combustion synthesis, a three-scale model is developed. The specimen-level model is based on the volume-averaged equations for species and temperature. Local thermal equilibrium is assumed and the macroscopic mass diffusion and convection fluxes are neglected. The particle-level model accounts for the interparticle diffusion (i.e., the liquid migration from liquid-rich to liquid-lean regions) and the intraparticle diffusion (i.e., the species mass diffusion within the product layer formed at the surface of the high melting temperature component). It is found that the interparticle diffusion controls the extent of conversion to the final product, the maximum temperature, and to a smaller degree the propagation velocity. The intraparticle diffusion controls the propagation velocity and to a smaller degree the maximum temperature. The initial stages of thermal degradation of EVA from molded specimens is modeled using volume-averaged equations for the species and empirical models for the kinetics of the thermal degradation, the vapor-liquid equilibrium, and the diffusion coefficient of acetic acid in the molten polymer. It is assumed that a bubble forms when the partial pressure of acetic acid exceeds the external ambient pressure. It is found that the removal of acetic acid is characterized by two regimes, a pre-charge dominated regime and a generation dominated regime. For the development of an optimum debinding schedule, the heating rate is modulated to avoid bubbling, while the concentration and temperature follow the bubble-point line for the mixture. The results show a strong dependence on the presence of a pre-charge. It is shown that isolation of the pre-charge effect by using temporary lower heating rates results in an optimum schedule for which the process time is reduced by over 70% when compared to a constant heating rate schedule.

Heat Transfer to a Thin Solid Combustible in Flame Spreading at Microgravity

NASA Technical Reports Server (NTRS)

Bhattacharjee, S.; Altenkirch, R. A.; Olson, S. L.; Sotos, R. G.

1991-01-01

The heat transfer rate to a thin solid combustible from an attached diffusion flame, spreading across the surface of the combustible in a quiescent, microgravity environment, was determined from measurements made in the drop tower facility at NASA-Lewis Research Center. With first-order Arrhenius pyrolysis kinetics, the solid-phase mass and energy equations along with the measured spread rate and surface temperature profiles were used to calculate the net heat flux to the surface. Results of the measurements are compared to the numerical solution of the complete set of coupled differential equations that describes the temperature, species, and velocity fields in the gas and solid phases. The theory and experiment agree on the major qualitative features of the heat transfer. Some fundamental differences are attributed to the neglect of radiation in the theoretical model.

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Quantitative Examination of Corrosion Damage by Means of Thermal Response Measurements

NASA Technical Reports Server (NTRS)

Rajic, Nik

1998-01-01

Two computational methods are presented that enable a characterization of corrosion damage to be performed from thermal response measurements derived from a standard flash thermographic inspection. The first is based upon a one dimensional analytical solution to the heat diffusion equation and presumes the lateral extent of damage is large compared to the residual structural thickness, such that lateral heat diffusion effects can be considered insignificant. The second proposed method, based on a finite element optimization scheme, addresses the more general case where these conditions are not met. Results from an experimental application are given to illustrate the precision, robustness and practical efficacy of both methods.

Steady MHD free convection heat and mass transfer flow about a vertical porous surface with thermal diffusion and induced magnetic field

NASA Astrophysics Data System (ADS)

Touhid Hossain, M. M.; Afruz-Zaman, Md.; Rahman, Fouzia; Hossain, M. Arif

2013-09-01

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution and induced magnetic field to the second order approximations are obtained for large suction with different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields and on the induced magnetic fields are exhibited under certain assumptions and are studied graphically in the present analysis. It is observed that the effects of thermal-diffusion and large suction have great importance on the velocity, temperature and induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

A near-wall four-equation turbulence model for compressible boundary layers

NASA Technical Reports Server (NTRS)

Sommer, T. P.; So, R. M. C.; Zhang, H. S.

1992-01-01

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.

A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

To analyse the frequently encountered thermo-chemo-mechanical problems in chemically active material applications, we develop a thermodynamically-consistent continuum theory of coupled deformation, mass diffusion, heat conduction and chemical reaction. Basic balance equations of force, mass and energy are presented at first, and then fully coupled constitutive laws interpreting multi-field interactions and evolving equations governing irreversible fluxes are constructed according to the energy dissipation inequality and the chemical kinetics. To consider the essential distinction between mass diffusion and chemical reactions in affecting free energy and dissipations of a highly coupled system, we regard both the concentrations of diffusive species and the extent of reaction as independent state variables. This new formulation then distinguishes between the energy contribution from the diffusive species entering the solid and that from the subsequent chemical reactions occurring among these species and the host solid, which not only interact with stresses or strains in different manners and on different time scales, but also induce different variations of solid microstructures and material properties. Taking advantage of this new description, we further establish a specialized isothermal model to predict precisely the transient chemo-mechanical response of a swelling solid with a proposed volumetric constraint that accounts for material incompressibility. Coupled kinetics is incorporated to capture the volumetric swelling of the solid caused by imbibition of external species and the simultaneous dilation arised from chemical reactions between the diffusing species and the solid. The model is then exemplified with two numerical examples of transient swelling accompanied by chemical reaction. Various ratios of characteristic times of diffusion and chemical reaction are taken into account to shed light on the dependency on kinetic time scales of evolution patterns for a diffusion-reaction controlled deformable solid.

Upscaling the diffusion equations in particulate media made of highly conductive particles. I. Theoretical aspects.

PubMed

Vassal, J-P; Orgéas, L; Favier, D; Auriault, J-L; Le Corre, S

2008-01-01

Many analytical and numerical works have been devoted to the prediction of macroscopic effective transport properties in particulate media. Usually, structure and properties of macroscopic balance and constitutive equations are stated a priori. In this paper, the upscaling of the transient diffusion equations in concentrated particulate media with possible particle-particle interfacial barriers, highly conductive particles, poorly conductive matrix, and temperature-dependent physical properties is revisited using the homogenization method based on multiple scale asymptotic expansions. This method uses no a priori assumptions on the physics at the macroscale. For the considered physics and microstructures and depending on the order of magnitude of dimensionless Biot and Fourier numbers, it is shown that some situations cannot be homogenized. For other situations, three different macroscopic models are identified, depending on the quality of particle-particle contacts. They are one-phase media, following the standard heat equation and Fourier's law. Calculations of the effective conductivity tensor and heat capacity are proved to be uncoupled. Linear and steady state continuous localization problems must be solved on representative elementary volumes to compute the effective conductivity tensors for the two first models. For the third model, i.e., for highly resistive contacts, the localization problem becomes simpler and discrete whatever the shape of particles. In paper II [Vassal, Phys. Rev. E 77, 011303 (2008)], diffusion through networks of slender, wavy, entangled, and oriented fibers is considered. Discrete localization problems can then be obtained for all models, as well as semianalytical or fully analytical expressions of the corresponding effective conductivity tensors.

Pseudo-time algorithms for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1986-01-01

A pseudo-time method is introduced to integrate the compressible Navier-Stokes equations to a steady state. This method is a generalization of a method used by Crocco and also by Allen and Cheng. We show that for a simple heat equation that this is just a renormalization of the time. For a convection-diffusion equation the renormalization is dependent only on the viscous terms. We implement the method for the Navier-Stokes equations using a Runge-Kutta type algorithm. This permits the time step to be chosen based on the inviscid model only. We also discuss the use of residual smoothing when viscous terms are present.

Estimation of optimal hologram recording modes on photothermal materials

NASA Astrophysics Data System (ADS)

Dzhamankyzov, Nasipbek Kurmanalievich; Ismanov, Yusupzhan Khakimzhanovich; Zhumaliev, Kubanychbek Myrzabekovich; Alymkulov, Samsaly Amanovich

2018-01-01

A theoretical analysis of the hologram recording process on photothermal media to estimate the required laser radiation power for the information recording as the function of the spatial frequency and radiation exposure duration is considered. Results of the analysis showed that materials with a low thermal diffusivity are necessary to increase the recording density in these media and the recording should be performed with short pulses to minimize the thermal diffusion length. A solution for the heat conduction equation for photothermal materials heated by an interference laser field was found. The solution obtained allows one to determine the required value of the recording temperature for given spatial frequencies, depending on the thermal physical parameters of the medium and on the power and duration of the heating radiation.

A one-dimensional heat-transport model for conduit flow in karst aquifers

USGS Publications Warehouse

Long, Andrew J.; Gilcrease, P.C.

2009-01-01

A one-dimensional heat-transport model for conduit flow in karst aquifers is presented as an alternative to two or three-dimensional distributed-parameter models, which are data intensive and require knowledge of conduit locations. This model can be applied for cases where water temperature in a well or spring receives all or part of its water from a phreatic conduit. Heat transport in the conduit is simulated by using a physically-based heat-transport equation that accounts for inflow of diffuse flow from smaller openings and fissures in the surrounding aquifer during periods of low recharge. Additional diffuse flow that is within the zone of influence of the well or spring but has not interacted with the conduit is accounted for with a binary mixing equation to proportion these different water sources. The estimation of this proportion through inverse modeling is useful for the assessment of contaminant vulnerability and well-head or spring protection. The model was applied to 7 months of continuous temperature data for a sinking stream that recharges a conduit and a pumped well open to the Madison aquifer in western South Dakota. The simulated conduit-flow fraction to the well ranged from 2% to 31% of total flow, and simulated conduit velocity ranged from 44 to 353 m/d.

Approximate Solution Methods for Spectral Radiative Transfer in High Refractive Index Layers

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1994-01-01

Some ceramic materials for high temperature applications are partially transparent for radiative transfer. The refractive indices of these materials can be substantially greater than one which influences internal radiative emission and reflections. Heat transfer behavior of single and laminated layers has been obtained in the literature by numerical solutions of the radiative transfer equations coupled with heat conduction and heating at the boundaries by convection and radiation. Two-flux and diffusion methods are investigated here to obtain approximate solutions using a simpler formulation than required for exact numerical solutions. Isotropic scattering is included. The two-flux method for a single layer yields excellent results for gray and two band spectral calculations. The diffusion method yields a good approximation for spectral behavior in laminated multiple layers if the overall optical thickness is larger than about ten. A hybrid spectral model is developed using the two-flux method in the optically thin bands, and radiative diffusion in bands that are optically thick.

Ballistic-diffusive approximation for the thermal dynamics of metallic nanoparticles in nanocomposite materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shirdel-Havar, A. H., E-mail: Amir.hushang.shirdel@gmail.com; Masoudian Saadabad, R.

2015-03-21

Based on ballistic-diffusive approximation, a method is presented to model heat transfer in nanocomposites containing metal nanoparticles. This method provides analytical expression for the temperature dynamics of metallic nanoparticles embedded in a dielectric medium. In this study, nanoparticles are considered as spherical shells, so that Boltzmann equation is solved using ballistic-diffusive approximation to calculate the electron and lattice thermal dynamics in gold nanoparticles, while thermal exchange between the particles is taken into account. The model was used to investigate the influence of particle size and metal concentration of the medium on the electron and lattice thermal dynamics. It is shownmore » that these two parameters are crucial in determining the nanocomposite thermal behavior. Our results showed that the heat transfer rate from nanoparticles to the matrix decreases as the nanoparticle size increases. On the other hand, increasing the metal concentration of the medium can also decrease the heat transfer rate.« less

Role of Rayleigh numbers on characteristics of double diffusive salt fingers

NASA Astrophysics Data System (ADS)

Rehman, F.; Singh, O. P.

2018-05-01

Double diffusion convection, driven by two constituents of the fluid with different molecular diffusivity, is widely applied in oceanography and large number of other fields like astrophysics, geology, chemistry and metallurgy. In case of ocean, heat (T) and salinity (S) are the two components with varying diffusivity, where heat diffuses hundred times faster than salt. Component (T) stabilizes the system whereas components (S) destabilizes the system with overall density remains stable and forms the rising and sinking fingers known as salt fingers. Recent observations suggest that salt finger characteristics such as growth rates, wavenumber, and fluxes are strongly depending on the Rayleigh numbers as major driving force. In this paper, we corroborate this observation with the help of experiments, numerical simulations and linear theory. An eigenvalue expression for growth rate is derived from the linearized governing equations with explicit dependence on Rayleigh numbers, density stability ratio, Prandtl number and diffusivity ratio. Expressions for fastest growing fingers are also derived as a function various non-dimensional parameter. The predicted results corroborate well with the data reported from the field measurements, experiments and numerical simulations.

Multigrid techniques for the solution of the passive scalar advection-diffusion equation

NASA Technical Reports Server (NTRS)

Phillips, R. E.; Schmidt, F. W.

1985-01-01

The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

Steady state model for the thermal regimes of shells of airships and hot air balloons

NASA Astrophysics Data System (ADS)

Luchev, Oleg A.

1992-10-01

A steady state model of the temperature regime of airships and hot air balloons shells is developed. The model includes three governing equations: the equation of the temperature field of airships or balloons shell, the integral equation for the radiative fluxes on the internal surface of the shell, and the integral equation for the natural convective heat exchange between the shell and the internal gas. In the model the following radiative fluxes on the shell external surface are considered: the direct and the earth reflected solar radiation, the diffuse solar radiation, the infrared radiation of the earth surface and that of the atmosphere. For the calculations of the infrared external radiation the model of the plane layer of the atmosphere is used. The convective heat transfer on the external surface of the shell is considered for the cases of the forced and the natural convection. To solve the mentioned set of the equations the numerical iterative procedure is developed. The model and the numerical procedure are used for the simulation study of the temperature fields of an airship shell under the forced and the natural convective heat transfer.

An Exponential Finite Difference Technique for Solving Partial Differential Equations. M.S. Thesis - Toledo Univ., Ohio

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

exponential finite difference technique for solving partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Handschuh, R.F.

1987-01-01

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that weremore » more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.« less

Quasilinear diffusion operator for wave-particle interactions in inhomogeneous magnetic fields

NASA Astrophysics Data System (ADS)

Catto, P. J.; Lee, J.; Ram, A. K.

2017-10-01

The Kennel-Engelmann quasilinear diffusion operator for wave-particle interactions is for plasmas in a uniform magnetic field. The operator is not suitable for fusion devices with inhomogeneous magnetic fields. Using drift kinetic and high frequency gyrokinetic equations for the particle distribution function, we have derived a quasilinear operator which includes magnetic drifts. The operator applies to RF waves in any frequency range and is particularly relevant for minority ion heating. In order to obtain a physically meaningful operator, the first order correction to the particle's magnetic moment has to be retained. Consequently, the gyrokinetic change of variables has to be retained to a higher order than usual. We then determine the perturbed distribution function from the gyrokinetic equation using a novel technique that solves the kinetic equation explicitly for certain parts of the function. The final form of the diffusion operator is compact and completely expressed in terms of the drift kinetic variables. It is not transit averaged and retains the full poloidal angle variation without any Fourier decomposition. The quasilinear diffusion operator reduces to the Kennel-Engelmann operator for uniform magnetic fields. Supported by DoE Grant DE-FG02-91ER-54109.

Magnetic flux and heat losses by diffusive, advective, and Nernst effects in magnetized liner inertial fusion-like plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.

The magnetized liner inertial fusion (MagLIF) approach to inertial confinement fusion [Slutz et al., Phys. Plasmas 17, 056303 (2010); Cuneo et al., IEEE Trans. Plasma Sci. 40, 3222 (2012)] involves subsonic/isobaric compression and heating of a deuterium-tritium plasma with frozen-in magnetic flux by a heavy cylindrical liner. The losses of heat and magnetic flux from the plasma to the liner are thereby determined by plasma advection and gradient-driven transport processes, such as thermal conductivity, magnetic field diffusion, and thermomagnetic effects. Theoretical analysis based on obtaining exact self-similar solutions of the classical collisional Braginskii's plasma transport equations in one dimension demonstratesmore » that the heat loss from the hot compressed magnetized plasma to the cold liner is dominated by transverse heat conduction and advection, and the corresponding loss of magnetic flux is dominated by advection and the Nernst effect. For a large electron Hall parameter (ω{sub e}τ{sub e}≫1), the effective diffusion coefficients determining the losses of heat and magnetic flux to the liner wall are both shown to decrease with ω{sub e}τ{sub e} as does the Bohm diffusion coefficient cT/(16eB), which is commonly associated with low collisionality and two-dimensional transport. We demonstrate how this family of exact solutions can be used for verification of codes that model the MagLIF plasma dynamics.« less

Solutions for Reacting and Nonreacting Viscous Shock Layers with Multicomponent Diffusion and Mass Injection. Ph.D. Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Moss, J. N.

1971-01-01

Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.

Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy.

PubMed

Shizgal, Bernie D

2018-05-01

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988)JSTPBS0022-471510.1007/BF01016429].

Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy

NASA Astrophysics Data System (ADS)

Shizgal, Bernie D.

2018-05-01

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988), 10.1007/BF01016429].

Steady-state solutions of a diffusive energy-balance climate model and their stability

NASA Technical Reports Server (NTRS)

Ghil, M.

1975-01-01

A diffusive energy-balance climate model, governed by a nonlinear parabolic partial differential equation, was studied. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. Models similar to the main one are considered, and the number of their steady states was determined. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The stability under small perturbations of the main model's climates was investigated. A stability criterion is derived, and its application shows that the present climate and the deep freeze are stable, whereas the model's glacial is unstable. The dependence was examined of the number of steady states and of their stability on the average solar radiation.

Sweat Rate Prediction Equations for Outdoor Exercise with Transient Solar Radiation

DTIC Science & Technology

2012-01-01

AD] 15 Interchangeable variables gSL W/m2 Global solar load Direct weather station data; pyranometer values 25 Direct measurement from weather station ...Fanger equations 2, 4, 13, Direct or weather station values Rdif W Diffuse irradiance Rref W Reflected irradiance AD m2 Body surface area (BSA) from DuBois...assuming the given weather station uses standard meteorological measuring instru- ments. In the heat flow form expressed by Matthew et al. (25

Benchmarking FEniCS for mantle convection simulations

NASA Astrophysics Data System (ADS)

Vynnytska, L.; Rognes, M. E.; Clark, S. R.

2013-01-01

This paper evaluates the usability of the FEniCS Project for mantle convection simulations by numerical comparison to three established benchmarks. The benchmark problems all concern convection processes in an incompressible fluid induced by temperature or composition variations, and cover three cases: (i) steady-state convection with depth- and temperature-dependent viscosity, (ii) time-dependent convection with constant viscosity and internal heating, and (iii) a Rayleigh-Taylor instability. These problems are modeled by the Stokes equations for the fluid and advection-diffusion equations for the temperature and composition. The FEniCS Project provides a novel platform for the automated solution of differential equations by finite element methods. In particular, it offers a significant flexibility with regard to modeling and numerical discretization choices; we have here used a discontinuous Galerkin method for the numerical solution of the advection-diffusion equations. Our numerical results are in agreement with the benchmarks, and demonstrate the applicability of both the discontinuous Galerkin method and FEniCS for such applications.

Topology optimisation for natural convection problems

NASA Astrophysics Data System (ADS)

Alexandersen, Joe; Aage, Niels; Andreasen, Casper Schousboe; Sigmund, Ole

2014-12-01

This paper demonstrates the application of the density-based topology optimisation approach for the design of heat sinks and micropumps based on natural convection effects. The problems are modelled under the assumptions of steady-state laminar flow using the incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation. In order to facilitate topology optimisation, the Brinkman approach is taken to penalise velocities inside the solid domain and the effective thermal conductivity is interpolated in order to accommodate differences in thermal conductivity of the solid and fluid phases. The governing equations are discretised using stabilised finite elements and topology optimisation is performed for two different problems using discrete adjoint sensitivity analysis. The study shows that topology optimisation is a viable approach for designing heat sink geometries cooled by natural convection and micropumps powered by natural convection.

The Prediction of Nozzle Performance and Heat Transfer in Hydrogen/Oxygen Rocket Engines with Transpiration Cooling, Film Cooling, and High Area Ratios

NASA Technical Reports Server (NTRS)

Kacynski, Kenneth J.; Hoffman, Joe D.

1994-01-01

An advanced engineering computational model has been developed to aid in the analysis of chemical rocket engines. The complete multispecies, chemically reacting and diffusing Navier-Stokes equations are modelled, including the Soret thermal diffusion and Dufour energy transfer terms. Demonstration cases are presented for a 1030:1 area ratio nozzle, a 25 lbf film-cooled nozzle, and a transpiration-cooled plug-and-spool rocket engine. The results indicate that the thrust coefficient predictions of the 1030:1 nozzle and the film-cooled nozzle are within 0.2 to 0.5 percent, respectively, of experimental measurements. Further, the model's predictions agree very well with the heat transfer measurements made in all of the nozzle test cases. It is demonstrated that thermal diffusion has a significant effect on the predicted mass fraction of hydrogen along the wall of the nozzle and was shown to represent a significant fraction of the diffusion fluxes occurring in the transpiration-cooled rocket engine.

Numerical Analysis of Transient Temperature Response of Soap Film

NASA Astrophysics Data System (ADS)

Tanaka, Seiichi; Tatesaku, Akihiro; Dantsuka, Yuki; Fujiwara, Seiji; Kunimine, Kanji

2015-11-01

Measurements of thermophysical properties of thin liquid films are important to understand interfacial phenomena due to film structures composed of amphiphilic molecules in soap film, phospholipid bilayer of biological cell and emulsion. A transient hot-wire technique for liquid films less than 1 \\upmu m thick such as soap film has been proposed to measure the thermal conductivity and diffusivity simultaneously. Two-dimensional heat conduction equations for a solid cylinder with a liquid film have been solved numerically. The temperature of a thin wire with liquid film increases steeply with its own heat generation. The feasibility of this technique is verified through numerical experiments for various thermal conductivities, diffusivities, and film thicknesses. Calculated results indicate that the increase in the volumetric average temperature of the thin wire sufficiently varies with the change of thermal conductivity and diffusivity of the soap film. Therefore, the temperature characteristics could be utilized to evaluate both the thermal conductivity and diffusivity using the Gauss-Newton method.

Thermobaricity, cabbeling, and water-mass conversion

NASA Astrophysics Data System (ADS)

McDougall, Trevor J.

1987-05-01

The efficient mixing of heat and salt along neutral surfaces (by mesoscale eddies) is shown to lead to vertical advection through these neutral surfaces. This is due to the nonlinearities of the equation of state of seawater through terms like ∂2ρ/∂θ∂p (thermobaric effect) and ∂2ρ/∂ θ2 (cabbeling). Cabbeling always causes a sinking or downwelling of fluid through neutral surfaces, whereas thermobaricity can lead to a vertical velocity (relative to neutral surfaces) of either sign. In this paper it is shown that for reasonable values of the lateral scalar diffusivity (especially below a depth of 1000 m), these two processes cause vertical velocities of the order of 10-7 m s-1 through neutral surfaces (usually downward!) and cause water-mass conversion of a magnitude equal to that caused by a vertical diffusivity of 10-4 m2 s-1 (often equivalent to a negative diffusivity). Both thermobaricity and cabbeling can occur in the presence of any nonzero amount of small-scale turbulence and so will not be detected by microstructure measurements. The conservation equations for tracers are considered in a nonorthogonal coordinate frame that moves with neutral surfaces in the ocean. Since only mixing processes cause advection across neutral surfaces, it is useful to regard this vertical advection as a symptom of various mixing processes rather than as a separate physical process. It is possible to derive conservative equations for scalars that do not contain the vertical advective term explicity. In these conservation equations, the terms that represent mixing processes are substantially altered. It is argued that this form of the conservation equations is the most appropriate when considering water-mass transformation, and some examples are given of its application in the North Atlantic. It is shown that the variation of the vertical diffusivity with height does not cause water-mass transformation. Also, salt fingering is often 3-4 times more effective at changing the potential temperature of a water mass than would be implied by simply calculating the vertical derivative of the fingering heat flux.

How long does it take to boil an egg? A simple approach to the energy transfer equation

NASA Astrophysics Data System (ADS)

Roura, P.; Fort, J.; Saurina, J.

2000-01-01

The heating of simple geometric objects immersed in an isothermal bath is analysed qualitatively through Fourier's law. The approximate temperature evolution is compared with the exact solution obtained by solving the transport differential equation, the discrepancies being smaller than 20%. Our method succeeds in giving the solution as a function of the Fourier modulus so that the scale laws hold. It is shown that the time needed to homogenize temperature variations that extend over mean distances xm is approximately xm2/icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/>, where icons/Journals/Common/alpha" ALT="alpha" ALIGN="MIDDLE"/> is the thermal diffusivity. This general relationship also applies to atomic diffusion. Within the approach presented there is no need to write down any differential equation. As an example, the analysis is applied to the process of boiling an egg.

Asymptotic analysis of the local potential approximation to the Wetterich equation

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D  <  2, one obtains a forward heat equation whose initial-value problem is well-posed. However, for D  >  2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

Thermal radiation and mass transfer effects on unsteady MHD free convection flow past a vertical oscillating plate

NASA Astrophysics Data System (ADS)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.

Imaging hydraulic fractures using temperature transients in the Belridge Diatomite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shahin, G.T.; Johnston, R.M.

1995-12-31

Results of a temperature transient analysis of Shell`s Phase 1 and Phase 2 Diatomite Steamdrive Pilots are used to image hydraulic injection fracture lengths, angles, and heat injectivities into the low-permeability formation. The Phase 1 Pilot is a limited-interval injection test. In Phase 2, steam is injected into two 350 ft upper and lower zones through separate hydraulic fractures. Temperature response of both pilots is monitored with sixteen logging observation wells. A perturbation analysis of the non-linear pressure diffusion and heat transport equations indicates that at a permeability of about 0.1 md or less, heat transport in the Diatomite tendsmore » to be dominated by thermal diffusivity, and pressure diffusion is dominated by the ratio of thermal expansion to fluid compressibility. Under these conditions, the temperature observed at a logging observation well is governed by a dimensionless quantity that depends on the perpendicular distance between the observation well and the hydraulic fracture, divided by the square root of time. Using this dependence, a novel method is developed for imaging hydraulic fracture geometry and relative heat injectivity from the temperature history of the pilot.« less

2ND EF Conference in Turbulent Heat Transfer, Manchester, UK 1998. Volume 1

DTIC Science & Technology

1998-06-01

study the effect of Pr on statistical properties characterizing the scalar field. Turbulent diffusivities are presented for Pr=0.1-2400. A time scale, r...can be defined from the kinetic energy, fc, and the dissipation of turbulence, e, where r = -. The observed influence of Pr (0.05-10) on a time ...dimensional, time -dependent Navier-Stokes equa- tion in a skew-symmetric form and the advection- diffusion equation. du = (u x w) - VIE - Pxex

Modeling of various heat adapter plate 4 and 6 array for optimization of thermoelectric generator element using modified diffusion equation

NASA Astrophysics Data System (ADS)

Defrianto; Tambunan, W.; Lazuardi

2017-07-01

The use of waste heat from exhaust gas and converting it to electricity is now an alternative to harvest a cheap and clean energy. Thermoelectric generator (TEG) has the ability to directly recover such waste heat and generate electricity. The aim of this study is to simulate the heat transfer on the aluminum adapter plate for homogeneity temperature distribution coupled with hot side of TEG type 40-40-10/100 from Firma Eureka and adjust their high temperatures to the TEG operating temperature to avoid the element damage. Modelling was carried out using MATLAB modified diffusion equation with Dirichlet boundary conditions at defined temperature which has been set at the ends of the heat source at 463K and 373K ± 10% on the hot side of the TEG element. The use of nylon insulated material is modeled after Neumann boundary condition in which the temperature gradient is ∂T/∂n = 0 out of boundary. Realization of the modelling is done by designing a heat conductive plate using software ACAD 2015 and converted into a binary file format of Mathlab to form a finite element mesh with geometry variations of solid model. The solid cubic model of aluminum adapter plate has a dimension of 40mm length, 40mm width and also 20mm, 30mm and 40mm thickness arranged in two arrays of 2×2 and 2×3 of TEG elements. Results showed a temperature decrease about 40.95% and 50.02% respectively from the initial source and appropriate with TEG temperature tolerance.

Parallel heat transport in integrable and chaotic magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Del-Castillo-Negrete, Diego B; Chacon, Luis

2012-01-01

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly chal- lenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), , and the perpendicular, , conductivities ( / may exceed 1010 in fusion plasmas); (ii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates; and (iii) Nonlocal parallel transport in the limit of small collisionality. Motivated by these issues, we present a Lagrangian Green s function method to solve themore » local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geom- etry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island chain), weakly chaotic (devil s staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local closures, is non-diffusive, thus casting doubts on the appropriateness of the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.« less

A numerical analysis of high-temperature heat pipe startup from the frozen state

NASA Technical Reports Server (NTRS)

Cao, Y.; Faghri, A.

1993-01-01

Continuum and rarefied vapor flows co-exist along the heat pipe length for most of the startup period. A two-region model is proposed in which the vapor flow in the continuum region is modeled by the compressible Navier-Stokes equations, and the vapor flow in the rarefied region is simulated by a self-diffusion model. The two vapor regions are linked with appropriate boundary conditions, and heat pipe wail, wick, and vapor flow are solved as a conjugate problem. The numerical solutions for the entire heat pipe startup process from the frozen state are compared with the corresponding experimental data with good agreement.

Diffusion in liquid metal systems. [information on electrical resistivity and thermal conductivity

NASA Technical Reports Server (NTRS)

Ukanwa, A. O.

1975-01-01

Physical properties of twenty liquid metals are reported; some of the data on such liquid metal properties as density, electrical resistivity, thermal conductivity, and heat capacity are summarized in graphical form. Data on laboratory handling and safety procedure are summarized for each metal; heat-transfer-correlations for liquid metals under various conditions of laminar and turbulent flow are included. Where sufficient data were available, temperature equations of properties were obtained by the method of least-squares fit. All values of properties given are valid in the given liquid phase ranges only. Additional tabular data on some 40 metals are reported in the appendix. Included is a brief description of experiments that were performed to investigate diffusion in liquid indium-gallium systems.

Kinetics of propagation of the lattice excitation in a swift heavy ion track

NASA Astrophysics Data System (ADS)

Lipp, V. P.; Volkov, A. E.; Sorokin, M. V.; Rethfeld, B.

2011-05-01

In this research we verify the applicability of the temperature and heat diffusion conceptions for the description of subpicosecond lattice excitations in nanometric tracks of swift heavy ions (SHI) decelerated in solids in the electronic stopping regime. The method is based on the molecular dynamics (MD) analysis of temporal evolutions of the local kinetic and configurational temperatures of a lattice. We used solid argon as the model system. MD simulations demonstrated that in a SHI track (a) thermalization of lattice excitations takes time of several picoseconds, and (b) application of the parabolic heat diffusion equations for the description of spatial and temporal propagation of lattice excitations is questionable at least up to 10 ps after the ion passage.

Compact scheme for systems of equations applied to fundamental problems of mechanics of continua

NASA Technical Reports Server (NTRS)

Klimkowski, Jerzy Z.

1990-01-01

Compact scheme formulation was used in the treatment of boundary conditions for a system of coupled diffusion and Poisson equations. Models and practical solutions of specific engineering problems arising in solid mechanics, chemical engineering, heat transfer and fuid mechanics are described and analyzed for efficiency and accuracy. Only 2-D cases are discussed and a new method of numerical treatment of boundary conditions common in the fundamental problems of mechanics of continua is presented.

Variable Refractive Index Effects on Radiation in Semitransparent Scattering Multilayered Regions

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1993-01-01

A simple set of equations is derived for predicting the temperature distribution and radiative energy flow in a semitransparent layer consisting of an arbitrary number of laminated sublayers that absorb, emit, and scatter radiation. Each sublayer can have a different refractive index and optical thickness. The plane composite region is heated on each exterior side by a different amount of incident radiation. The results are for the limiting case where heat conduction within the layers is very small relative to radiative transfer, and is neglected. The interfaces are assumed diffuse, and all interface reflections are included in the analysis. The thermal behavior is readily calculated from the analytical expressions that are obtained. By using many sublayers, expressions provide the temperature distribution and heat flow for a diffusing medium with a continually varying refractive index, including internal reflection effects caused by refractive index gradients. Temperature and heat flux results are given to show the effect of variations in refractive index and optical thickness through the multilayer laminate.

Effect of Water on the Thermo-Mechanical Behavior of Carbon Cloth Phenolic

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.; Stokes, Eric; Baker, Eric H.

2011-01-01

The results of thermo-mechanical experiments, which were conducted previously by one of the authors, are reviewed. The strain in the direction normal to the fabric plane was measured as a function of temperature for a variety of initial moisture contents and heating rates. In this paper, the general features of the thermo-mechanical response are discussed and the effect of heating rate and initial moisture content are highlighted. The mechanical interaction between the phenolic polymer and water trapped within its free volumes as the polymer is heated to high temperatures is discussed. An equation for the internal stresses which are generated within the polymer due to trapped water is obtained from the total stress expression for a binary mixture of polymer and water. Numerical solutions for moisture diffusion in the thermo-mechanical experiments were performed and the results of these solutions are presented. The results of the moisture diffusion solutions help to explain the effects of heating rate and moisture content on the strain behavior normal to the fabric plane.

Variable Refractive Index Effects on Radiation in Semitransparent Scattering Multilayered Regions

NASA Technical Reports Server (NTRS)

Siegel, R.; Spuckler, C. M.

1993-01-01

A simple set of equations is derived for predicting the temperature distribution and radiative energy flow in a semitransparent layer consisting of an arbitrary number of laminated sublayers that absorb, emit, and scatter radiation. Each sublayer can have a different refractive index and optical thickness. The plane composite region is heated on each exterior side by a different amount of incident radiation. The results are for the limiting case where heat conduction within the layers is very small relative to radiative transfer, and is neglected. The interfaces are assumed diffuse, and all interface reflections are included in the analysis. The thermal behavior is readily calculated from the analytical expressions that are obtained. By using many sublayers, the analytical expressions provide the temperature distribution and heat flow for a diffusing medium with a continuously varying refractive index, including internal reflection effects caused by refractive index gradients. Temperature and heat flux results are given to show the effect of variations in refractive index and optical thickness through the multilayer laminate.

Slip and barodiffusion phenomena in slow flows of a gas mixture

NASA Astrophysics Data System (ADS)

Zhdanov, V. M.

2017-03-01

The slip and barodiffusion problems for the slow flows of a gas mixture are investigated on the basis of the linearized moment equations following from the Boltzmann equation. We restrict ourselves to the set of the third-order moment equations and state two general relations (resembling conservation equations) for the moments of the distribution function similar to the conditions used by Loyalka [S. K. Loyalka, Phys. Fluids 14, 2291 (1971), 10.1063/1.1693331] in his approximation method (the modified Maxwell method). The expressions for the macroscopic velocities of the gas mixture species, the partial viscous stress tensors, and the reduced heat fluxes for the stationary slow flow of a gas mixture in the semi-infinite space over a plane wall are obtained as a result of the exact solution of the linearized moment equations in the 10- and 13-moment approximations. The general expression for the slip velocity and the simple and accurate expressions for the viscous, thermal, diffusion slip, and baroslip coefficients, which are given in terms of the basic transport coefficients, are derived by using the modified Maxwell method. The solutions of moment equations are also used for investigation of the flow and diffusion of a gas mixture in a channel formed by two infinite parallel plates. A fundamental result is that the barodiffusion factor in the cross-section-averaged expression for the diffusion flux contains contributions associated with the viscous transfer of momentum in the gas mixture and the effect of the Knudsen layer. Our study revealed that the barodiffusion factor is equal to the diffusion slip coefficient (correct to the opposite sign). This result is consistent with the Onsager's reciprocity relations for kinetic coefficients following from nonequilibrium thermodynamics of the discontinuous systems.

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Zubova, N. A.

2017-06-01

This paper presents the results of numerical simulation of the Soret-induced convection of ternary mixture in the rectangular cavity elongated in horizontal direction in gravity field. The cavity has rigid impermeable boundaries. It is heated from the bellow and undergoes translational linearly polarized vibrations of finite amplitude and frequency in the horizontal direction. The problem is solved by finite difference method in the framework of full unsteady non-linear approach. The procedure of diagonalization of the molecular diffusion coefficient matrix is applied, allowing to eliminate cross-diffusion components in the equations and to reduce the number of the governing parameters. The calculations are performed for model ternary mixture with positive separation ratios of the components. The data on the vibration effect on temporal evolution of instantaneous and average fields and integral characteristics of the flow and heat and mass transfer at different levels of gravity are obtained.

Heat and water rate transfer processes in the human respiratory tract at various altitudes.

PubMed

Kandjov, I M

2001-02-01

The process of the respiratory air conditioning as a process of heat and mass exchange at the interface inspired air-airways surface was studied. Using a model of airways (Olson et al., 1970) where the segments of the respiratory tract are like cylinders with a fixed length and diameter, the corresponding heat transfer equations, in the paper are founded basic rate exchange parameters-convective heat transfer coefficient h(c)(W m(-2) degrees C(-1)) and evaporative heat transfer coefficient h(e)(W m(-2)hPa(-1)). The rate transfer parameters assumed as sources with known heat power are connected to airflow rate in different airways segments. Relationships expressing warming rate of inspired air due to convection, warming rate of inspired air due to evaporation, water diffused in the inspired air from the airways wall, i.e. a system of air conditioning parameters, was composed. The altitude dynamics of the relations is studied. Every rate conditioning parameter is an increasing function of altitude. The process of diffusion in the peripheral bronchial generations as a basic transfer process is analysed. The following phenomenon is in effect: the diffusion coefficient increases with altitude and causes a compensation of simultaneous decreasing of O(2)and CO(2)densities in atmospheric air. Due to this compensation, the diffusion in the peripheral generations with altitude is approximately constant. The elements of the human anatomy optimality as well as the established dynamics are discussed and assumed. The square form of the airways after the trachea expressed in terms of transfer supposes (in view of maximum contact surface), that a maximum heat and water exchange is achieved, i.e. high degree of air condition at fixed environmental parameters and respiration regime. Copyright 2001 Academic Press.

Double Diffusive Magnetohydrodynamic (MHD) Mixed Convective Slip Flow along a Radiating Moving Vertical Flat Plate with Convective Boundary Condition

PubMed Central

Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360

Grating formation by a high power radio wave in near-equator ionosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singh, Rohtash; Sharma, A. K.; Tripathi, V. K.

2011-11-15

The formation of a volume grating in the near-equator regions of ionosphere due to a high power radio wave is investigated. The radio wave, launched from a ground based transmitter, forms a standing wave pattern below the critical layer, heating the electrons in a space periodic manner. The thermal conduction along the magnetic lines of force inhibits the rise in electron temperature, limiting the efficacy of heating to within a latitude of few degrees around the equator. The space periodic electron partial pressure leads to ambipolar diffusion creating a space periodic density ripple with wave vector along the vertical. Suchmore » a volume grating is effective to cause strong reflection of radio waves at a frequency one order of magnitude higher than the maximum plasma frequency in the ionosphere. Linearly mode converted plasma wave could scatter even higher frequency radio waves.« less

INTERNATIONAL CONFERENCE ON SEMICONDUCTOR INJECTION LASERS SELCO-87: Transient heat conduction in laser diodes

NASA Astrophysics Data System (ADS)

Enders, P.; Galley, J.

1988-11-01

The dynamics of heat transfer in stripe GaAlAs laser diodes is investigated by solving the linear diffusion equation for a quasitwo-dimensional multilayer structure. The calculations are rationalized drastically by the transfer matrix method and also using for the first time the asymptotes of the decay constants. Special attention is given to the convergence of the Fourier series. A comparison with experimental results reveals however that this is essentially the Stefan problem (with moving boundary conditions).

Modeling the burnout of solid polydisperse fuel under the conditions of external heat transfer

NASA Astrophysics Data System (ADS)

Skorik, I. A.; Goldobin, Yu. M.; Tolmachev, E. M.; Gal'perin, L. G.

2013-11-01

A self-similar burnout mode of solid polydisperse fuel is considered taking into consideration heat transfer between fuel particles, gases, and combustion chamber walls. A polydisperse composition of fuel is taken into account by introducing particle distribution functions by radiuses obtained for the kinetic and diffusion combustion modes. Equations for calculating the temperatures of particles and gases are presented, which are written for particles average with respect to their distribution functions by radiuses taking into account the fuel burnout ratio. The proposed equations take into consideration the influence of fuel composition, air excess factor, and gas recirculation ratio. Calculated graphs depicting the variation of particle and gas temperatures, and the fuel burnout ratio are presented for an anthracite-fired boiler.

Homogeneous-heterogeneous reactions in curved channel with porous medium

NASA Astrophysics Data System (ADS)

Hayat, T.; Ayub, Sadia; Alsaedi, A.

2018-06-01

Purpose of the present investigation is to examine the peristaltic flow through porous medium in a curved conduit. Problem is modeled for incompressible electrically conducting Ellis fluid. Influence of porous medium is tackled via modified Darcy's law. The considered model utilizes homogeneous-heterogeneous reactions with equal diffusivities for reactant and autocatalysis. Constitutive equations are formulated in the presence of viscous dissipation. Channel walls are compliant in nature. Governing equations are modeled and simplified under the assumptions of small Reynolds number and large wavelength. Graphical results for velocity, temperature, heat transfer coefficient and homogeneous-heterogeneous reaction parameters are examined for the emerging parameters entering into the problem. Results reveal an activation in both homogenous-heterogenous reaction effect and heat transfer rate with increasing curvature of the channel.

On two parabolic systems: Convergence and blowup

NASA Astrophysics Data System (ADS)

Huang, Yamin

1998-12-01

This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

Turbulent Flow past High Temperature Surfaces

NASA Astrophysics Data System (ADS)

Mehmedagic, Igbal; Thangam, Siva; Carlucci, Pasquale; Buckley, Liam; Carlucci, Donald

2014-11-01

Flow over high-temperature surfaces subject to wall heating is analyzed with applications to projectile design. In this study, computations are performed using an anisotropic Reynolds-stress model to study flow past surfaces that are subject to radiative flux. The model utilizes a phenomenological treatment of the energy spectrum and diffusivities of momentum and heat to include the effects of wall heat transfer and radiative exchange. The radiative transport is modeled using Eddington approximation including the weighted effect of nongrayness of the fluid. The time-averaged equations of motion and energy are solved using the modeled form of transport equations for the turbulence kinetic energy and the scalar form of turbulence dissipation with an efficient finite-volume algorithm. The model is applied for available test cases to validate its predictive capabilities for capturing the effects of wall heat transfer. Computational results are compared with experimental data available in the literature. Applications involving the design of projectiles are summarized. Funded in part by U.S. Army, ARDEC.

Closed-form solution of temperature and heat flux in embedded cooling channels

NASA Astrophysics Data System (ADS)

Griggs, Steven Craig

1997-11-01

An analytical method is discussed for predicting temperature in a layered composite material with embedded cooling channels. The cooling channels are embedded in the material to maintain its temperature at acceptable levels. Problems of this type are encountered in the aerospace industry and include high-temperature or high-heat-flux protection for advanced composite-material skins of high-speed air vehicles; thermal boundary-layer flow control on supersonic transports; or infrared signature suppression on military vehicles. A Green's function solution of the diffusion equation is used to simultaneously predict the global and localized effects of temperature in the material and in the embedded cooling channels. The integral method is used to solve the energy equation with fluid flow to find the solution of temperature and heat flux in the cooling fluid and material simultaneously. This method of calculation preserves the three-dimensional nature of this problem.

Strain-based diffusion solver for realistic representation of diffusion front in physical reactions

PubMed Central

2017-01-01

When simulating fluids, such as water or fire, interacting with solids, it is a challenging problem to represent details of diffusion front in physical reaction. Previous approaches commonly use isotropic or anisotropic diffusion to model the transport of a quantity through a medium or long interface. We have identified unrealistic monotonous patterns with previous approaches and therefore, propose to extend these approaches by integrating the deformation of the material with the diffusion process. Specifically, stretching deformation represented by strain is incorporated in a divergence-constrained diffusion model. A novel diffusion model is introduced to increase the global rate at which the solid acquires relevant quantities, such as heat or saturation. This ensures that the equations describing fluid flow are linked to the change of solid geometry, and also satisfy the divergence-free condition. Experiments show that our method produces convincing results. PMID:28448591

Theoretical and Experimental Investigation of the Translational Diffusion of Proteins in the Vicinity of Temperature-Induced Unfolding Transition.

PubMed

Molchanov, Stanislav; Faizullin, Dzhigangir A; Nesmelova, Irina V

2016-10-06

Translational diffusion is the most fundamental form of transport in chemical and biological systems. The diffusion coefficient is highly sensitive to changes in the size of the diffusing species; hence, it provides important information on the variety of macromolecular processes, such as self-assembly or folding-unfolding. Here, we investigate the behavior of the diffusion coefficient of a macromolecule in the vicinity of heat-induced transition from folded to unfolded state. We derive the equation that describes the diffusion coefficient of the macromolecule in the vicinity of the transition and use it to fit the experimental data from pulsed-field-gradient nuclear magnetic resonance (PFG NMR) experiments acquired for two globular proteins, lysozyme and RNase A, undergoing temperature-induced unfolding. A very good qualitative agreement between the theoretically derived diffusion coefficient and experimental data is observed.

Relativistic theory of particles in a scattering flow III: photon transport.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We use the theory developed in Achterberg & Norman (2018a) and Achterberg & Norman (2018b) to calculate the stress due to photons that are scattered elastically by a relativistic flow. We show that the energy-momentum tensor of the radiation takes the form proposed by Eckart (1940). In particular we show that no terms associated with a bulk viscosity appear if one makes the diffusion approximation for radiation transport and treats the radiation as a separate fluid. We find only shear (dynamic) viscosity terms and heat flow terms in our expression for the energy-momentum tensor. This conclusion holds quite generally for different forms of scattering: Krook-type integral scattering, diffusive (Fokker-Planck) scattering and Thomson scattering. We also derive the transport equation in the diffusion approximation that shows the effects of the flow on the photon gas in the form of a combination of adiabatic heating and an irreversible heating term. We find no diffusive changes to the comoving number density and energy density of the scattered photons, in contrast with some published results in Radiation Hydrodynamics. It is demonstrated that these diffusive corrections to the number- and energy density of the photons are in fact higher-order terms that can (and should) be neglected in the diffusion approximation. Our approach eliminates these terms at the root of the expansion that yields the anisotropic terms in the phase-space density of particles and photons, the terms responsible for the photon viscosity.

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

NASA Astrophysics Data System (ADS)

Mortensen, Dag

1999-02-01

A finite-element method model for the time-dependent heat and fluid flows that develop during direct-chill (DC) semicontinuous casting of aluminium ingots is presented. Thermal convection and turbulence are included in the model formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The boundary conditions involve calculations of the air gap along the mold wall as well as the heat transfer to the falling water film with forced convection, nucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the casting, the ingot domain expands over the starting-block level. The numerical method applies a fractional-step method for the dynamic Navier-Stokes equations and the “streamline upwind Petrov-Galerkin” (SUPG) method for mixed diffusion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperature measurements in an AA1050 200×600 mm sheet ingot.

TEMPEST. Transient 3-D Thermal-Hydraulic

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eyler, L.L.

TEMPEST is a transient, three-dimensional, hydrothermal program that is designed to analyze a range of coupled fluid dynamic and heat transfer systems of particular interest to the Fast Breeder Reactor (FBR) thermal-hydraulic design community. The full three-dimensional, time-dependent equations of motion, continuity, and heat transport are solved for either laminar or turbulent fluid flow, including heat diffusion and generation in both solid and liquid materials. The equations governing mass, momentum, and energy conservation for incompressible flows and small density variations (Boussinesq approximation) are solved using finite-difference techniques. Analyses may be conducted in either cylindrical or Cartesian coordinate systems. Turbulence ismore » treated using a two-equation model. Two auxiliary plotting programs, SEQUEL and MANPLOT, for use with TEMPEST output are included. SEQUEL may be operated in batch or interactive mode; it generates data required for vector plots, contour plots of scalar quantities, line plots, grid and boundary plots, and time-history plots. MANPLOT reads the SEQUEL-generated data and creates the hardcopy plots. TEMPEST can be a valuable hydrothermal design analysis tool in areas outside the intended FBR thermal-hydraulic design community.« less

Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

Determination of heat transfer parameters by use of finite integral transform and experimental data for regular geometric shapes

NASA Astrophysics Data System (ADS)

Talaghat, Mohammad Reza; Jokar, Seyyed Mohammad

2017-12-01

This article offers a study on estimation of heat transfer parameters (coefficient and thermal diffusivity) using analytical solutions and experimental data for regular geometric shapes (such as infinite slab, infinite cylinder, and sphere). Analytical solutions have a broad use in experimentally determining these parameters. Here, the method of Finite Integral Transform (FIT) was used for solutions of governing differential equations. The temperature change at centerline location of regular shapes was recorded to determine both the thermal diffusivity and heat transfer coefficient. Aluminum and brass were used for testing. Experiments were performed for different conditions such as in a highly agitated water medium ( T = 52 °C) and in air medium ( T = 25 °C). Then, with the known slope of the temperature ratio vs. time curve and thickness of slab or radius of the cylindrical or spherical materials, thermal diffusivity value and heat transfer coefficient may be determined. According to the method presented in this study, the estimated of thermal diffusivity of aluminum and brass is 8.395 × 10-5 and 3.42 × 10-5 for a slab, 8.367 × 10-5 and 3.41 × 10-5 for a cylindrical rod and 8.385 × 10-5 and 3.40 × 10-5 m2/s for a spherical shape, respectively. The results showed there is close agreement between the values estimated here and those already published in the literature. The TAAD% is 0.42 and 0.39 for thermal diffusivity of aluminum and brass, respectively.

Modelling thermal radiation in buoyant turbulent diffusion flames

NASA Astrophysics Data System (ADS)

Consalvi, J. L.; Demarco, R.; Fuentes, A.

2012-10-01

This work focuses on the numerical modelling of radiative heat transfer in laboratory-scale buoyant turbulent diffusion flames. Spectral gas and soot radiation is modelled by using the Full-Spectrum Correlated-k (FSCK) method. Turbulence-Radiation Interactions (TRI) are taken into account by considering the Optically-Thin Fluctuation Approximation (OTFA), the resulting time-averaged Radiative Transfer Equation (RTE) being solved by the Finite Volume Method (FVM). Emission TRIs and the mean absorption coefficient are then closed by using a presumed probability density function (pdf) of the mixture fraction. The mean gas flow field is modelled by the Favre-averaged Navier-Stokes (FANS) equation set closed by a buoyancy-modified k-ɛ model with algebraic stress/flux models (ASM/AFM), the Steady Laminar Flamelet (SLF) model coupled with a presumed pdf approach to account for Turbulence-Chemistry Interactions, and an acetylene-based semi-empirical two-equation soot model. Two sets of experimental pool fire data are used for validation: propane pool fires 0.3 m in diameter with Heat Release Rates (HRR) of 15, 22 and 37 kW and methane pool fires 0.38 m in diameter with HRRs of 34 and 176 kW. Predicted flame structures, radiant fractions, and radiative heat fluxes on surrounding surfaces are found in satisfactory agreement with available experimental data across all the flames. In addition further computations indicate that, for the present flames, the gray approximation can be applied for soot with a minor influence on the results, resulting in a substantial gain in Computer Processing Unit (CPU) time when the FSCK is used to treat gas radiation.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Chaotic Motion of Relativistic Electrons Driven by Whistler Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Telnikhin, A. A.; Kronberg, Tatiana K.

2007-01-01

Canonical equations governing an electron motion in electromagnetic field of the whistler mode waves propagating along the direction of an ambient magnetic field are derived. The physical processes on which the equations of motion are based .are identified. It is shown that relativistic electrons interacting with these fields demonstrate chaotic motion, which is accompanied by the particle stochastic heating and significant pitch angle diffusion. Evolution of distribution functions is described by the Fokker-Planck-Kolmogorov equations. It is shown that the whistler mode waves could provide a viable mechanism for stochastic energization of electrons with energies up to 50 MeV in the Jovian magnetosphere.

Estimation of the Thermal Process in the Honeycomb Panel by a Monte Carlo Method

NASA Astrophysics Data System (ADS)

Gusev, S. A.; Nikolaev, V. N.

2018-01-01

A new Monte Carlo method for estimating the thermal state of the heat insulation containing honeycomb panels is proposed in the paper. The heat transfer in the honeycomb panel is described by a boundary value problem for a parabolic equation with discontinuous diffusion coefficient and boundary conditions of the third kind. To obtain an approximate solution, it is proposed to use the smoothing of the diffusion coefficient. After that, the obtained problem is solved on the basis of the probability representation. The probability representation is the expectation of the functional of the diffusion process corresponding to the boundary value problem. The process of solving the problem is reduced to numerical statistical modelling of a large number of trajectories of the diffusion process corresponding to the parabolic problem. It was used earlier the Euler method for this object, but that requires a large computational effort. In this paper the method is modified by using combination of the Euler and the random walk on moving spheres methods. The new approach allows us to significantly reduce the computation costs.

Bioheat model evaluations of laser effects on tissues: role of water evaporation and diffusion

NASA Astrophysics Data System (ADS)

Nagulapally, Deepthi; Joshi, Ravi P.; Thomas, Robert J.

2011-03-01

A two-dimensional, time-dependent bioheat model is applied to evaluate changes in temperature and water content in tissues subjected to laser irradiation. Our approach takes account of liquid-to-vapor phase changes and a simple diffusive flow of water within the biotissue. An energy balance equation considers blood perfusion, metabolic heat generation, laser absorption, and water evaporation. The model also accounts for the water dependence of tissue properties (both thermal and optical), and variations in blood perfusion rates based on local tissue injury. Our calculations show that water diffusion would reduce the local temperature increases and hot spots in comparison to simple models that ignore the role of water in the overall thermal and mass transport. Also, the reduced suppression of perfusion rates due to tissue heating and damage with water diffusion affect the necrotic depth. Two-dimensional results for the dynamic temperature, water content, and damage distributions will be presented for skin simulations. It is argued that reduction in temperature gradients due to water diffusion would mitigate local refractive index variations, and hence influence the phenomenon of thermal lensing. Finally, simple quantitative evaluations of pressure increases within the tissue due to laser absorption are presented.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis ismore » on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.« less

SEAWAT Version 4: A Computer Program for Simulation of Multi-Species Solute and Heat Transport

USGS Publications Warehouse

Langevin, Christian D.; Thorne, Daniel T.; Dausman, Alyssa M.; Sukop, Michael C.; Guo, Weixing

2008-01-01

The SEAWAT program is a coupled version of MODFLOW and MT3DMS designed to simulate three-dimensional, variable-density, saturated ground-water flow. Flexible equations were added to the program to allow fluid density to be calculated as a function of one or more MT3DMS species. Fluid density may also be calculated as a function of fluid pressure. The effect of fluid viscosity variations on ground-water flow was included as an option. Fluid viscosity can be calculated as a function of one or more MT3DMS species, and the program includes additional functions for representing the dependence on temperature. Although MT3DMS and SEAWAT are not explicitly designed to simulate heat transport, temperature can be simulated as one of the species by entering appropriate transport coefficients. For example, the process of heat conduction is mathematically analogous to Fickian diffusion. Heat conduction can be represented in SEAWAT by assigning a thermal diffusivity for the temperature species (instead of a molecular diffusion coefficient for a solute species). Heat exchange with the solid matrix can be treated in a similar manner by using the mathematically equivalent process of solute sorption. By combining flexible equations for fluid density and viscosity with multi-species transport, SEAWAT Version 4 represents variable-density ground-water flow coupled with multi-species solute and heat transport. SEAWAT Version 4 is based on MODFLOW-2000 and MT3DMS and retains all of the functionality of SEAWAT-2000. SEAWAT Version 4 also supports new simulation options for coupling flow and transport, and for representing constant-head boundaries. In previous versions of SEAWAT, the flow equation was solved for every transport timestep, regardless of whether or not there was a large change in fluid density. A new option was implemented in SEAWAT Version 4 that allows users to control how often the flow field is updated. New options were also implemented for representing constant-head boundaries with the Time-Variant Constant-Head (CHD) Package. These options allow for increased flexibility when using CHD flow boundaries with the zero-dispersive flux solute boundaries implemented by MT3DMS at constant-head cells. This report contains revised input instructions for the MT3DMS Dispersion (DSP) Package, Variable-Density Flow (VDF) Package, Viscosity (VSC) Package, and CHD Package. The report concludes with seven cases of an example problem designed to highlight many of the new features.

The Stressing Effect of Electromigration from the Maxwell Stress and a Preliminary Mean-Time-to-Failure Analysis

NASA Astrophysics Data System (ADS)

Zhou, Peng

2013-06-01

As temperature increases, it is suggested that atoms on lattice sites serve as dynamic defects and cause a much more homogeneous distribution of the Maxwell stress throughout the crystal lattice compared with that caused by static defects. Though this stressing effect mostly leads to Joule heating, it also results in distortion of the crystal lattice, which leads to a decrease in the activation energy for atomic diffusion and causes enhancements in the phase growth rates at both interfaces of diffusion couples. Due to this stressing effect, the decrease in the activation energy is proportional to a square term of the current density J. A mean-time-to-failure analysis is performed for failure caused by excessive growth of intermediate phases, and a mean-time-to-failure (MTTF) equation is found. This equation appears similar to Black's equation but with an extra exponential term arising from the stressing effect of the crystal lattice.

An analysis of the flow field near the fuel injection location in a gas core reactor.

NASA Technical Reports Server (NTRS)

Weinstein, H.; Murty, B. G. K.; Porter, R. W.

1971-01-01

An analytical study is presented which shows the effects of large energy release and the concurrent high acceleration of inner stream fluid on the coaxial flow field in a gas core reactor. The governing equations include the assumptions of only radial radiative transport of energy represented as an energy diffusion term in the Euler equations. The method of integral relations is used to obtain the numerical solution. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.

Heat generation in aircraft tires

NASA Technical Reports Server (NTRS)

Clark, S. K.; Dodge, R. N.

1985-01-01

A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.

Heat generation in aircraft tires

NASA Technical Reports Server (NTRS)

Clark, S. K.

1983-01-01

A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.

Turbulent circulation above the surface heat source in a stably stratified environment

NASA Astrophysics Data System (ADS)

Kurbatskii, A. F.; Kurbatskaya, L. I.

2016-09-01

The results of the numerical modeling of turbulent structure of the penetrating convection above the urban heat island with a small aspect ratio in a stably stratified medium at rest are presented. The gradient diffusion representations for turbulent momentum and heat fluxes are used, which depend on three parameters — the turbulence kinetic energy, the velocity of its spectral expenditure, and the dispersion of temperature fluctuations. These parameters are found from the closed differential equations of balance in the RANS approach of turbulence description. The distributions of averaged velocity and temperature fields as well as turbulent characteristics agree well with measurement data.

TEMPEST: A three-dimensional time-dependent computer program for hydrothermal analysis: Volume 1, Numerical methods and input instructions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Trent, D.S.; Eyler, L.L.; Budden, M.J.

This document describes the numerical methods, current capabilities, and the use of the TEMPEST (Version L, MOD 2) computer program. TEMPEST is a transient, three-dimensional, hydrothermal computer program that is designed to analyze a broad range of coupled fluid dynamic and heat transfer systems of particular interest to the Fast Breeder Reactor thermal-hydraulic design community. The full three-dimensional, time-dependent equations of motion, continuity, and heat transport are solved for either laminar or turbulent fluid flow, including heat diffusion and generation in both solid and liquid materials. 10 refs., 22 figs., 2 tabs.

Moisture contamination and welding parameter effects on flux cored arc welding diffusible hydrogen

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kiefer, J.J.

1994-12-31

Gas metal arc (GMAW) and flux cored arc (FCAW) welding are gas shielded semiautomatic processes widely used for achieving high productivity in steel fabrication. Contamination of the shielding has can occur due to poorly maintained gas distribution systems. Moisture entering as a gas contaminant is a source of hydrogen that can cause delayed cold cracking in welds. Limiting heat-affected zone hardness is one method of controlling cracking. Even this is based on some assumptions about the hydrogen levels in the weld. A study was conducted to investigate the effect of shielding gas moisture contamination and welding parameters on the diffusiblemore » hydrogen content of gas shielded flux cored arc welding. The total wire hydrogen of various electrodes was also tested and compared to the diffusible weld hydrogen. An empirical equation has been developed that estimates the diffusible hydrogen in weld metal for gas shielded flux cored arc welding. The equation is suitable for small diameter electrodes and welding parameter ranges commonly used for out-of-position welding. by combining this with the results from the total wire hydrogen tests, it is possible to estimate diffusible hydrogen directly from measured welding parameters, shielding gas dew point, and total hydrogen of the consumable. These equations are also useful for evaluating the effect of welding procedure variations from known baseline conditions.« less

Using hybrid implicit Monte Carlo diffusion to simulate gray radiation hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cleveland, Mathew A., E-mail: cleveland7@llnl.gov; Gentile, Nick

This work describes how to couple a hybrid Implicit Monte Carlo Diffusion (HIMCD) method with a Lagrangian hydrodynamics code to evaluate the coupled radiation hydrodynamics equations. This HIMCD method dynamically applies Implicit Monte Carlo Diffusion (IMD) [1] to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) [2] to regions where the diffusion approximation is invalid. We show that this method significantly improves the computational efficiency as compared to a standard IMC/Hydrodynamics solver, when optically thick diffusive material is present, while maintaining accuracy. Two test cases are used to demonstrate the accuracy andmore » performance of HIMCD as compared to IMC and IMD. The first is the Lowrie semi-analytic diffusive shock [3]. The second is a simple test case where the source radiation streams through optically thin material and heats a thick diffusive region of material causing it to rapidly expand. We found that HIMCD proves to be accurate, robust, and computationally efficient for these test problems.« less

Model of convection mass transfer in titanium alloy at low energy high current electron beam action

NASA Astrophysics Data System (ADS)

Sarychev, V. D.; Granovskii, A. Yu; Nevskii, S. A.; Konovalov, S. V.; Gromov, V. E.

2017-01-01

The convection mixing model is proposed for low-energy high-current electron beam treatment of titanium alloys, pre-processed by heterogeneous plasma flows generated via explosion of carbon tape and powder TiB2. The model is based on the assumption vortices in the molten layer are formed due to the treatment by concentrated energy flows. These vortices evolve as the result of thermocapillary convection, arising because of the temperature gradient. The calculation of temperature gradient and penetration depth required solution of the heat problem with taking into account the surface evaporation. However, instead of the direct heat source the boundary conditions in phase transitions were changed in the thermal conductivity equation, assuming the evaporated material takes part in the heat exchange. The data on the penetration depth and temperature distribution are used for the thermocapillary model. The thermocapillary model embraces Navier-Stocks and convection heat transfer equations, as well as the boundary conditions with the outflow of evaporated material included. The solution of these equations by finite elements methods pointed at formation of a multi-vortices structure when electron-beam treatment and its expansion over new zones of material. As the result, strengthening particles are found at the depth exceeding manifold their penetration depth in terms of the diffusion mechanism.

Comparison of the Radiative Two-Flux and Diffusion Approximations

NASA Technical Reports Server (NTRS)

Spuckler, Charles M.

2006-01-01

Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and radiation scattered back by internal scattering sites while the Fresnel reflection only accounts for surface reflections.

Coupled thermo-chemical boundary conditions in double-diffusive geodynamo models at arbitrary Lewis numbers.

NASA Astrophysics Data System (ADS)

Bouffard, M.

2016-12-01

Convection in the Earth's outer core is driven by the combination of two buoyancy sources: a thermal source directly related to the Earth's secular cooling, the release of latent heat and possibly the heat generated by radioactive decay, and a compositional source due to the crystallization of the growing inner core which releases light elements into the liquid outer core. The dynamics of fusion/crystallization being dependent on the heat flux distribution, the thermochemical boundary conditions are coupled at the inner core boundary which may affect the dynamo in various ways, particularly if heterogeneous conditions are imposed at one boundary. In addition, the thermal and compositional molecular diffusivities differ by three orders of magnitude. This can produce significant differences in the convective dynamics compared to pure thermal or compositional convection due to the potential occurence of double-diffusive phenomena. Traditionally, temperature and composition have been combined into one single variable called codensity under the assumption that turbulence mixes all physical properties at an "eddy-diffusion" rate. This description does not allow for a proper treatment of the thermochemical coupling and is certainly incorrect within stratified layers in which double-diffusive phenomena can be expected. For a more general and rigorous approach, two distinct transport equations should therefore be solved for temperature and composition. However, the weak compositional diffusivity is technically difficult to handle in current geodynamo codes and requires the use of a semi-Lagrangian description to minimize numerical diffusion. We implemented a "particle-in-cell" method into a geodynamo code to properly describe the compositional field. The code is suitable for High Parallel Computing architectures and was successfully tested on two benchmarks. Following the work by Aubert et al. (2008) we use this new tool to perform dynamo simulations including thermochemical coupling at the inner core boundary as well as exploration of the infinite Lewis number limit to study the effect of a heterogeneous core mantle boundary heat flow on the inner core growth.

Lattice Boltzmann heat transfer model for permeable voxels

NASA Astrophysics Data System (ADS)

Pereira, Gerald G.; Wu, Bisheng; Ahmed, Shakil

2017-12-01

We develop a gray-scale lattice Boltzmann (LB) model to study fluid flow combined with heat transfer for flow through porous media where voxels may be partially solid (or void). Heat transfer in rocks may lead to deformation, which in turn can modulate the fluid flow and so has significant contribution to rock permeability. The LB temperature field is compared to a finite difference solution of the continuum partial differential equations for fluid flow in a channel. Excellent quantitative agreement is found for both Poiseuille channel flow and Brinkman flow. The LB model is then applied to sample porous media such as packed beds and also more realistic sandstone rock sample, and both the convective and diffusive regimes are recovered when varying the thermal diffusivity. It is found that while the rock permeability can be comparatively small (order milli-Darcy), the temperature field can show significant variation depending on the thermal convection of the fluid. This LB method has significant advantages over other numerical methods such as finite and boundary element methods in dealing with coupled fluid flow and heat transfer in rocks which have irregular and nonsmooth pore spaces.

The one-dimensional asymmetric persistent random walk

NASA Astrophysics Data System (ADS)

Rossetto, Vincent

2018-04-01

Persistent random walks are intermediate transport processes between a uniform rectilinear motion and a Brownian motion. They are formed by successive steps of random finite lengths and directions travelled at a fixed speed. The isotropic and symmetric 1D persistent random walk is governed by the telegrapher’s equation, also called the hyperbolic heat conduction equation. These equations have been designed to resolve the paradox of the infinite speed in the heat and diffusion equations. The finiteness of both the speed and the correlation length leads to several classes of random walks: Persistent random walk in one dimension can display anomalies that cannot arise for Brownian motion such as anisotropy and asymmetries. In this work we focus on the case where the mean free path is anisotropic, the only anomaly leading to a physics that is different from the telegrapher’s case. We derive exact expression of its Green’s function, for its scattering statistics and distribution of first-passage time at the origin. The phenomenology of the latter shows a transition for quantities like the escape probability and the residence time.

Diffuse charge dynamics in ionic thermoelectrochemical systems.

PubMed

Stout, Robert F; Khair, Aditya S

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1/Dκ^{2}, where D is the Brownian diffusion coefficient of both ion species, and κ^{-1} is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L^{2}/D, where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

Diffuse charge dynamics in ionic thermoelectrochemical systems

NASA Astrophysics Data System (ADS)

Stout, Robert F.; Khair, Aditya S.

2017-08-01

Thermoelectrics are increasingly being studied as promising electrical generators in the ongoing search for alternative energy sources. In particular, recent experimental work has examined thermoelectric materials containing ionic charge carriers; however, the majority of mathematical modeling has been focused on their steady-state behavior. Here, we determine the time scales over which the diffuse charge dynamics in ionic thermoelectrochemical systems occur by analyzing the simplest model thermoelectric cell: a binary electrolyte between two parallel, blocking electrodes. We consider the application of a temperature gradient across the device while the electrodes remain electrically isolated from each other. This results in a net voltage, called the thermovoltage, via the Seebeck effect. At the same time, the Soret effect results in migration of the ions toward the cold electrode. The charge dynamics are described mathematically by the Poisson-Nernst-Planck equations for dilute solutions, in which the ion flux is driven by electromigration, Brownian diffusion, and thermal diffusion under a temperature gradient. The temperature evolves according to the heat equation. This nonlinear set of equations is linearized in the (experimentally relevant) limit of a "weak" temperature gradient. From this, we show that the time scale on which the thermovoltage develops is the Debye time, 1 /D κ2 , where D is the Brownian diffusion coefficient of both ion species, and κ-1 is the Debye length. However, the concentration gradient due to the Soret effect develops on the bulk diffusion time, L2/D , where L is the distance between the electrodes. For thin diffuse layers, which is the condition under which most real devices operate, the Debye time is orders of magnitude less than the diffusion time. Therefore, rather surprisingly, the majority of ion motion occurs after the steady thermovoltage has developed. Moreover, the dynamics are independent of the thermal diffusion coefficients, which simply set the magnitude of the steady-state thermovoltage.

Reconstructing thermal properties of firn at Summit, Greenland from a temperature profile

NASA Astrophysics Data System (ADS)

Giese, A. L.; Hawley, R. L.

2013-12-01

Thermodynamic properties of firn are important factors when considering energy balance and temperature-dependent physical processes in the near-surface of glaciers. Of particular interest is thermal diffusivity, which can take a range of values and which governs both the temperature gradient and its evolution through time. Given that temperature is a well-established driver of firn densification, a better understanding of heat transfer will permit greater accuracy in the compaction models essential for interpreting inter-annual and seasonal ice surface elevation changes detected by airborne and satellite altimetry. Due to its dependence on microstructure, diffusivity can vary significantly by location. Rather than directly measuring diffusivity or one of its proxies (e.g. density, hardness, shear strength), this study inverts the heat equation to reconstruct diffusivity values. This is a less logistically-intensive approach which circumvents many of the challenges associated with imperfect proxies and snow metamorphism during measurement. Hourly records (May 2004 - July 2008) from 8 thermistors placed in the top 10 m at Summit, Greenland provide temperature values for Summit's firn, which is broadly representative of firn across the ice sheet's dry snow zone. In this study, we use both physical analysis and a finite-difference numerical model to determine a diffusivity magnitude and gradient; we find that diffusivity of Summit firn falls in the lower end of the range expected from local density and temperature conditions alone (i.e. 15 - 36 m^2/a for firn at -30C). Further, we assess the utility of our modeling approach, explore the validity of assuming bulk conductive heat transfer when modeling temperature changes in non-homogeneous firn, and investigate the implications of a low-end diffusivity value for surface compaction modeling in Greenland.

Heat transfer to and from vegetated surfaces - An analytical method for the bulk exchange coefficients

NASA Technical Reports Server (NTRS)

Massman, William J.

1987-01-01

The semianalytical model outlined in a previous study (Massman, 1987) to describe momentum exchange between the atmosphere and vegetated surfaces is extended to include the exchange of heat. The methods employed are based on one-dimensional turbulent diffusivities, and use analytical solutions to the steady-state diffusion equation. The model is used to assess the influence that the canopy foliage structure and density, the wind profile structure within the canopy, and the shelter factor can have upon the inverse surface Stanton number (kB exp -1), as well as to explore the consequences of introducing a scalar displacement height which can be different from the momentum displacement height. In general, the triangular foliage area density function gives results which agree more closely with observations than that for constant foliage area density. The intended application of this work is for parameterizing the bulk aerodynamic resistances for heat and momentum exchange for use within large-scale models of plant-atmosphere exchanges.

From the Highly Compressible Navier-Stokes Equations to Fast Diffusion and Porous Media Equations, Existence of Global Weak Solution for the Quasi-Solutions

NASA Astrophysics Data System (ADS)

Haspot, Boris

2016-06-01

We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.

Study of heat and mass transfer of water evaporation in a gypsum board subjected to natural convection

NASA Astrophysics Data System (ADS)

Zannouni, K.; El Abrach, H.; Dhahri, H.; Mhimid, A.

2017-06-01

The present paper reports a numerical study to investigate the drying of rectangular gypsum sample based on a diffusive model. Both vertical and low sides of the porous media are treated as adiabatic and impermeable surfaces plate. The upper face of the plate represents the permeable interface. The energy equation model is based on the local thermal equilibrium assumption between the fluid and the solid phases. The lattice Boltzmann method (LBM) is used for solving the governing differential equations system. The obtained numerical results concerning the moisture content and the temperature within a gypsum sample were discussed. A comprehensive analysis of the influence of the mass transfer coefficient, the convective heat transfer coefficient, the external temperature, the relative humidity and the diffusion coefficient on macroscopic fields are also investigated. They all presented results in this paper and obtained in the stable regime correspond to time superior than 4000 s. Therefore the numerical error is inferior to 2%. The experimental data and the descriptive information of the approach indicate an excellent agreement between the results of our developed numerical code based on the LBM and the published ones.

Chlorine dioxide-induced and Congo red-inhibited Marangoni effect on the chlorite-trithionate reaction front

NASA Astrophysics Data System (ADS)

Liu, Yang; Ren, Xingfeng; Pan, Changwei; Zheng, Ting; Yuan, Ling; Zheng, Juhua; Gao, Qingyu

2017-10-01

Hydrodynamic flows can exert multiple effects on an exothermal autocatalytic reaction, such as buoyancy and the Marangoni convection, which can change the structure and velocity of chemical waves. Here we report that in the chlorite-trithionate reaction, the production and consumption of chlorine dioxide can induce and inhibit Marangoni flow, respectively, leading to different chemo-hydrodynamic patterns. The horizontal propagation of a reaction-diffusion-convection front was investigated with the upper surface open to the air. The Marangoni convection, induced by gaseous chlorine dioxide on the surface, produced from chlorite disproportionation after the proton autocatalysis, has the same effect as the heat convection. When the Marangoni effect is removed by the reaction of chlorine dioxide with the Congo red (CR) indicator, an oscillatory propagation of the front tip is observed under suitable conditions. Replacing CR with bromophenol blue (BPB) distinctly enhanced the floating, resulting in multiple vortexes, owing to the coexistence between BPB and chlorine dioxide. Using the incompressible Navier-Stokes equations coupled with reaction-diffusion and heat conduction equations, we numerically obtain various experimental scenarios of front instability for the exothermic autocatalytic reaction coupled with buoyancy-driven convection and Marangoni convection.

Analytic Couple Modeling Introducing Device Design Factor, Fin Factor, Thermal Diffusivity Factor, and Inductance Factor

NASA Technical Reports Server (NTRS)

Mackey, Jon; Sehirlioglu, Alp; Dynys, Fred

2014-01-01

A set of convenient thermoelectric device solutions have been derived in order to capture a number of factors which are previously only resolved with numerical techniques. The concise conversion efficiency equations derived from governing equations provide intuitive and straight-forward design guidelines. These guidelines allow for better device design without requiring detailed numerical modeling. The analytical modeling accounts for factors such as i) variable temperature boundary conditions, ii) lateral heat transfer, iii) temperature variable material properties, and iv) transient operation. New dimensionless parameters, similar to the figure of merit, are introduced including the device design factor, fin factor, thermal diffusivity factor, and inductance factor. These new device factors allow for the straight-forward description of phenomenon generally only captured with numerical work otherwise. As an example a device design factor of 0.38, which accounts for thermal resistance of the hot and cold shoes, can be used to calculate a conversion efficiency of 2.28 while the ideal conversion efficiency based on figure of merit alone would be 6.15. Likewise an ideal couple with efficiency of 6.15 will be reduced to 5.33 when lateral heat is accounted for with a fin factor of 1.0.

Experimental thermal conductivity, thermal diffusivity, and specific heat values for mixtures of nitrogen, oxygen, and argon

NASA Technical Reports Server (NTRS)

Perkins, R. A.; Cieszkiewicz, M. T.

1991-01-01

Experimental measurements of thermal conductivity and thermal diffusivity obtained with a transient hot-wire apparatus are reported for three mixtures of nitrogen, oxygen, and argon. Values of the specific heat, Cp, are calculated from these measured values and the density calculated with an equation of state. The measurements were made at temperatures between 65 and 303 K with pressures between 0.1 and 70 MPa. The data cover the vapor, liquid, and supercritical gas phases for the three mixtures. The total reported points are 1066 for the air mixture (78.11 percent nitrogen, 20.97 percent oxygen, and 0.92 percent argon), 1058 for the 50 percent nitrogen, 50 percent oxygen mixture, and 864 for the 25 percent nitrogen, 75 oxygen mixture. Empirical thermal conductivity correlations are provided for the three mixtures.

Double diffusive magnetohydrodynamic (MHD) mixed convective slip flow along a radiating moving vertical flat plate with convective boundary condition.

PubMed

Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid

2014-01-01

In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

NASA Technical Reports Server (NTRS)

Siegel, Robert

1996-01-01

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Recent advances in computational-analytical integral transforms for convection-diffusion problems

NASA Astrophysics Data System (ADS)

Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.; Almeida, A. P.

2017-10-01

An unifying overview of the Generalized Integral Transform Technique (GITT) as a computational-analytical approach for solving convection-diffusion problems is presented. This work is aimed at bringing together some of the most recent developments on both accuracy and convergence improvements on this well-established hybrid numerical-analytical methodology for partial differential equations. Special emphasis is given to novel algorithm implementations, all directly connected to enhancing the eigenfunction expansion basis, such as a single domain reformulation strategy for handling complex geometries, an integral balance scheme in dealing with multiscale problems, the adoption of convective eigenvalue problems in formulations with significant convection effects, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Then, selected examples are presented that illustrate the improvement achieved in each class of extension, in terms of convergence acceleration and accuracy gain, which are related to conjugated heat transfer in complex or multiscale microchannel-substrate geometries, multidimensional Burgers equation model, and diffusive metal extraction through polymeric hollow fiber membranes. Numerical results are reported for each application and, where appropriate, critically compared against the traditional GITT scheme without convergence enhancement schemes and commercial or dedicated purely numerical approaches.

Quantum diffusion during inflation and primordial black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pattison, Chris; Assadullahi, Hooshyar; Wands, David

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. Inmore » the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ∼ 1 e -fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.« less

Quantum diffusion during inflation and primordial black holes

NASA Astrophysics Data System (ADS)

Pattison, Chris; Vennin, Vincent; Assadullahi, Hooshyar; Wands, David

2017-10-01

We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-δ N formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than ~ 1 e-fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

Diffuse-interface model for rapid phase transformations in nonequilibrium systems.

PubMed

Galenko, Peter; Jou, David

2005-04-01

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

Steady-state heat transport: Ballistic-to-diffusive with Fourier's law

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maassen, Jesse, E-mail: jmaassen@purdue.edu; Lundstrom, Mark

2015-01-21

It is generally understood that Fourier's law does not describe ballistic phonon transport, which is important when the length of a material is similar to the phonon mean-free-path. Using an approach adapted from electron transport, we demonstrate that Fourier's law and the heat equation do capture ballistic effects, including temperature jumps at ideal contacts, and are thus applicable on all length scales. Local thermal equilibrium is not assumed, because allowing the phonon distribution to be out-of-equilibrium is important for ballistic and quasi-ballistic transport. The key to including the non-equilibrium nature of the phonon population is to apply the proper boundarymore » conditions to the heat equation. Simple analytical solutions are derived, showing that (i) the magnitude of the temperature jumps is simply related to the material properties and (ii) the observation of reduced apparent thermal conductivity physically stems from a reduction in the temperature gradient and not from a reduction in actual thermal conductivity. We demonstrate how our approach, equivalent to Fourier's law, easily reproduces results of the Boltzmann transport equation, in all transport regimes, even when using a full phonon dispersion and mean-free-path distribution.« less

Diffusion for holographic lattices

NASA Astrophysics Data System (ADS)

Donos, Aristomenis; Gauntlett, Jerome P.; Ziogas, Vaios

2018-03-01

We consider black hole spacetimes that are holographically dual to strongly coupled field theories in which spatial translations are broken explicitly. We discuss how the quasinormal modes associated with diffusion of heat and charge can be systematically constructed in a long wavelength perturbative expansion. We show that the dispersion relation for these modes is given in terms of the thermoelectric DC conductivity and static susceptibilities of the dual field theory and thus we derive a generalised Einstein relation from Einstein's equations. A corollary of our results is that thermodynamic instabilities imply specific types of dynamical instabilities of the associated black hole solutions.

Evolution of Edge Pedestal Profiles Over the L-H Transition

NASA Astrophysics Data System (ADS)

Sayer, M. S.; Stacey, W. M.; Floyd, J. P.; Groebner, R. J.

2012-10-01

The detailed time evolution of thermal diffusivities, electromagnetic forces, pressure gradients, particle pinch and momentum transport frequencies (which determine the diffusion coefficient) have been analyzed during the L-H transition in a DIII-D discharge. Density, temperature, rotation velocity and electric field profiles at times just before and after the L-H transition are analyzed in terms of these quantities. The analysis is based on the fluid particle balance, energy balance, force balance and heat conduction equations, as in Ref. [1], but with much greater time resolution and with account for thermal ion orbit loss. The variation of diffusive and non-diffusive transport over the L-H transition is determined from the variation in the radial force balance (radial electric field, VxB force, and pressure gradient) and the variation in the interpreted diffusive transport coefficients. 6pt [1] W.M. Stacey and R.J. Groebner, Phys. Plasmas 17, 112512 (2010).

Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain

DOE PAGES

Hua, Chengyun; Minnich, Austin J.

2018-01-10

Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fourier's law; however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean-free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistancemore » rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We further demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.« less

Heat dissipation in the quasiballistic regime studied using the Boltzmann equation in the spatial frequency domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hua, Chengyun; Minnich, Austin J.

Quasiballistic heat conduction, in which some phonons propagate ballistically over a thermal gradient, has recently become of intense interest. Most works report that the thermal resistance associated with nanoscale heat sources is far larger than predicted by Fourier's law; however, recent experiments show that in certain cases the difference is negligible despite the heaters being far smaller than phonon mean-free paths. In this work, we examine how thermal resistance depends on the heater geometry using analytical solutions of the Boltzmann equation. We show that the spatial frequencies of the heater pattern play the key role in setting the thermal resistancemore » rather than any single geometric parameter, and that for many geometries the thermal resistance in the quasiballistic regime is no different than the Fourier prediction. We further demonstrate that the spectral distribution of the heat source also plays a major role in the resulting transport, unlike in the diffusion regime. Our work provides an intuitive link between the heater geometry, spectral heating distribution, and the effective thermal resistance in the quasiballistic regime, a finding that could impact strategies for thermal management in electronics and other applications.« less

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Determination of drying kinetics and convective heat transfer coefficients of ginger slices

NASA Astrophysics Data System (ADS)

Akpinar, Ebru Kavak; Toraman, Seda

2016-10-01

In the present work, the effects of some parametric values on convective heat transfer coefficients and the thin layer drying process of ginger slices were investigated. Drying was done in the laboratory by using cyclone type convective dryer. The drying air temperature was varied as 40, 50, 60 and 70 °C and the air velocity is 0.8, 1.5 and 3 m/s. All drying experiments had only falling rate period. The drying data were fitted to the twelve mathematical models and performance of these models was investigated by comparing the determination of coefficient ( R 2), reduced Chi-square ( χ 2) and root mean square error between the observed and predicted moisture ratios. The effective moisture diffusivity and activation energy were calculated using an infinite series solution of Fick's diffusion equation. The average effective moisture diffusivity values and activation energy values varied from 2.807 × 10-10 to 6.977 × 10-10 m2/s and 19.313-22.722 kJ/mol over the drying air temperature and velocity range, respectively. Experimental data was used to evaluate the values of constants in Nusselt number expression by using linear regression analysis and consequently, convective heat transfer coefficients were determined in forced convection mode. Convective heat transfer coefficient of ginger slices showed changes in ranges 0.33-2.11 W/m2 °C.

Diffusion of phonons through (along and across) the ultrathin crystalline films

NASA Astrophysics Data System (ADS)

Šetrajčić, J. P.; Jaćimovski, S. K.; Vučenović, S. M.

2017-11-01

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film-structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is-that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

Ocean Turbulence, III: New GISS Vertical Mixing Scheme

NASA Technical Reports Server (NTRS)

Canuto, V. M.; Howard, A. M.; Cheng, Y.; Muller, C. J.; Leboissetier, A.; Jayne, S. R.

2010-01-01

We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma-alpha (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation Epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma-alpha s are functions of both Ri and Rq (Richardson number and density ratio representing double diffusion, DD); the Gamma-alpha are different for heat, salt and momentum; in the case of heat, the traditional value Gamma-h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Gamma-h can be three times as large, a result that we reproduce. The salt Gamma-s is given in terms of Gamma-h. The momentum Gamma-m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma-m(Ri,R-rho). Having tested Gamma-h, we then test the momentum Gamma-m by showing that the turbulent Prandtl number Gamma-m/Gamma-h vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean;s bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon/N(exp 2) from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma-alpha = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma-alpha; the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma-h(Ri,Rq). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon (Ri < 1) approximately equals 10epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri much greater than 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve.

A comparison of critical heat flux in tubes and bilaterally heated annuli

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doerffer, S.; Groeneveld, D.C.; Cheng, S.C.

1995-09-01

This paper examines the critical heat flux (CHF) behaviour for annular flow in bilaterally heated annuli and compares it to that in tubes and unilaterally heated annuli. It was found that the differences in CHF between bilaterally and unilaterally heated annuli or tubes strongly depend on pressure and quality. the CHF in bilaterally heated annuli can be predicted by tube CHF prediction methods for the simultaneous CHF occurrence at both surfaces, and the following flow conditions: pressure 7-10 MPa, mass flux 0.5-4.0 Mg/m{sup 2}s and critical quality 0.23-0.9. The effect on CHF of the outer-to-inner surface heat flux ratio, wasmore » also examined. The prediction of CHF for bilaterally heated annuli was based on the droplet-diffusion model proposed by Kirillov and Smogalev. While their model refers only to CHF occurrence at the inner surface, we extended it to cases where CHF occurs at the outer surface, and simultaneously at both surfaces, thus covering all cases of CHF occurrence in bilaterally heated annuli. From the annuli CHF data of Becker and Letzter, we derived empirical functions required by the model. the proposed equations provide good accuracy for the CHF data used in this study. Moreover, the equations can predict conditions at which CHF occurs simultaneously at both surfaces. Also, this method can be used for cases with only one heated surface.« less

Transverse particle acceleration and diffusion in a planetary magnetic field

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1994-01-01

A general model of particle acceleration by plasma waves coupled with adiabatic radial diffusion in a planetary magnetic field is developed. The model assumes that a spectrum of lower hybird waves is present to resonantly accelerate ions transverse to the magnetic field. The steady state Green's function for the combined radial diffusion and wave acceleration equation is found in terms of a series expansion. The results provide a rigorous demonstration of how a quasi-Maxwellian distribution function is formed in the absence of particle collisons and elucidate the nature of turbulent heating of magnetospheric plasmas. The solution is applied to the magnetosphere of Neptune for which a number of examples are given illustrating how the spectrum of pickup N(+) ions from Triton evolves.

Heat generation in aircraft tires under free rolling conditions

NASA Technical Reports Server (NTRS)

Clark, S. K.; Dodge, R. N.

1982-01-01

A method was developed for calculating the internal temperature distribution in an aircraft tire while free rolling under load. The method uses an approximate stress analysis of each point in the tire as it rolls through the contact patch, and from this stress change the mechanical work done on each volume element may be obtained and converted into a heat release rate through a knowledge of material characteristics. The tire cross-section is then considered as a body with internal heat generation, and the diffusion equation is solved numerically with appropriate boundary conditions of the wheel and runway surface. Comparison with data obtained with buried thermocouples in tires shows good agreement.

Computations of the three-dimensional flow and heat transfer within a coolant passage of a radial turbine blade

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Roelke, R. J.; Steinthorsson, E.

1991-01-01

A numerical code is developed for computing three-dimensional, turbulent, compressible flow within coolant passages of turbine blades. The code is based on a formulation of the compressible Navier-Stokes equations in a rotating frame of reference in which the velocity dependent variable is specified with respect to the rotating frame instead of the inertial frame. The algorithm employed to obtain solutions to the governing equation is a finite-volume LU algorithm that allows convection, source, as well as diffusion terms to be treated implicitly. In this study, all convection terms are upwind differenced by using flux-vector splitting, and all diffusion terms are centrally differenced. This paper describes the formulation and algorithm employed in the code. Some computed solutions for the flow within a coolant passage of a radial turbine are also presented.

Magnon spin transport driven by the magnon chemical potential in a magnetic insulator

NASA Astrophysics Data System (ADS)

Cornelissen, L. J.; Peters, K. J. H.; Bauer, G. E. W.; Duine, R. A.; van Wees, B. J.

2016-07-01

We develop a linear-response transport theory of diffusive spin and heat transport by magnons in magnetic insulators with metallic contacts. The magnons are described by a position-dependent temperature and chemical potential that are governed by diffusion equations with characteristic relaxation lengths. Proceeding from a linearized Boltzmann equation, we derive expressions for length scales and transport coefficients. For yttrium iron garnet (YIG) at room temperature we find that long-range transport is dominated by the magnon chemical potential. We compare the model's results with recent experiments on YIG with Pt contacts [L. J. Cornelissen et al., Nat. Phys. 11, 1022 (2015), 10.1038/nphys3465] and extract a magnon spin conductivity of σm=5 ×105 S/m. Our results for the spin Seebeck coefficient in YIG agree with published experiments. We conclude that the magnon chemical potential is an essential ingredient for energy and spin transport in magnetic insulators.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Evolution and Growth Competition of Salt Fingers in Saline Lake with Slight Wind Shear

NASA Astrophysics Data System (ADS)

Yang, Ray-Yeng; Hwung, Hwung-Hweng; Shugan, Igor

2010-05-01

Since the discover of double-diffusive convection by Stommel, Arons & Blanchard (1956), 'evidence has accumulated for the widespread presence of double-diffusion throughout the ocean' and for its 'significant effects on global water-mass structure and the thermohaline convection' (Schmitt, 1998). The salt-fingering form of double-diffusion has particularly attracted interest because of salt-finger convection being now widely recognized as an important mechanism for mixing heat and salt both vertically and laterally in the ocean and saline lake. In oceanographic situations or saline lake where salt fingers may be an important mechanism for the transport of heat and salt in the vertical, velocity shears may also be present. Salt finger convection is analogous to Bénard convection in that the kinetic energy of the motions is obtained from the potential energy stored in the unstable distribution of a stratifying component. On the basis of the thermal analogy it is of interest to discover whether salt fingers are converted into two-dimensional sheets by the wind shear, and how the vertical fluxes of heat and salt are changed by the wind shear. Salt finger convection under the effect of steady wind shear is theoretically examined in this paper. The evolution of developing in the presence of a vertical density gradient disturbance and the horizontal Couette flow is considered near the onset of salt fingers in the saline lake under a moderate rate of wind shear. We use velocity as the basic variable and solve the pressure Poisson equation in terms of the associated Green function. Growth competition between the longitudinal rolls (LR) and the transverse rolls (TR), whose axes are respectively in the direction parallel to and perpendicular to the Couette flow, is investigated by the weakly nonlinear analysis of coupled-mode equations. The results show that the TR mode is characterized in some range of the effective Rayleigh number, and that the stability is dominated by the LR mode in the system. KEY WORDS: evolution, saline lake, salt finger convection, wind shear, growth competition, longitudinal rolls, transverse rolls, coupled-mode equations.

The significance of vertical moisture diffusion on drifting snow sublimation near snow surface

NASA Astrophysics Data System (ADS)

Huang, Ning; Shi, Guanglei

2017-12-01

Sublimation of blowing snow is an important parameter not only for the study of polar ice sheets and glaciers, but also for maintaining the ecology of arid and semi-arid lands. However, sublimation of near-surface blowing snow has often been ignored in previous studies. To study sublimation of near-surface blowing snow, we established a sublimation of blowing snow model containing both a vertical moisture diffusion equation and a heat balance equation. The results showed that although sublimation of near-surface blowing snow was strongly reduced by a negative feedback effect, due to vertical moisture diffusion, the relative humidity near the surface does not reach 100 %. Therefore, the sublimation of near-surface blowing snow does not stop. In addition, the sublimation rate near the surface is 3-4 orders of magnitude higher than that at 10 m above the surface and the mass of snow sublimation near the surface accounts for more than half of the total snow sublimation when the friction wind velocity is less than about 0.55 m s-1. Therefore, the sublimation of near-surface blowing snow should not be neglected.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.

PubMed

Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W

2009-03-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

A Diffusion Tensor Imaging Tractography Algorithm Based on Navier-Stokes Fluid Mechanics

PubMed Central

Hageman, Nathan S.; Toga, Arthur W.; Narr, Katherine; Shattuck, David W.

2009-01-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color (DEC) images of the DTI dataset. PMID:19244007

Modeling Vertical Structure and Heat Transport within the Oceans of Ice-covered Worlds (Invited)

NASA Astrophysics Data System (ADS)

Goodman, J. C.

2010-12-01

Indirect observational evidence provides a strong case for liquid oceans beneath the icy crust of Europa and several other frozen moons in the outer solar system. However, little is known about the fluid circulation within these exotic oceans. As a first step toward understanding circulations driven by buoyancy (rather than mechanical forcing from tides), one must understand the typical vertical structure of temperature, salinity, and thus density within the ocean. Following a common approach from terrestrial oceanography, I have built a "single column convection model" for icy world oceans, which describes the density structure of the ocean as a function of depth only: horizontal variations are ignored. On Earth, this approach is of limited utility, because of the strong influence of horizontal wind-driven currents and sea-surface temperature gradients set in concert with the overlying atmosphere. Neither of these confounding issues is present in an icy world's ocean. In the model, mixing of fluid properties via overturning convection is modeled as a strong diffusive process which only acts when the ocean is vertically unstable. "Double diffusive" processes (salt fingering and diffusive layering) are included: these are mixing processes resulting from the unequal molecular diffusivities of heat and salt. Other important processes, such as heating on adiabatic compression, and freshwater fluxes from melting overlying ice, are also included. As a simple test case, I considered an ocean of Europa-like depth (~100 km) and gravity, heated from the seafloor. To simplify matters, I specified an equation of state appropriate to terrestrial seawater, and a simple isothermal ocean as an initial condition. As expected, convection gradually penetrates upward, warming the ocean to an adiabatic, unstratified equilibrium density profile on a timescale of 50 kyr if 4.5 TW of heat are emitted by the silicate interior; the same result is achieved in proportionally more/less time for weaker/stronger internal heating. Unlike Earth's oceans, I predict that since icy worlds' oceans are heated from below, they will generally be unstratified, with constant potential density from top to bottom. There will be no pycnocline as on Earth, so global ocean currents supported by large-scale density gradients seem unlikely. However, icy world oceans may be "weird" in ways which are unheard-of in terrestrial oceanography The density of sulfate brine has a very different equation of state than chloride brines: does this affect the vertical structure? If the ocean water is very pure, cold water can be less dense than warm. Can this lead to periodic catastrophic overturning, as proposed by other authors? These and other questions are currently being investigated using the single-column convection model as a primary tool.

Analysis of forced convective modified Burgers liquid flow considering Cattaneo-Christov double diffusion

NASA Astrophysics Data System (ADS)

Waqas, M.; Hayat, T.; Shehzad, S. A.; Alsaedi, A.

2018-03-01

A mathematical model is formulated to characterize the non-Fourier and Fick's double diffusive models of heat and mass in moving flow of modified Burger's liquid. Temperature-dependent conductivity of liquid is taken into account. The concept of stratification is utilized to govern the equations of energy and mass species. The idea of boundary layer theory is employed to obtain the mathematical model of considered physical problem. The obtained partial differential system is converted into ordinary ones with the help of relevant variables. The homotopic concept lead to the convergent solutions of governing expressions. Convergence is attained and acceptable values are certified by expressing the so called ℏ -curves and numerical benchmark. Several graphs are made for different values of physical constraints to explore the mechanism of heat and mass transportation. We explored that the liquid temperature and concentration are retard for the larger thermal/concentration relaxation time constraint.

B2.5-Eirene modeling of radial transport in the MAGPIE linear plasma device

NASA Astrophysics Data System (ADS)

Owen, L. W.; Caneses, J. F.; Canik, J.; Lore, J. D.; Corr, C.; Blackwell, B.; Bonnin, X.; Rapp, J.

2017-05-01

Radial transport in helicon heated hydrogen plasmas in the MAGnetized Plasma Interaction Experiment (MAGPIE) is studied with the B2.5-Eirene (SOLPS5.0) code. Radial distributions of plasma density, temperature and ambipolar potential are computed for several magnetic field configurations and compared to double Langmuir probe measurements. Evidence for an unmagnetized ion population is seen in the requirement for a convective pinch term in the continuity equation in order to fit the centrally peaked density profile data. The measured slightly hollow electron temperature profiles are reproduced with combinations of on-axis and edge heating which can be interpreted as helicon and Trivelpiece-Gould wave absorption, respectively. Pressure gradient driven radial charged particle diffusion is chosen to describe the diffusive particle flux since the hollowness of the temperature profiles assists the establishment of on-axis density peaking.

Free-cooling: A total HVAC design concept

DOE Office of Scientific and Technical Information (OSTI.GOV)

Janeke, C.E.

1982-01-01

This paper discusses a total ''free cooling'' HVAC design concept in which mechanical refrigeration is practically obviated via the refined application of existing technological strategies and a new diffuser terminal. The principles being applied are as follows; Thermal Swing: This is the active contribution of programmed heat storage to overall HVAC system performance. Reverse Diffuser: This is a new air terminal design that facilitates manifesting the thermal storage gains. Developing the thermal storage equation system into a generalized simulation model, optimizing the thermal storage and operating strategies with a computer program and developing related algorithms are subsequently illustrated. Luminair Aspiration:more » This feature provides for exhausting all luminair heat totally out of the building envelope, via an exhaust duct system and insulated boots. Two/Three-Stage Evaporative Cooling: This concept comprises a system of air conditioning that entails a combination of closed and open loop evaporative cooling with standby refrigeration only.« less

Mixed convection of magnetohydrodynamic nanofluids inside microtubes at constant wall temperature

NASA Astrophysics Data System (ADS)

Moshizi, S. A.; Zamani, M.; Hosseini, S. J.; Malvandi, A.

2017-05-01

Laminar fully developed mixed convection of magnetohydrodynamic nanofluids inside microtubes at a constant wall temperature (CWT) under the effects of a variable directional magnetic field is investigated numerically. Nanoparticles are assumed to have slip velocities relative to the base fluid owing to thermophoretic diffusion (temperature gradient driven force) and Brownian diffusion (concentration gradient driven force). The no-slip boundary condition is avoided at the fluid-solid mixture to assess the non-equilibrium region at the fluid-solid interface. A scale analysis is performed to estimate the relative significance of the pertaining parameters that should be included in the governing equations. After the effects of pertinent parameters on the pressure loss and heat transfer enhancement were considered, the figure of merit (FoM) is employed to evaluate and optimize the thermal performance of heat exchange equipment. The results indicate the optimum thermal performance is obtained when the thermophoresis overwhelms the Brownian diffusion, which is for larger nanoparticles. This enhancement boosts when the buoyancy force increases. In addition, increasing the magnetic field strength and slippage at the fluid-solid interface enhances the thermal performance.

Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamba, Irene M.; Tharkabhushanam, Sri Harsha

We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S{sup d-1}. The conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibilitymore » (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: ()]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M. Ernst, Velocity distributions in homogeneously cooling and heated granular fluids, Granular Matter 1(57) (1998); M.H. Ernst, R. Brito, Scaling solutions of inelastic Boltzmann equations with over-populated high energy tails, Journal of Statistical Physics 109 (2002) 407-432; S.J. Moon, M.D. Shattuck, J. Swift, Velocity distributions and correlations in homogeneously heated granular media, Physical Review E 64 (2001) 031303; I.M. Gamba, S. Rjasanow, W. Wagner, Direct simulation of the uniformly heated granular Boltzmann equation, Mathematical and Computer Modelling 42 (2005) 683-700] and rigorously proven in Gamba et al. [I.M. Gamba, V. Panferov, C. Villani, On the Boltzmann equation for diffusively excited granular media, Communications in Mathematical Physics 246 (2004) 503-541(39)] and [A.V. Bobylev, I.M. Gamba, V. Panferov, Moment inequalities and high-energy tails for Boltzmann equations with inelastic interactions, Journal of Statistical Physics 116 (2004) 1651-1682].« less

Using Laboratory Experiments to Improve Ice-Ocean Parameterizations

NASA Astrophysics Data System (ADS)

McConnochie, C. D.; Kerr, R. C.

2017-12-01

Numerical models of ice-ocean interactions are typically unable to resolve the transport of heat and salt to the ice face. Instead, models rely upon parameterizations that have not been sufficiently validated by observations. Recent laboratory experiments of ice-saltwater interactions allow us to test the standard parameterization of heat and salt transport to ice faces - the three-equation model. The three-equation model predicts that the melt rate is proportional to the fluid velocity while the experimental results typically show that the melt rate is independent of the fluid velocity. By considering an analysis of the boundary layer that forms next to a melting ice face, we suggest a resolution to this disagreement. We show that the three-equation model makes the implicit assumption that the thickness of the diffusive sublayer next to the ice is set by a shear instability. However, at low flow velocities, the sublayer is instead set by a convective instability. This distinction leads to a threshold velocity of approximately 4 cm/s at geophysically relevant conditions, above which the form of the parameterization should be valid. In contrast, at flow speeds below 4 cm/s, the three-equation model will underestimate the melt rate. By incorporating such a minimum velocity into the three-equation model, predictions made by numerical simulations could be easily improved.

A laboratory examination of the three-equation model of ice-ocean interactions

NASA Astrophysics Data System (ADS)

McConnochie, Craig; Kerr, Ross

2017-11-01

Numerical models of ice-ocean interactions are typically unable to resolve the transport of heat and salt to the ice face. As such, models rely upon parameterizations that have not been properly validated by data. Recent laboratory experiments of ice-saltwater interactions allow us to test the standard parameterization of heat and salt transport to ice faces - the `three equation model'. We find a significant disagreement in the dependence of the melt rate on the fluid velocity. The three-equation model predicts that the melt rate is proportional to the fluid velocity while the experimental results typically show that the melt rate is independent of the fluid velocity. By considering a theoretical analysis of the boundary layer next to a melting ice face we suggest a resolution to this disagreement. We show that the three-equation model assumes that the thickness of the diffusive sublayer is set by a shear instability. However, at low flow velocities, the sublayer is instead set by a convective instability. This distinction leads to a threshold velocity of approximately 4 cm/s at geophysically relevant conditions, above which the form of the parameterization should be valid. In contrast, at flow speeds below 4 cm/s, the three-equation model will underestimate the melt rate. ARC DP120102772.

Heat source reconstruction from noisy temperature fields using an optimised derivative Gaussian filter

NASA Astrophysics Data System (ADS)

Delpueyo, D.; Balandraud, X.; Grédiac, M.

2013-09-01

The aim of this paper is to present a post-processing technique based on a derivative Gaussian filter to reconstruct heat source fields from temperature fields measured by infrared thermography. Heat sources can be deduced from temperature variations thanks to the heat diffusion equation. Filtering and differentiating are key-issues which are closely related here because the temperature fields which are processed are unavoidably noisy. We focus here only on the diffusion term because it is the most difficult term to estimate in the procedure, the reason being that it involves spatial second derivatives (a Laplacian for isotropic materials). This quantity can be reasonably estimated using a convolution of the temperature variation fields with second derivatives of a Gaussian function. The study is first based on synthetic temperature variation fields corrupted by added noise. The filter is optimised in order to reconstruct at best the heat source fields. The influence of both the dimension and the level of a localised heat source is discussed. Obtained results are also compared with another type of processing based on an averaging filter. The second part of this study presents an application to experimental temperature fields measured with an infrared camera on a thin plate in aluminium alloy. Heat sources are generated with an electric heating patch glued on the specimen surface. Heat source fields reconstructed from measured temperature fields are compared with the imposed heat sources. Obtained results illustrate the relevancy of the derivative Gaussian filter to reliably extract heat sources from noisy temperature fields for the experimental thermomechanics of materials.

Learning the dynamics of objects by optimal functional interpolation.

PubMed

Ahn, Jong-Hoon; Kim, In Young

2012-09-01

Many areas of science and engineering rely on functional data and their numerical analysis. The need to analyze time-varying functional data raises the general problem of interpolation, that is, how to learn a smooth time evolution from a finite number of observations. Here, we introduce optimal functional interpolation (OFI), a numerical algorithm that interpolates functional data over time. Unlike the usual interpolation or learning algorithms, the OFI algorithm obeys the continuity equation, which describes the transport of some types of conserved quantities, and its implementation shows smooth, continuous flows of quantities. Without the need to take into account equations of motion such as the Navier-Stokes equation or the diffusion equation, OFI is capable of learning the dynamics of objects such as those represented by mass, image intensity, particle concentration, heat, spectral density, and probability density.

Transformations of fluxes and forces describing the simultaneous transport of water and heat in unsaturated porous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raats, P.A.C.

1975-12-01

Balances of mass for the water in N distinct phases and a balance of heat for the medium as a whole were formulated. Following Philip and de Vries, it was assumed that the flux of water in each phase is proportional to the gradient of the pressure in that phase and that the diffusive component of the flux of heat is proportional to the gradient of the temperature. Clapeyron equations were used to express the gradient of the pressure in any phase in terms of the gradient of the pressure in a reference state and of the temperature. The referencemore » state may be the water in one of the phases or the water in some measuring device such as a tensiometer or a psychrometer. Expressions for the total flux of water and for the diffusive flux of heat plus the convective flux of heat associated with the conversion from any phase to the reference state were shown to satisfy the onsager reciprocal relations. A theorem due to Meixner was used to delineate the class of fluxes and forces that preserves these relations. In particular, it was shown that if the gradients of water content and temperature are used as the driving forces, the onsager relations are no longer satisfied.« less

Modeling ground thermal regime of an ancient buried ice body in Beacon Valley, Antarctica using a 1-D heat equation with latent heat effect

NASA Astrophysics Data System (ADS)

Liu, L.; Sletten, R. S.; Hallet, B.; Waddington, E. D.; Wood, S. E.

2013-12-01

An ancient massive ice body buried under several decimeters of debris in Beacon Valley, Antarctica is believed to be over one million years old, making it older than any known glacier or ice cap. It is fundamentally important as a reservoir of water, proxy for climatic information, and an expression of the periglacial landscape. It is also one of Earth's closest analog for widespread, near-surface ice found in Martian soils and ice-cored landforms. We are interested in understanding controls on how long this ice may persist since our physical model of sublimation suggests it should not be stable. In these models, the soil temperatures and the gradient are important because it determines the direction and magnitude of the vapor flux, and thus sublimation rates. To better understand the heat transfer processes and constrain the rates of processes governing ground ice stability, a model of the thermal behavior of the permafrost is applied to Beacon Valley, Antarctica. It calculates soil temperatures based on a 1-D thermal diffusion equation using a fully implicit finite volume method (FVM). This model is constrained by soil physical properties and boundary conditions of in-situ ground surface temperature measurements (with an average of -23.6oC, a maximum of 20.5oC and a minimum of -54.3oC) and ice-core temperature record at ~30 m. Model results are compared to in-situ temperature measurements at depths of 0.10 m, 0.20 m, 0.30 m, and 0.45 m to assess the model's ability to reproduce the temperature profile for given thermal properties of the debris cover and ice. The model's sensitivity to the thermal diffusivity of the permafrost and the overlaying debris is also examined. Furthermore, we incorporate the role of ice condensation/sublimation which is calculated using our vapor diffusion model in the 1-D thermal diffusion model to assess potential latent heat effects that in turn affect ground ice sublimation rates. In general, the model simulates the ground thermal regime well. Detailed temperature comparison suggests that the 1-D thermal diffusion model results closely approximate the measured temperature at all depths with the average square root of the mean squared error (SRMSE) of 0.15oC; a linear correlation between modeled and measured temperatures yields an average R2 value of 0.9997. Prominent seasonal temperature variations diminish with depth, and it equilibrates to mean annual temperature at about 21.5 m depth. The amount of heat generated/consumed by ice condensation/sublimation is insufficient to significantly impact the thermal regime.

Enceladus is not in Steady State

NASA Astrophysics Data System (ADS)

Cheunchitra, T.; Stevenson, D. J.

2016-12-01

Libration data tell us there is a global ocean. Topography and gravity tell us that there is substantial compensation at degree 2, meaning that the underside of the ice shell must have topography. This topography will decay, typically on a timescale of order a million years (fortuitously similar to thermal diffusion times through the ice shell), by viscous lateral flow of the ice. This could in principle be compensated in steady state by net melting beneath the poles and a compensating net freezing at the equator. In that model, the ice shell beneath the poles is partially melted with water being continuously produced and percolating to the base (or expelled if there are cracks, as at the South Pole). We have modeled this without an a priori assumption about the strength of tidal heating. We find that even if the tidal heating is zero on average around the equator, then the latent heat release from the required freezing can only be accommodated in steady state if the ice shell is 18km. The ice thickness must be even less at the poles in order to satisfy gravity and topography. Moreover, there must then be substantial tidal heating at the poles and it is physically unreasonable to have the volumetric tidal heating at the equator be enormously less than at the North Pole. For example, if the volumetric tidal heating at the equator is on average one quarter of that at the North Pole then marginal consistency with gravity and topography may be possible for a mean ice thickness at the equator of 12km. The global heat flow may exceed 40GW, much higher than the detectable IR excess (the observed south polar tiger stripe heat flow). Recent work (Fuller et al.) admits orbital evolutions with large heat flow at least for a recent part of the orbital history. However, this thin shell steady state model has difficulty reconciling observed gravity and topography as well as the libration data. We conclude that it is unlikely that Enceladus has no net melting or freezing. The ice shell can be thicker on average if there is net freezing at present but in that case it is difficult to explain the observed topography and gravity. A more likely scenario is that Enceladus has more melting beneath the poles than the current freezing (if any) beneath the equator. In that non-steady state model, the current ice thickness can be compatible with all current data.

Variational bounds on the temperature distribution

NASA Astrophysics Data System (ADS)

Kalikstein, Kalman; Spruch, Larry; Baider, Alberto

1984-02-01

Upper and lower stationary or variational bounds are obtained for functions which satisfy parabolic linear differential equations. (The error in the bound, that is, the difference between the bound on the function and the function itself, is of second order in the error in the input function, and the error is of known sign.) The method is applicable to a range of functions associated with equalization processes, including heat conduction, mass diffusion, electric conduction, fluid friction, the slowing down of neutrons, and certain limiting forms of the random walk problem, under conditions which are not unduly restrictive: in heat conduction, for example, we do not allow the thermal coefficients or the boundary conditions to depend upon the temperature, but the thermal coefficients can be functions of space and time and the geometry is unrestricted. The variational bounds follow from a maximum principle obeyed by the solutions of these equations.

A study of hydrogen diffusion flames using PDF turbulence model

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1991-01-01

The application of probability density function (pdf) turbulence models is addressed. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional computational fluid dynamic (CFD) flow solver with the Monte Carlo simulation of the pdf evolution equation was developed. The algorithm was validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames was carried out using this algorithm. Numerical results compared favorably with experimental data. The computations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

A study of hydrogen diffusion flames using PDF turbulence model

NASA Technical Reports Server (NTRS)

Hsu, Andrew T.

1991-01-01

The application of probability density function (pdf) turbulence models is addressed in this work. For the purpose of accurate prediction of turbulent combustion, an algorithm that combines a conventional CFD flow solver with the Monte Carlo simulation of the pdf evolution equation has been developed. The algorithm has been validated using experimental data for a heated turbulent plane jet. The study of H2-F2 diffusion flames has been carried out using this algorithm. Numerical results compared favorably with experimental data. The computuations show that the flame center shifts as the equivalence ratio changes, and that for the same equivalence ratio, similarity solutions for flames exist.

A New Numerical Scheme for Cosmic-Ray Transport

NASA Astrophysics Data System (ADS)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

Radiative and Convective Heat Transfer over Ablating Composite Flat Surface in Hypersonic Flow Regime.

DTIC Science & Technology

1987-04-22

absorptivity in the presence of scatteringsc B Defined in equation (40) B wBE Diffuse surface radiosity C Mass fraction of injected species D. jiCoefficient of...Then 20 A eb)x 8 eb- (49) where B and B., are the surface radiosities . It follows invnediately that wX 0 T to d 2e (50) ~ f ~ b W 2 L 3 ( ) 2 1 - 1

Diffusion in shear flow

NASA Astrophysics Data System (ADS)

Dufty, J. W.

1984-09-01

Diffusion of a tagged particle in a fluid with uniform shear flow is described. The continuity equation for the probability density describing the position of the tagged particle is considered. The diffusion tensor is identified by expanding the irreversible part of the probability current to first order in the gradient of the probability density, but with no restriction on the shear rate. The tensor is expressed as the time integral of a nonequilibrium autocorrelation function for the velocity of the tagged particle in its local fluid rest frame, generalizing the Green-Kubo expression to the nonequilibrium state. The tensor is evaluated from results obtained previously for the velocity autocorrelation function that are exact for Maxwell molecules in the Boltzmann limit. The effects of viscous heating are included and the dependence on frequency and shear rate is displayed explicitly. The mode-coupling contributions to the frequency and shear-rate dependent diffusion tensor are calculated.

Effects of non-unity Lewis numbers in diffusion flames

NASA Technical Reports Server (NTRS)

Linan, A.; Orlandi, P.; Verzicco, R.; Higuera, F. J.

1994-01-01

The purpose of this work is to carry out direct numerical simulations of diffusion controlled combustion with non-unity Lewis numbers for the reactants and products, thus accounting for the differential diffusion effects of the temperature and concentration fields. We use a formulation based on combining the conservation equations in a way to eliminate the reaction terms similar to the method used by Burke and Schumann (1928) for unity Lewis numbers. We present calculations for an axisymmetric fuel jet and for a planar, time evolving mixing layer, leaving out the effects of thermal expansion and variations of the transport coefficients due to the heat release. Our results show that the front of the flame shifts toward the fuel or oxygen sides owing to the effect of the differential diffusion and that the location of maximum temperature may not coincide with the flame. The dependence of the distribution of the reaction products on their Lewis number has been investigated.

A Computational Fluid Dynamic and Heat Transfer Model for Gaseous Core and Gas Cooled Space Power and Propulsion Reactors

NASA Technical Reports Server (NTRS)

Anghaie, S.; Chen, G.

1996-01-01

A computational model based on the axisymmetric, thin-layer Navier-Stokes equations is developed to predict the convective, radiation and conductive heat transfer in high temperature space nuclear reactors. An implicit-explicit, finite volume, MacCormack method in conjunction with the Gauss-Seidel line iteration procedure is utilized to solve the thermal and fluid governing equations. Simulation of coolant and propellant flows in these reactors involves the subsonic and supersonic flows of hydrogen, helium and uranium tetrafluoride under variable boundary conditions. An enthalpy-rebalancing scheme is developed and implemented to enhance and accelerate the rate of convergence when a wall heat flux boundary condition is used. The model also incorporated the Baldwin and Lomax two-layer algebraic turbulence scheme for the calculation of the turbulent kinetic energy and eddy diffusivity of energy. The Rosseland diffusion approximation is used to simulate the radiative energy transfer in the optically thick environment of gas core reactors. The computational model is benchmarked with experimental data on flow separation angle and drag force acting on a suspended sphere in a cylindrical tube. The heat transfer is validated by comparing the computed results with the standard heat transfer correlations predictions. The model is used to simulate flow and heat transfer under a variety of design conditions. The effect of internal heat generation on the heat transfer in the gas core reactors is examined for a variety of power densities, 100 W/cc, 500 W/cc and 1000 W/cc. The maximum temperature, corresponding with the heat generation rates, are 2150 K, 2750 K and 3550 K, respectively. This analysis shows that the maximum temperature is strongly dependent on the value of heat generation rate. It also indicates that a heat generation rate higher than 1000 W/cc is necessary to maintain the gas temperature at about 3500 K, which is typical design temperature required to achieve high efficiency in the gas core reactors. The model is also used to predict the convective and radiation heat fluxes for the gas core reactors. The maximum value of heat flux occurs at the exit of the reactor core. Radiation heat flux increases with higher wall temperature. This behavior is due to the fact that the radiative heat flux is strongly dependent on wall temperature. This study also found that at temperature close to 3500 K the radiative heat flux is comparable with the convective heat flux in a uranium fluoride failed gas core reactor.

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

NASA Technical Reports Server (NTRS)

Siegel, Robert

1995-01-01

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Modeling condensation with a noncondensable gas for mixed convection flow

NASA Astrophysics Data System (ADS)

Liao, Yehong

2007-05-01

This research theoretically developed a novel mixed convection model for condensation with a noncondensable gas. The model developed herein is comprised of three components: a convection regime map; a mixed convection correlation; and a generalized diffusion layer model. These components were developed in a way to be consistent with the three-level methodology in MELCOR. The overall mixed convection model was implemented into MELCOR and satisfactorily validated with data covering a wide variety of test conditions. In the development of the convection regime map, two analyses with approximations of the local similarity method were performed to solve the multi-component two-phase boundary layer equations. The first analysis studied effects of the bulk velocity on a basic natural convection condensation process and setup conditions to distinguish natural convection from mixed convection. It was found that the superimposed velocity increases condensation heat transfer by sweeping away the noncondensable gas accumulated at the condensation boundary. The second analysis studied effects of the buoyancy force on a basic forced convection condensation process and setup conditions to distinguish forced convection from mixed convection. It was found that the superimposed buoyancy force increases condensation heat transfer by thinning the liquid film thickness and creating a steeper noncondensable gas concentration profile near the condensation interface. In the development of the mixed convection correlation accounting for suction effects, numerical data were obtained from boundary layer analysis for the three convection regimes and used to fit a curve for the Nusselt number of the mixed convection regime as a function of the Nusselt numbers of the natural and forced convection regimes. In the development of the generalized diffusion layer model, the driving potential for mass transfer was expressed as the temperature difference between the bulk and the liquid-gas interface using the Clausius-Clapeyron equation. The model was developed on a mass basis instead of a molar basis to be consistent with general conservation equations. It was found that vapor diffusion is not only driven by a gradient of the molar fraction but also a gradient of the mixture molecular weight at the diffusion layer.

Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme

NASA Astrophysics Data System (ADS)

Luo, Xiao-Ping; Wang, Cun-Hai; Zhang, Yong; Yi, Hong-Liang; Tan, He-Ping

2018-06-01

The radiative transfer equation (RTE) has two asymptotic regimes characterized by the optical thickness, namely, optically thin and optically thick regimes. In the optically thin regime, a ballistic or kinetic transport is dominant. In the optically thick regime, energy transport is totally dominated by multiple collisions between photons; that is, the photons propagate by means of diffusion. To obtain convergent solutions to the RTE, conventional numerical schemes have a strong dependence on the number of spatial grids, which leads to a serious computational inefficiency in the regime where the diffusion is predominant. In this work, a discrete unified gas kinetic scheme (DUGKS) is developed to predict radiative heat transfer in participating media. Numerical performances of the DUGKS are compared in detail with conventional methods through three cases including one-dimensional transient radiative heat transfer, two-dimensional steady radiative heat transfer, and three-dimensional multiscale radiative heat transfer. Due to the asymptotic preserving property, the present method with relatively coarse grids gives accurate and reliable numerical solutions for large, small, and in-between values of optical thickness, and, especially in the optically thick regime, the DUGKS demonstrates a pronounced computational efficiency advantage over the conventional numerical models. In addition, the DUGKS has a promising potential in the study of multiscale radiative heat transfer inside the participating medium with a transition from optically thin to optically thick regimes.

SEAWAT-based simulation of axisymmetric heat transport.

PubMed

Vandenbohede, Alexander; Louwyck, Andy; Vlamynck, Nele

2014-01-01

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10(-10) ) than for solute transport (10(-6) ). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only. © 2013, National Ground Water Association.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Modeling of ultrashort pulsed laser irradiation in the cornea based on parabolic and hyperbolic heat equations using electrical analogy

NASA Astrophysics Data System (ADS)

Gheitaghy, A. M.; Takabi, B.; Alizadeh, M.

2014-03-01

Hyperbolic and parabolic heat equations are formulated to study a nonperfused homogeneous transparent cornea irradiated by high power and ultrashort pulsed laser in the Laser Thermo Keratoplasty (LTK) surgery. Energy absorption inside the cornea is modeled using the Beer-Lambert law that is incorporated as an exponentially decaying heat source. The hyperbolic and parabolic bioheat models of the tissue were solved by exploiting the mathematical analogy between thermal and electrical systems, by using robust circuit simulation program called Hspice to get the solutions of simultaneous RLC and RC transmission line networks. This method can be used to rapidly calculate the temperature in laser-irradiated tissue at time and space domain. It is found that internal energy gained from the irradiated field results in a rapid rise of temperature in the cornea surface during the early heating period, while the hyperbolic wave model predicts a higher temperature rise than the classical heat diffusion model. In addition, this paper investigates and examines the effect of some critical parameters such as relaxation time, convection coefficient, radiation, tear evaporation and variable thermal conductivity of cornea. Accordingly, it is found that a better accordance between hyperbolic and parabolic models will be achieved by time.

Construction of sequences of exact analytical solutions for heat diffusion in graded heterogeneous materials by the Darboux transformation method. Examples for half-space

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2016-09-01

The Darboux transformation is a differential transformation which, like other related methods (supersymmetry quantum mechanics-SUSYQM, factorization method) allows generating sequences of solvable potentials for the stationary 1D Schrodinger equation. It was recently shown that the heat equation in graded heterogeneous media, after a Liouville transformation, reduces to a pair of Schrödinger equations sharing the same potential function, one for the transformed temperature and one for the square root of effusivity. Repeated joint PROperty and Field Darboux Transformations (PROFIDT method) then yield two sequences of solutions: one of new solvable effusivity profiles and one of the corresponding temperature fields. In this paper we present and discuss the outcome in the case of a graded half-space domain. The interest in this methodology is that it provides closed-form solutions based on elementary functions. They are thus easily amenable to an implementation in an inversion process aimed, for example, at retrieving a subsurface effusivity profile from a modulated or transient surface temperature measurement (photothermal characterization).

Heat Transfer Characteristics of Mixed Electroosmotic and Pressure Driven Micro-Flows

NASA Astrophysics Data System (ADS)

Horiuchi, Keisuke; Dutta, Prashanta

We analyze heat transfer characteristics of steady electroosmotic flows with an arbitrary pressure gradient in two-dimensional straight microchannels considering the effects of Joule heating in electroosmotic pumping. Both the temperature distribution and local Nusselt number are mathematically derived in this study. The thermal analysis takes into consideration of the interaction among advective, diffusive, and Joule heating terms to obtain the thermally developing behavior. Unlike macro-scale pipes, axial conduction in micro-scale cannot be negligible, and the governing energy equation is not separable. Thus, a method that considers an extended Graetz problem is introduced. Analytical results show that the Nusselt number of pure electrooosmotic flow is higher than that of plane Poiseulle flow. Moreover, when the electroosmotic flow and pressure driven flow coexist, it is found that adverse pressure gradient to the electroosmotic flow makes the thermal entrance length smaller and the heat transfer ability stronger than pure electroosmotic flow case.

The effect of the shape and size of gold seeds irradiated with ultrasound on the bio-heat transfer in tissue.

PubMed

Gkigkitzis, Ioannis; Austerlitz, Carlos; Haranas, Ioannis; Campos, Diana

2015-01-01

The aim of this report is to propose a new methodology to treat prostate cancer with macro-rod-shaped gold seeds irradiated with ultrasound and develop a new computational method for temperature and thermal dose control of hyperthermia therapy induced by the proposed procedure. A computer code representation, based on the bio-heat diffusion equation, was developed to calculate the heat deposition and temperature elevation patterns in a gold rod and in the tissue surrounding it as a result of different therapy durations and ultrasound power simulations. The numerical results computed provide quantitative information on the interaction between high-energy ultrasound, gold seeds and biological tissues and can replicate the pattern observed in experimental studies. The effect of differences in shapes and sizes of gold rod targets irradiated with ultrasound is calculated and the heat enhancement and the bio-heat transfer in tissue are analyzed.

Double diffusion in arbitrary porous cavity: Part II

NASA Astrophysics Data System (ADS)

Ahamad, N. Ameer; Kamangar, Sarfaraz; Salman Ahmed N., J.; Soudagar, Manzoor Elahi M.; Khan, T. M. Yunus

2017-07-01

Heat and mass transfer in porous medium is one of the fundamental topics of interest. The present article is dedicated to study the effect of a small block placed at center of left vertical surface of the cavity. The block is maintained at isothermal temperature That three of its edges attached with porous medium. The left surface of cavity is maintained at highest concentration and right surface at lowest concentration. The right surface of cavity is at cold isothermal temperature Tc. Governing equations are converted into matrix form of equations with the help of finite element method and solved iteratively by using a computer code generated in MATLAB.

The photoacoustic effect generated by an incompressible sphere.

PubMed

Diebold, Gerald J; Beveridge, Andrew C; Hamilton, Theron J

2002-11-01

An incompressible sphere with a vanishing thermal expansivity suspended in a fluid can generate a photoacoustic effect when the heat deposited in the sphere by a light beam diffuses into the surrounding liquid causing it to expand and launch a sound wave. The properties of the photoacoustic effect for the sphere are found using a Green's function solution to the wave equation for pressure with Neumann boundary conditions. The results of the calculation show that the acoustic wave for fast heat liberation is an outgoing compressive pulse followed by a reflected pulse whose time profile is modified as a result of frequency dependent reflection from the sphere. For slow heat release by the sphere, the photoacoustic effect is shown to be proportional to the first time derivative of the heat flux at the particle-fluid interface.

Numerical simulation of nanofluids based on power-law fluids with flow and heat transfer

NASA Astrophysics Data System (ADS)

Li, Lin; Jiang, Yongyue; Chen, Aixin

2017-04-01

In this paper, we investigate the heat transfer of nanofluids based on power-law fluids and movement of nanoparticles with the effect of thermophoresis in a rotating circular groove. The velocity of circular groove rotating is a constant and the temperature on the wall is kept to be zero all the time which is different from the temperature of nanofluids in the initial time. The effects of thermophoresis and Brownian diffusion are considered in temperature and concentration equations, and it is assumed that the thermal conductivity of nanofluids is a function of concentration of nanoparticles. Based on numerical results, it can be found that nanofluids improve the process of heat transfer than base fluids in a rotating circular groove. The enhancement of heat transfer increases as the power law index of base fluids decreases.

The prediction of nozzle performance and heat transfer in hydrogen/oxygen rocket engines with transpiration cooling, film cooling, and high area ratios

NASA Technical Reports Server (NTRS)

Kacynski, Kenneth J.; Hoffman, Joe D.

1993-01-01

An advanced engineering computational model has been developed to aid in the analysis and design of hydrogen/oxygen chemical rocket engines. The complete multi-species, chemically reacting and diffusing Navier-Stokes equations are modelled, finite difference approach that is tailored to be conservative in an axisymmetric coordinate system for both the inviscid and viscous terms. Demonstration cases are presented for a 1030:1 area ratio nozzle, a 25 lbf film cooled nozzle, and transpiration cooled plug-and-spool rocket engine. The results indicate that the thrust coefficient predictions of the 1030:1 nozzle and the film cooled nozzle are within 0.2 to 0.5 percent, respectively, of experimental measurements when all of the chemical reaction and diffusion terms are considered. Further, the model's predictions agree very well with the heat transfer measurements made in all of the nozzle test cases. The Soret thermal diffusion term is demonstrated to have a significant effect on the predicted mass fraction of hydrogen along the wall of the nozzle in both the laminar flow 1030:1 nozzle and the turbulent plug-and-spool rocket engine analysis cases performed. Further, the Soret term was shown to represent a significant fraction of the diffusion fluxes occurring in the transpiration cooled rocket engine.

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Transient Nonequilibrium Molecular Dynamic Simulations of Thermal Conductivity: 1. Simple Fluids

NASA Astrophysics Data System (ADS)

Hulse, R. J.; Rowley, R. L.; Wilding, W. V.

2005-01-01

Thermal conductivity has been previously obtained from molecular dynamics (MD) simulations using either equilibrium (EMD) simulations (from Green--Kubo equations) or from steady-state nonequilibrium (NEMD) simulations. In the case of NEMD, either boundary-driven steady states are simulated or constrained equations of motion are used to obtain steady-state heat transfer rates. Like their experimental counterparts, these nonequilibrium steady-state methods are time consuming and may have convection problems. Here we report a new transient method developed to provide accurate thermal conductivity predictions from MD simulations. In the proposed MD method, molecules that lie within a specified volume are instantaneously heated. The temperature decay of the system of molecules inside the heated volume is compared to the solution of the transient energy equation, and the thermal diffusivity is regressed. Since the density of the fluid is set in the simulation, only the isochoric heat capacity is needed in order to obtain the thermal conductivity. In this study the isochoric heat capacity is determined from energy fluctuations within the simulated fluid. The method is valid in the liquid, vapor, and critical regions. Simulated values for the thermal conductivity of a Lennard-Jones (LJ) fluid were obtained using this new method over a temperature range of 90 to 900 K and a density range of 1-35 kmol · m-3. These values compare favorably with experimental values for argon. The new method has a precision of ±10%. Compared to other methods, the algorithm is quick, easy to code, and applicable to small systems, making the simulations very efficient.

Numerical Solution of the Electron Heat Transport Equation and Physics-Constrained Modeling of the Thermal Conductivity via Sequential Quadratic Programming Optimization in Nuclear Fusion Plasmas

NASA Astrophysics Data System (ADS)

Paloma, Cynthia S.

The plasma electron temperature (Te) plays a critical role in a tokamak nu- clear fusion reactor since temperatures on the order of 108K are required to achieve fusion conditions. Many plasma properties in a tokamak nuclear fusion reactor are modeled by partial differential equations (PDE's) because they depend not only on time but also on space. In particular, the dynamics of the electron temperature is governed by a PDE referred to as the Electron Heat Transport Equation (EHTE). In this work, a numerical method is developed to solve the EHTE based on a custom finite-difference technique. The solution of the EHTE is compared to temperature profiles obtained by using TRANSP, a sophisticated plasma transport code, for specific discharges from the DIII-D tokamak, located at the DIII-D National Fusion Facility in San Diego, CA. The thermal conductivity (also called thermal diffusivity) of the electrons (Xe) is a plasma parameter that plays a critical role in the EHTE since it indicates how the electron temperature diffusion varies across the minor effective radius of the tokamak. TRANSP approximates Xe through a curve-fitting technique to match experimentally measured electron temperature profiles. While complex physics-based model have been proposed for Xe, there is a lack of a simple mathematical model for the thermal diffusivity that could be used for control design. In this work, a model for Xe is proposed based on a scaling law involving key plasma variables such as the electron temperature (Te), the electron density (ne), and the safety factor (q). An optimization algorithm is developed based on the Sequential Quadratic Programming (SQP) technique to optimize the scaling factors appearing in the proposed model so that the predicted electron temperature and magnetic flux profiles match predefined target profiles in the best possible way. A simulation study summarizing the outcomes of the optimization procedure is presented to illustrate the potential of the proposed modeling method.

3D discrete angiogenesis dynamic model and stochastic simulation for the assessment of blood perfusion coefficient and impact on heat transfer between nanoparticles and malignant tumors.

PubMed

Yifat, Jonathan; Gannot, Israel

2015-03-01

Early detection of malignant tumors plays a crucial role in the survivability chances of the patient. Therefore, new and innovative tumor detection methods are constantly searched for. Tumor-specific magnetic-core nano-particles can be used with an alternating magnetic field to detect and treat tumors by hyperthermia. For the analysis of the method effectiveness, the bio-heat transfer between the nanoparticles and the tissue must be carefully studied. Heat diffusion in biological tissue is usually analyzed using the Pennes Bio-Heat Equation, where blood perfusion plays an important role. Malignant tumors are known to initiate an angiogenesis process, where endothelial cell migration from neighboring vasculature eventually leads to the formation of a thick blood capillary network around them. This process allows the tumor to receive its extensive nutrition demands and evolve into a more progressive and potentially fatal tumor. In order to assess the effect of angiogenesis on the bio-heat transfer problem, we have developed a discrete stochastic 3D model & simulation of tumor-induced angiogenesis. The model elaborates other angiogenesis models by providing high resolution 3D stochastic simulation, capturing of fine angiogenesis morphological features, effects of dynamic sprout thickness functions, and stochastic parent vessel generator. We show that the angiogenesis realizations produced are well suited for numerical bio-heat transfer analysis. Statistical study on the angiogenesis characteristics was derived using Monte Carlo simulations. According to the statistical analysis, we provide analytical expression for the blood perfusion coefficient in the Pennes equation, as a function of several parameters. This updated form of the Pennes equation could be used for numerical and analytical analyses of the proposed detection and treatment method. Copyright © 2014 Elsevier Inc. All rights reserved.

A Unified Theory for the Great Plains Nocturnal Low-Level Jet

NASA Astrophysics Data System (ADS)

Shapiro, A.; Fedorovich, E.; Rahimi, S.

2014-12-01

The nocturnal low-level jet (LLJ) is a warm-season atmospheric boundary layer phenomenon common to the Great Plains of the United States and other places worldwide, typically in regions east of mountain ranges. Low-level jets develop around sunset in fair weather conditions conducive to strong radiational cooling, reach peak intensity in the pre-dawn hours, and then dissipate with the onset of daytime convective mixing. In this study we consider the LLJ as a diurnal oscillation of a stably stratified atmosphere overlying a planar slope on the rotating Earth. The oscillations arise from diurnal cycles in both the heating of the slope (mechanism proposed by Holton in 1967) and the turbulent mixing (mechanism proposed by Blackadar in 1957). The governing equations are the equations of motion, incompressibility condition, and thermal energy in the Boussinesq approximation, with turbulent heat and momentum exchange parameterized through spatially constant but diurnally varying turbulent diffusion coefficients (diffusivities). Analytical solutions are obtained for diffusivities with piecewise constant waveforms (step-changes at sunrise and sunset) and slope temperatures/buoyancies with piecewise linear waveforms (saw-tooth function with minimum at sunrise and maximum before sunset). The jet characteristics are governed by eleven parameters: slope angle, Coriolis parameter, environmental buoyancy frequency, geostrophic wind strength, daytime and nighttime diffusivities, maximum (daytime) and minimum (nighttime) slope buoyancies, duration of daylight, lag time between peak slope buoyancy and sunset, and a Newtonian cooling time scale. An exploration of the parameter space yields results that are broadly consistent with findings particular to the Holton and Blackadar theories, and agree with climatological observations, for example, that stronger jets tend to occur over slopes of 0.15-0.25 degrees characteristic of the Great Plains. The solutions also yield intriguing predictions that peak jet strength increases with attenuation of the minimum surface buoyancy, and that the single most important parameter determining jet height is the nighttime diffusivity, with weaker nightime diffusion associated with smaller jet heights. These and other highlights will be discussed in the presentation.

High power densities from high-temperature material interactions. [in thermionic energy conversion and metallic fluid heat pipes

NASA Technical Reports Server (NTRS)

Morris, J. F.

1981-01-01

Thermionic energy conversion (TEC) and metallic-fluid heat pipes (MFHPs), offering unique advantages in terrestrial and space energy processing by virtue of operating on working-fluid vaporization/condensation cycles that accept great thermal power densities at high temperatures, share complex materials problems. Simplified equations are presented that verify and solve such problems, suggesting the possibility of cost-effective applications in the near term for TEC and MFHP devices. Among the problems discussed are: the limitation of alkali-metal corrosion, protection against hot external gases, external and internal vaporization, interfacial reactions and diffusion, expansion coefficient matching, and creep deformation.

Numerical Study of Buoyancy and Different Diffusion Effects on the Structure and Dynamics of Triple Flames

NASA Technical Reports Server (NTRS)

Chen, Jyh-Yuan; Echekki, Tarek

2001-01-01

Numerical simulations of 2-D triple flames under gravity force have been implemented to identify the effects of gravity on triple flame structure and propagation properties and to understand the mechanisms of instabilities resulting from both heat release and buoyancy effects. A wide range of gravity conditions, heat release, and mixing widths for a scalar mixing layer are computed for downward-propagating (in the same direction with the gravity vector) and upward-propagating (in the opposite direction of the gravity vector) triple flames. Results of numerical simulations show that gravity strongly affects the triple flame speed through its contribution to the overall flow field. A simple analytical model for the triple flame speed, which accounts for both buoyancy and heat release, is developed. Comparisons of the proposed model with the numerical results for a wide range of gravity, heat release and mixing width conditions, yield very good agreement. The analysis shows that under neutral diffusion, downward propagation reduces the triple flame speed, while upward propagation enhances it. For the former condition, a critical Froude number may be evaluated, which corresponds to a vanishing triple flame speed. Downward-propagating triple flames at relatively strong gravity effects have exhibited instabilities. These instabilities are generated without any artificial forcing of the flow. Instead disturbances are initiated by minute round-off errors in the numerical simulations, and subsequently amplified by instabilities. A linear stability analysis on mean profiles of stable triple flame configurations have been performed to identify the most amplified frequency in spatially developed flows. The eigenfunction equations obtained from the linearized disturbance equations are solved using the shooting method. The linear stability analysis yields reasonably good agreements with the observed frequencies of the unstable triple flames. The frequencies and amplitudes of disturbances increase with the magnitude of the gravity vector. Moreover, disturbances appear to be most amplified just downstream of the premixed branches. The effects of mixing width and differential diffusion are investigated and their roles on the flame stability are studied.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Horizontal density-gradient effects on simulation of flow and transport in the Potomac Estuary

USGS Publications Warehouse

Schaffranek, Raymond W.; Baltzer, Robert A.; ,

1990-01-01

A two-dimensional, depth-integrated, hydrodynamic/transport model of the Potomac Estuary between Indian Head and Morgantown, Md., has been extended to include treatment of baroclinic forcing due to horizontal density gradients. The finite-difference model numerically integrates equations of mass and momentum conservation in conjunction with a transport equation for heat, salt, and constituent fluxes. Lateral and longitudinal density gradients are determined from salinity distributions computed from the convection-diffusion equation and an equation of state that expresses density as a function of temperature and salinity; thus, the hydrodynamic and transport computations are directly coupled. Horizontal density variations are shown to contribute significantly to momentum fluxes determined in the hydrodynamic computation. These fluxes lead to enchanced tidal pumping, and consequently greater dispersion, as is evidenced by numerical simulations. Density gradient effects on tidal propagation and transport behavior are discussed and demonstrated.

Calculating the True and Observed Rates of Complex Heterogeneous Catalytic Reactions

NASA Astrophysics Data System (ADS)

Avetisov, A. K.; Zyskin, A. G.

2018-06-01

Equations of the theory of steady-state complex reactions are considered in matrix form. A set of stage stationarity equations is given, and an algorithm is described for deriving the canonic set of stationarity equations with appropriate corrections for the existence of fast stages in a mechanism. A formula for calculating the number of key compounds is presented. The applicability of the Gibbs rule to estimating the number of independent compounds in a complex reaction is analyzed. Some matrix equations relating the rates of dependent and key substances are derived. They are used as a basis to determine the general diffusion stoichiometry relationships between temperature, the concentrations of dependent reaction participants, and the concentrations of key reaction participants in a catalyst grain. An algorithm is described for calculating heat and mass transfer in a catalyst grain with respect to arbitrary complex heterogeneous catalytic reactions.

Conjugate heat and mass transfer in the lattice Boltzmann equation method.

PubMed

Li, Like; Chen, Chen; Mei, Renwei; Klausner, James F

2014-04-01

An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer in porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.

Conjugate heat and mass transfer in the lattice Boltzmann equation method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, LK; Chen, C; Mei, RW

2014-04-22

An interface treatment for conjugate heat and mass transfer in the lattice Boltzmann equation method is proposed based on our previously proposed second-order accurate Dirichlet and Neumann boundary schemes. The continuity of temperature (concentration) and its flux at the interface for heat (mass) transfer is intrinsically satisfied without iterative computations, and the interfacial temperature (concentration) and their fluxes are conveniently obtained from the microscopic distribution functions without finite-difference calculations. The present treatment takes into account the local geometry of the interface so that it can be directly applied to curved interface problems such as conjugate heat and mass transfer inmore » porous media. For straight interfaces or curved interfaces with no tangential gradient, the coupling between the interfacial fluxes along the discrete lattice velocity directions is eliminated and thus the proposed interface schemes can be greatly simplified. Several numerical tests are conducted to verify the applicability and accuracy of the proposed conjugate interface treatment, including (i) steady convection-diffusion in a channel containing two different fluids, (ii) unsteady convection-diffusion in the channel, (iii) steady heat conduction inside a circular domain with two different solid materials, and (iv) unsteady mass transfer from a spherical droplet in an extensional creeping flow. The accuracy and order of convergence of the simulated interior temperature (concentration) field, the interfacial temperature (concentration), and heat (mass) flux are examined in detail and compared with those obtained from the "half-lattice division" treatment in the literature. The present analysis and numerical results show that the half-lattice division scheme is second-order accurate only when the interface is fixed at the center of the lattice links, while the present treatment preserves second-order accuracy for arbitrary link fractions. For curved interfaces, the present treatment yields second-order accurate interior and interfacial temperatures (concentrations) and first-order accurate interfacial heat (mass) flux. An increase of order of convergence by one degree is obtained for each of these three quantities compared with the half-lattice division scheme. The surface-averaged Sherwood numbers computed in test (iv) agree well with published results.« less

Estimation of Land Surface Fluxes and Their Uncertainty via Variational Data Assimilation Approach

NASA Astrophysics Data System (ADS)

Abdolghafoorian, A.; Farhadi, L.

2016-12-01

Accurate estimation of land surface heat and moisture fluxes as well as root zone soil moisture is crucial in various hydrological, meteorological, and agricultural applications. "In situ" measurements of these fluxes are costly and cannot be readily scaled to large areas relevant to weather and climate studies. Therefore, there is a need for techniques to make quantitative estimates of heat and moisture fluxes using land surface state variables. In this work, we applied a novel approach based on the variational data assimilation (VDA) methodology to estimate land surface fluxes and soil moisture profile from the land surface states. This study accounts for the strong linkage between terrestrial water and energy cycles by coupling the dual source energy balance equation with the water balance equation through the mass flux of evapotranspiration (ET). Heat diffusion and moisture diffusion into the column of soil are adjoined to the cost function as constraints. This coupling results in more accurate prediction of land surface heat and moisture fluxes and consequently soil moisture at multiple depths with high temporal frequency as required in many hydrological, environmental and agricultural applications. One of the key limitations of VDA technique is its tendency to be ill-posed, meaning that a continuum of possibilities exists for different parameters that produce essentially identical measurement-model misfit errors. On the other hand, the value of heat and moisture flux estimation to decision-making processes is limited if reasonable estimates of the corresponding uncertainty are not provided. In order to address these issues, in this research uncertainty analysis will be performed to estimate the uncertainty of retrieved fluxes and root zone soil moisture. The assimilation algorithm is tested with a series of experiments using a synthetic data set generated by the simultaneous heat and water (SHAW) model. We demonstrate the VDA performance by comparing the (synthetic) true measurements (including profile of soil moisture and temperature, land surface water and heat fluxes, and root water uptake) with VDA estimates. In addition, the feasibility of extending the proposed approach to use remote sensing observations is tested by limiting the number of LST observations and soil moisture observations.

Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media.

PubMed

Karani, Hamid; Huber, Christian

2015-02-01

In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics in complex geometries.

Random element method for numerical modeling of diffusional processes

NASA Technical Reports Server (NTRS)

Ghoniem, A. F.; Oppenheim, A. K.

1982-01-01

The random element method is a generalization of the random vortex method that was developed for the numerical modeling of momentum transport processes as expressed in terms of the Navier-Stokes equations. The method is based on the concept that random walk, as exemplified by Brownian motion, is the stochastic manifestation of diffusional processes. The algorithm based on this method is grid-free and does not require the diffusion equation to be discritized over a mesh, it is thus devoid of numerical diffusion associated with finite difference methods. Moreover, the algorithm is self-adaptive in space and explicit in time, resulting in an improved numerical resolution of gradients as well as a simple and efficient computational procedure. The method is applied here to an assortment of problems of diffusion of momentum and energy in one-dimension as well as heat conduction in two-dimensions in order to assess its validity and accuracy. The numerical solutions obtained are found to be in good agreement with exact solution except for a statistical error introduced by using a finite number of elements, the error can be reduced by increasing the number of elements or by using ensemble averaging over a number of solutions.

An Equation Governing Ultralow-Velocity Zones: Implications for Holes in the ULVZ, Lateral Chemical Reactions at the Core-Mantle Boundary, and Damping of Heat Flux Variations in the Core

NASA Astrophysics Data System (ADS)

Hernlund, J. W.; Matsui, H.

2017-12-01

Ultralow-velocity zones (ULVZ) are increasingly illuminated by seismology, revealing surprising diversity in size, shape, and physical characteristics. The only viable hypotheses are that ULVZs are a compositionally distinct FeO-enriched dense material, which could have formed by fractional crystallization of a basal magma ocean, segregation of subducted banded iron formations, precipitation of solids from the outer core, partial melting and segregation of iron-rich melts from subducted basalts, or most likely a combination of many different processes. But many questions remain: Are ULVZ partially molten in some places, and not in others? Are ULVZ simply the thicker portions of an otherwise global thin layer, covering the entire CMB and thus blocking or moderating chemical interactions between the core and overlying mantle? Is such a layer inter-connected and able to conduct electrical currents that allow electro-magnetic coupling of core and mantle angular momentum? Are they being eroded and shrinking in size due to viscous entrainment, or is more material being added to ULVZ over time? Here we derive an advection-diffusion-like equation that governs the dynamical evolution of a chemically distinct ULVZ. Analysis of this equation shows that ULVZ should become readily swept aside by viscous mantle flows at the CMB, exposing "ordinary mantle" to the top of the core, thus inducing chemical heterogeneity that drives lateral CMB chemical reactions. These reactions are correlated with heat flux, thus maintaining large-scale pressure variations atop the core that induce cyclone-like flows centered around ULVZ and ponded subducted slabs. We suggest that turbulent diffusion across adjacent cyclone streams inside a stratified region atop the core readily accommodates lateral transport and re-distribution of components such as O and Si, in addition to heat. Our model implies that the deeper core is at least partly shielded from the influence of strong heat flux variations at the CMB which might otherwise cause problems for producing a geodynamo.

Thermal Characterization of Edible Oils by Using Photopyroelectric Technique

NASA Astrophysics Data System (ADS)

Lara-Hernández, G.; Suaste-Gómez, E.; Cruz-Orea, A.; Mendoza-Alvarez, J. G.; Sánchez-Sinéncio, F.; Valcárcel, J. P.; García-Quiroz, A.

2013-05-01

Thermal properties of several edible oils such as olive, sesame, and grape seed oils were obtained by using the photopyroelectric technique. The inverse photopyroelectric configuration was used in order to obtain the thermal effusivity of the oil samples. The theoretical equation for the photopyroelectric signal in this configuration, as a function of the incident light modulation frequency, was fitted to the experimental data in order to obtain the thermal effusivity of these samples. Also, the back photopyroelectric configuration was used to obtain the thermal diffusivity of these oils; this thermal parameter was obtained by fitting the theoretical equation for this configuration, as a function of the sample thickness (called the thermal wave resonator cavity), to the experimental data. All measurements were done at room temperature. A complete thermal characterization of these edible oils was achieved by the relationship between the obtained thermal diffusivities and thermal effusivities with their thermal conductivities and volumetric heat capacities. The obtained results are in agreement with the thermal properties reported for the case of the olive oil.

Numerical simulation of the hydrodynamical combustion to strange quark matter

NASA Astrophysics Data System (ADS)

Niebergal, Brian; Ouyed, Rachid; Jaikumar, Prashanth

2010-12-01

We present results from a numerical solution to the burning of neutron matter inside a cold neutron star into stable u,d,s quark matter. Our method solves hydrodynamical flow equations in one dimension with neutrino emission from weak equilibrating reactions, and strange quark diffusion across the burning front. We also include entropy change from heat released in forming the stable quark phase. Our numerical results suggest burning front laminar speeds of 0.002-0.04 times the speed of light, much faster than previous estimates derived using only a reactive-diffusive description. Analytic solutions to hydrodynamical jump conditions with a temperature-dependent equation of state agree very well with our numerical findings for fluid velocities. The most important effect of neutrino cooling is that the conversion front stalls at lower density (below ≈2 times saturation density). In a two-dimensional setting, such rapid speeds and neutrino cooling may allow for a flame wrinkle instability to develop, possibly leading to detonation.

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

NASA Technical Reports Server (NTRS)

Menart, J. A.; Lee, Haeok S.; Kim, Tae-Kuk

1993-01-01

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

A Bayesian Framework for Coupled Estimation of Key Unknown Parameters of Land Water and Energy Balance Equations

NASA Astrophysics Data System (ADS)

Farhadi, L.; Abdolghafoorian, A.

2015-12-01

The land surface is a key component of climate system. It controls the partitioning of available energy at the surface between sensible and latent heat, and partitioning of available water between evaporation and runoff. Water and energy cycle are intrinsically coupled through evaporation, which represents a heat exchange as latent heat flux. Accurate estimation of fluxes of heat and moisture are of significant importance in many fields such as hydrology, climatology and meteorology. In this study we develop and apply a Bayesian framework for estimating the key unknown parameters of terrestrial water and energy balance equations (i.e. moisture and heat diffusion) and their uncertainty in land surface models. These equations are coupled through flux of evaporation. The estimation system is based on the adjoint method for solving a least-squares optimization problem. The cost function consists of aggregated errors on state (i.e. moisture and temperature) with respect to observation and parameters estimation with respect to prior values over the entire assimilation period. This cost function is minimized with respect to parameters to identify models of sensible heat, latent heat/evaporation and drainage and runoff. Inverse of Hessian of the cost function is an approximation of the posterior uncertainty of parameter estimates. Uncertainty of estimated fluxes is estimated by propagating the uncertainty for linear and nonlinear function of key parameters through the method of First Order Second Moment (FOSM). Uncertainty analysis is used in this method to guide the formulation of a well-posed estimation problem. Accuracy of the method is assessed at point scale using surface energy and water fluxes generated by the Simultaneous Heat and Water (SHAW) model at the selected AmeriFlux stations. This method can be applied to diverse climates and land surface conditions with different spatial scales, using remotely sensed measurements of surface moisture and temperature states

Radiative transfer in dusty nebulae. III - The effects of dust albedo

NASA Technical Reports Server (NTRS)

Petrosian, V.; Dana, R. A.

1980-01-01

The effects of an albedo of internal dust, such as ionization structure and temperature of dust grain, were studied by the quasi-diffusion method with an iterative technique for solving the radiative heat transfer equations. It was found that the generalized on-the-spot approximation solution is adequate for most astrophysical applications for a zero albedo; for a nonzero albedo, the Eddington approximation is more accurate. The albedo increases the average energy of the diffuse photons, increasing the ionization level of hydrogen and heavy elements if the Eddington approximation is applied; the dust thermal gradient is reduced so that the infrared spectrum approaches blackbody spectrum with an increasing albedo.

Comparison of different bioheat transfer models for assessment of burns injuries

NASA Astrophysics Data System (ADS)

Łapka, Piotr; Furmański, Piotr; Wiśniewski, Tomasz S.

2016-12-01

Two bioheat transfer models i.e.: the classical Pennes model and a more realistic two-equation model which accounted for blood vessel structure in the skin as well as heat transfer in the tissue and arteria blood were coupled with heat and mass transfer model in the protective multilayer garment. The clothing model included conductive-radiative heat transfer with water vapor diffusion in pores and air gaps as well as sorption and desorption of water in fibers. Thermal radiation was modeled rigorously e.g.: both the tissue and fabrics were assumed non-gray, absorbing, emitting and anisotropically scattering. Additionally different refractive indices of fabrics, air and tissue and resulting optical phenomena at separating interfaces were accounted for. Both bioheat models were applied for predicting skin temperature distributions and possibility of burns for different exposition times and radiative heat fluxes incident on external surface of the protective garment. Performed analyses revealed that heat transfer in the skin subjected to high heat flux is independent of the blood vessel structure.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Laser surface modification of medical grade alloys for reduced heating in a magnetic resonance imaging environment

NASA Astrophysics Data System (ADS)

Benafan, O.; Chen, S.-Y.; Kar, A.; Vaidyanathan, R.

2015-12-01

Nanoscale surface modification of medical grade metallic alloys was conducted using a neodymium-doped yttrium aluminum garnet laser-based dopant diffusion technique. The objective of this approach was to minimize the induction heating by reducing the absorbed radio frequency field. Such an approach is advantageous in that the dopant is diffused into the alloy and is not susceptible to detachment or spallation as would an externally applied coating, and is expected to not deteriorate the mechanical and electrical properties of the base alloy or device. Experiments were conducted using a controlled environment laser system with the ability to control laser properties (i.e., laser power, spot size, and irradiation time) and dopant characteristics (i.e., temperature, concentration, and pressure). The reflective and transmissive properties of both the doped and untreated samples were measured in a radio frequency (63.86 MHz) magnetic field using a system comprising a high power signal generator, a localized magnetic field source and sensor, and a signal analyzer. The results indicate an increase in the reflectivity of the laser-treated samples compared to untreated samples. The effect of reflectivity on the heating of the alloys is investigated through a mathematical model incorporating Maxwell's equations and heat conduction.

Heating-frequency-dependent thermal conductivity: An analytical solution from diffusive to ballistic regime and its relevance to phonon scattering measurements

NASA Astrophysics Data System (ADS)

Yang, Fan; Dames, Chris

2015-04-01

The heating-frequency dependence of the apparent thermal conductivity in a semi-infinite body with periodic planar surface heating is explained by an analytical solution to the Boltzmann transport equation. This solution is obtained using a two-flux model and gray mean free time approximation and verified numerically with a lattice Boltzmann method and numerical results from the literature. Extending the gray solution to the nongray regime leads to an integral transform and accumulation-function representation of the phonon scattering spectrum, where the natural variable is mean free time rather than mean free path, as often used in previous work. The derivation leads to an approximate cutoff conduction similar in spirit to that of Koh and Cahill [Phys. Rev. B 76, 075207 (2007), 10.1103/PhysRevB.76.075207] except that the most appropriate criterion involves the heater frequency rather than thermal diffusion length. The nongray calculations are consistent with Koh and Cahill's experimental observation that the apparent thermal conductivity shows a stronger heater-frequency dependence in a SiGe alloy than in natural Si. Finally these results are demonstrated using a virtual experiment, which fits the phase lag between surface temperature and heat flux to obtain the apparent thermal conductivity and accumulation function.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

A theoretical study of the global F region for June solstice, solar maximum, and low magnetic activity

NASA Technical Reports Server (NTRS)

Sojka, J. J.; Schunk, R. W.

1985-01-01

A time-dependent, three-dimensional, multi-ion model of the ionospheric F region at 120-800 km altitude is presented. Account is taken of field-aligned diffusion, cross-field electrodynamic drifts in equatorial and high latitude regions, interhemispheric flow, thermospheric winds, polar wind escape, energy-dependent chemical reactions and neutral composition changes. Attention is also given to the effects of ion production by solar EUV radiation and auroral precipitation, thermal conduction, diffusion-thermal heat flow, local heating and cooling processes, offsets between the geomagnetic and geographic poles, and bending of field lines near the magnetic equator. The model incorporates all phenomena described by previous models and can be applied to tracing magnetic storm and substorm disturbances from high to low latitudes on a global scale. Sample results are provided for ionospheric features during a June solstice, the solar maximum and in a period of low geomagnetic activity. The model will eventually be used to study coupled ionosphere-thermosphere activity.

Calculation of thermal conductivity, thermal diffusivity and specific heat capacity of sedimentary rocks using petrophysical well logs

NASA Astrophysics Data System (ADS)

Fuchs, Sven; Balling, Niels; Förster, Andrea

2015-12-01

In this study, equations are developed that predict for synthetic sedimentary rocks (clastics, carbonates and evapourates) thermal properties comprising thermal conductivity, specific heat capacity and thermal diffusivity. The rock groups are composed of mineral assemblages with variable contents of 15 major rock-forming minerals and porosities of 0-30 per cent. Petrophysical properties and their well-logging-tool-characteristic readings were assigned to these rock-forming minerals and to pore-filling fluids. Relationships are explored between each thermal property and other petrophysical properties (density, sonic interval transit time, hydrogen index, volume fraction of shale and photoelectric absorption index) using multivariate statistics. The application of these relations allows computing continuous borehole profiles for each rock thermal property. The uncertainties in the prediction of each property vary depending on the selected well-log combination. Best prediction is in the range of 2-8 per cent for the specific heat capacity, of 5-10 per cent for the thermal conductivity, and of 8-15 for the thermal diffusivity, respectively. Well-log derived thermal conductivity is validated by laboratory data measured on cores from deep boreholes of the Danish Basin, the North German Basin, and the Molasse Basin. Additional validation of thermal conductivity was performed by comparing predicted and measured temperature logs. The maximum deviation between these logs is <3 °C. The thermal-conductivity calculation allowed an evaluation of the depth range in which the palaeoclimatic effect on the subsurface temperature field can be observed in the North German Basin. This effect reduces the surface heat-flow density by 25 mW m-2.

A new paradigm for predicting zonal-mean climate and climate change

NASA Astrophysics Data System (ADS)

Armour, K.; Roe, G.; Donohoe, A.; Siler, N.; Markle, B. R.; Liu, X.; Feldl, N.; Battisti, D. S.; Frierson, D. M.

2016-12-01

How will the pole-to-equator temperature gradient, or large-scale patterns of precipitation, change under global warming? Answering such questions typically involves numerical simulations with comprehensive general circulation models (GCMs) that represent the complexities of climate forcing, radiative feedbacks, and atmosphere and ocean dynamics. Yet, our understanding of these predictions hinges on our ability to explain them through the lens of simple models and physical theories. Here we present evidence that zonal-mean climate, and its changes, can be understood in terms of a moist energy balance model that represents atmospheric heat transport as a simple diffusion of latent and sensible heat (as a down-gradient transport of moist static energy, with a diffusivity coefficient that is nearly constant with latitude). We show that the theoretical underpinnings of this model derive from the principle of maximum entropy production; that its predictions are empirically supported by atmospheric reanalyses; and that it successfully predicts the behavior of a hierarchy of climate models - from a gray radiation aquaplanet moist GCM, to comprehensive GCMs participating in CMIP5. As an example of the power of this paradigm, we show that, given only patterns of local radiative feedbacks and climate forcing, the moist energy balance model accurately predicts the evolution of zonal-mean temperature and atmospheric heat transport as simulated by the CMIP5 ensemble. These results suggest that, despite all of its dynamical complexity, the atmosphere essentially responds to energy imbalances by simply diffusing latent and sensible heat down-gradient; this principle appears to explain zonal-mean climate and its changes under global warming.

A preliminary compressible second-order closure model for high speed flows

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu

1989-01-01

A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

Model for visualizing high energy laser (HEL) damage

NASA Astrophysics Data System (ADS)

Erten, Gail

2017-11-01

This paper describes and presents results from a model created in MATLAB® to calculate and display the time dependent temperature profile on a target aimpoint as it is being engaged by a high energy laser (HEL) beam. The model uses public domain information namely physics equations of heat conduction and phase changes and material properties such as thermal conductivity/diffusivity, latent heat, specific heat, melting and evaporation points as well as user input material type and thickness. The user also provides time varying characteristics of the HEL beam on the aimpoint, including beam size and intensity distribution (in Watts per centimeter square). The model calculates the temperature distribution at and around the aimpoint and also shows the phase changes of the aimpoint with the material first melting and then evaporating. User programmable features (selecting materials and thickness, erosion rates for melting) make the model highly versatile. The objective is to bridge the divide between remaining faithful to theoretical formulations such as the partial differential equations of heat conduction and at the same time serving practical concerns of the model user who needs to rapidly evaluate HEL thermal effects. One possible use of the tool is to assess lethality values of different aimpoints without costly (as well as often dangerous and destructive) experiments.

DIFFUSE AURORA ON GANYMEDE DRIVEN BY ELECTROSTATIC WAVES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singhal, R. P.; Tripathi, A. K.; Halder, S.

The role of electrostatic electron cyclotron harmonic (ECH) waves in producing diffuse auroral emission O i 1356 Å on Ganymede is investigated. Electron precipitation flux entering the atmosphere of Ganymede due to pitch-angle diffusion by ECH waves into the atmospheric loss-cone is calculated. The analytical yield spectrum approach for electron energy degradation in gases is used for calculating diffuse auroral intensities. It is found that calculated O i 1356 Å intensity resulting from the precipitation of magnetospheric electrons observed near Ganymede is insufficient to account for the observed diffuse auroral intensity. This is in agreement with estimates made in earliermore » works. Heating and acceleration of ambient electrons by ECH wave turbulence near the magnetic equator on the field line connecting Ganymede and Jupiter are considered. Two electron distribution functions are used to simulate the heating effect by ECH waves. Use of a Maxwellian distribution with temperature 100 eV can produce about 50–70 Rayleigh O i 1356 Å intensities, and the kappa distribution with characteristic energy 50 eV also gives rise to intensities with similar magnitude. Numerical experiments are performed to study the effect of ECH wave spectral intensity profile, ECH wave amplitude, and temperature/characteristic energy of electron distribution functions on the calculated diffuse auroral intensities. The proposed missions, joint NASA/ESA Jupiter Icy Moon Explorer and the present JUNO mission to Jupiter, would provide new data to constrain the ECH wave and other physical parameters near Ganymede. These should help confirm the findings of the present study.« less

Numerical simulation of transient, incongruent vaporization induced by high power laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, C.H.

1981-01-01

A mathematical model and numerical calculations were developed to solve the heat and mass transfer problems specifically for uranum oxide subject to laser irradiation. It can easily be modified for other heat sources or/and other materials. In the uranium-oxygen system, oxygen is the preferentially vaporizing component, and as a result of the finite mobility of oxygen in the solid, an oxygen deficiency is set up near the surface. Because of the bivariant behavior of uranium oxide, the heat transfer problem and the oxygen diffusion problem are coupled and a numerical method of simultaneously solving the two boundary value problems ismore » studied. The temperature dependence of the thermal properties and oxygen diffusivity, as well as the highly ablative effect on the surface, leads to considerable non-linearities in both the governing differential equations and the boundary conditions. Based on the earlier work done in this laboratory by Olstad and Olander on Iron and on Zirconium hydride, the generality of the problem is expanded and the efficiency of the numerical scheme is improved. The finite difference method, along with some advanced numerical techniques, is found to be an efficient way to solve this problem.« less

Thermal Transport Model for Heat Sink Design

NASA Technical Reports Server (NTRS)

Chervenak, James A.; Kelley, Richard L.; Brown, Ari D.; Smith, Stephen J.; Kilbourne, Caroline a.

2009-01-01

A document discusses the development of a finite element model for describing thermal transport through microcalorimeter arrays in order to assist in heat-sinking design. A fabricated multi-absorber transition edge sensor (PoST) was designed in order to reduce device wiring density by a factor of four. The finite element model consists of breaking the microcalorimeter array into separate elements, including the transition edge sensor (TES) and the silicon substrate on which the sensor is deposited. Each element is then broken up into subelements, whose surface area subtends 10 10 microns. The heat capacity per unit temperature, thermal conductance, and thermal diffusivity of each subelement are the model inputs, as are the temperatures of each subelement. Numerical integration using the Finite in Time Centered in Space algorithm of the thermal diffusion equation is then performed in order to obtain a temporal evolution of the subelement temperature. Thermal transport across interfaces is modeled using a thermal boundary resistance obtained using the acoustic mismatch model. The document concludes with a discussion of the PoST fabrication. PoSTs are novel because they enable incident x-ray position sensitivity with good energy resolution and low wiring density.

A 3-D wellbore simulator (WELLTHER-SIM) to determine the thermal diffusivity of rock-formations

NASA Astrophysics Data System (ADS)

Wong-Loya, J. A.; Santoyo, E.; Andaverde, J.

2017-06-01

Acquiring thermophysical properties of rock-formations in geothermal systems is an essential task required for the well drilling and completion. Wellbore thermal simulators require such properties for predicting the thermal behavior of a wellbore and the formation under drilling and shut-in conditions. The estimation of static formation temperatures also needs the use of these properties for the wellbore and formation materials (drilling fluids and pipes, cements, casings, and rocks). A numerical simulator (WELLTHER-SIM) has been developed for modeling the drilling fluid circulation and shut-in processes of geothermal wellbores, and for the in-situ determination of thermal diffusivities of rocks. Bottomhole temperatures logged under shut-in conditions (BHTm), and thermophysical and transport properties of drilling fluids were used as main input data. To model the thermal disturbance and recovery processes in the wellbore and rock-formation, initial drilling fluid and static formation temperatures were used as initial and boundary conditions. WELLTHER-SIM uses these temperatures together with an initial thermal diffusivity for the rock-formation to solve the governing equations of the heat transfer model. WELLTHER-SIM was programmed using the finite volume technique to solve the heat conduction equations under 3-D and transient conditions. Thermal diffusivities of rock-formations were inversely computed by using an iterative and efficient numerical simulation, where simulated thermal recovery data sets (BHTs) were statistically compared with those temperature measurements (BHTm) logged in some geothermal wellbores. The simulator was validated using a well-documented case reported in the literature, where the thermophysical properties of the rock-formation are known with accuracy. The new numerical simulator has been successfully applied to two wellbores drilled in geothermal fields of Japan and Mexico. Details of the physical conceptual model, the numerical algorithm, and the validation and application results are outlined in this work.

Microwave heating and joining of ceramic cylinders: A mathematical model

NASA Technical Reports Server (NTRS)

Booty, Michael R.; Kriegsmann, Gregory A.

1994-01-01

A thin cylindrical ceramic sample is placed in a single mode microwave applicator in such a way that the electric field strength is allowed to vary along its axis. The sample can either be a single rod or two rods butted together. We present a simple mathematical model which describes the microwave heating process. It is built on the assumption that the Biot number of the material is small, and that the electric field is known and uniform throughout the cylinder's cross-section. The model takes the form of a nonlinear parabolic equation of reaction-diffusion type, with a spatially varying reaction term that corresponds to the spatial variation of the electromagnetic field strength in the waveguide. The equation is analyzed and a solution is found which develops a hot spot near the center of the cylindrical sample and which then propagates outwards until it stabilizes. The propagation and stabilization phenomenon concentrates the microwave energy in a localized region about the center where elevated temperatures may be desirable.

Impact of generalized Fourier's and Fick's laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions

NASA Astrophysics Data System (ADS)

Ramzan, M.; Bilal, M.; Chung, Jae Dong; Lu, Dian Chen; Farooq, Umer

2017-09-01

A mathematical model has been established to study the magnetohydrodynamic second grade nanofluid flow past a bidirectional stretched surface. The flow is induced by Cattaneo-Christov thermal and concentration diffusion fluxes. Novel characteristics of Brownian motion and thermophoresis are accompanied by temperature dependent thermal conductivity and convective heat and mass boundary conditions. Apposite transformations are betrothed to transform a system of nonlinear partial differential equations to nonlinear ordinary differential equations. Analytic solutions of the obtained nonlinear system are obtained via a convergent method. Graphs are plotted to examine how velocity, temperature, and concentration distributions are affected by varied physical involved parameters. Effects of skin friction coefficients along the x- and y-direction versus various parameters are also shown through graphs and are well debated. Our findings show that velocities along both the x and y axes exhibit a decreasing trend for the Hartmann number. Moreover, temperature and concentration distributions are decreasing functions of thermal and concentration relaxation parameters.

A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis

NASA Astrophysics Data System (ADS)

Roubíček, Tomáš; Tomassetti, Giuseppe

2018-06-01

A theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn-Hilliard equations are used. The formulation of the problem uses Lagrangian (reference) configuration while the transport processes are pulled back. Except the static problem, the demagnetizing energy is ignored and only local non-self-penetration is considered. The analysis as far as existence of weak solutions of the (thermo) dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetallics under diffusion of hydrogen accompanied possibly by magnetic effects (and in particular ferro-to-antiferromagnetic phase transformation), all in the full thermodynamical context under large strains.

Heat-induced redistribution of surface oxide in uranium

NASA Astrophysics Data System (ADS)

Swissa, Eli; Shamir, Noah; Mintz, Moshe H.; Bloch, Joseph

1990-09-01

The redistribution of oxygen and uranium metal at the vicinity of the metal-oxide interface of native and grown oxides due to vacuum thermal annealing was studied for uranium and uranium-chromium alloy using Auger depth profiling and metallographic techniques. It was found that uranium metal is segregating out through the uranium oxide layer for annealing temperatures above 450°C. At the same time the oxide is redistributed in the metal below the oxide-metal interface in a diffusion like process. By applying a diffusion equation of a finite source, the diffusion coefficients for the process were obtained from the oxygen depth profiles measured for different annealing times. An Arrhenius like behavior was found for the diffusion coefficient between 400 and 800°C. The activation energy obtained was Ea = 15.4 ± 1.9 kcal/mole and the pre-exponential factor, D0 = 1.1 × 10 -8cm2/ s. An internal oxidation mechanism is proposed to explain the results.

Energy absorption by a magnetic nanoparticle suspension in a rotating field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raikher, Yu. L.; Stepanov, V. I., E-mail: stepanov@icmm.ru

Heat generation by viscous dissipation in a dilute suspension of single-domain ferromagnetic particles in a rotating magnetic field is analyzed by assuming that the suspended particles have a high magnetic rigidity. The problem is solved by using a kinetic approach based on a rotational diffusion equation. Behavior of specific loss power (SLP) as a function of field strength H and frequency {omega} is examined at constant temperature. SLP increases as either of these parameters squared when the other is constant, eventually approaching a saturation value. The function SLP(H, {omega}) can be used to determine optimal and admissible ranges of magneticallymore » induced heating.« less

High power densities from high-temperature materials interactions. [thermionic energy conversion and metallic fluid heat pipes

NASA Technical Reports Server (NTRS)

Morris, J. F.

1981-01-01

Thermionic energy converters and metallic-fluid heat pipes are well suited to serve together synergistically. The two operating cycles appear as simple and isolated as their material problems seem forebodingly deceptive and complicated. Simplified equations verify material properties and interactions as primary influences on the operational effectiveness of both. Each experiences flow limitations in thermal emission and vaporization because of temperature restrictions redounding from thermophysicochemical stability considerations. Topics discussed include: (1) successful limitation of alkali-metal corrosion; (2) protection against external hot corrosive gases; (3) coping with external and internal vaporization; (4) controlling interfacial reactions and diffusion; and (5) meeting other thermophysical challenges; expansion matches and creep.

An analytic model of axisymmetric mantle plume due to thermal and chemical diffusion

NASA Technical Reports Server (NTRS)

Liu, Mian; Chase, Clement G.

1990-01-01

An analytic model of axisymmetric mantle plumes driven by either thermal diffusion or combined diffusion of both heat and chemical species from a point source is presented. The governing equations are solved numerically in cylindrical coordinates for a Newtonian fluid with constant viscosity. Instead of starting from an assumed plume source, constraints on the source parameters, such as the depth of the source regions and the total heat input from the plume sources, are deduced using the geophysical characteristics of mantle plumes inferred from modelling of hotspot swells. The Hawaiian hotspot and the Bermuda hotspot are used as examples. Narrow mantle plumes are expected for likely mantle viscosities. The temperature anomaly and the size of thermal plumes underneath the lithosphere can be sensitive indicators of plume depth. The Hawaiian plume is likely to originate at a much greater depth than the Bermuda plume. One suggestive result puts the Hawaiian plume source at a depth near the core-mantle boundary and the source of the Bermuda plume in the upper mantle, close to the 700 km discontinuity. The total thermal energy input by the source region to the Hawaiian plume is about 5 x 10(10) watts. The corresponding diameter of the source region is about 100 to 150 km. Chemical diffusion from the same source does not affect the thermal structure of the plume.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Heterogeneous nanofluids: natural convection heat transfer enhancement

NASA Astrophysics Data System (ADS)

Oueslati, Fakhreddine Segni; Bennacer, Rachid

2011-12-01

Convective heat transfer using different nanofluid types is investigated. The domain is differentially heated and nanofluids are treated as heterogeneous mixtures with weak solutal diffusivity and possible Soret separation. Owing to the pronounced Soret effect of these materials in combination with a considerable solutal expansion, the resulting solutal buoyancy forces could be significant and interact with the initial thermal convection. A modified formulation taking into account the thermal conductivity, viscosity versus nanofluids type and concentration and the spatial heterogeneous concentration induced by the Soret effect is presented. The obtained results, by solving numerically the full governing equations, are found to be in good agreement with the developed solution based on the scale analysis approach. The resulting convective flows are found to be dependent on the local particle concentration φ and the corresponding solutal to thermal buoyancy ratio N. The induced nanofluid heterogeneity showed a significant heat transfer modification. The heat transfer in natural convection increases with nanoparticle concentration but remains less than the enhancement previously underlined in forced convection case.

Heterogeneous nanofluids: natural convection heat transfer enhancement

PubMed Central

2011-01-01

Convective heat transfer using different nanofluid types is investigated. The domain is differentially heated and nanofluids are treated as heterogeneous mixtures with weak solutal diffusivity and possible Soret separation. Owing to the pronounced Soret effect of these materials in combination with a considerable solutal expansion, the resulting solutal buoyancy forces could be significant and interact with the initial thermal convection. A modified formulation taking into account the thermal conductivity, viscosity versus nanofluids type and concentration and the spatial heterogeneous concentration induced by the Soret effect is presented. The obtained results, by solving numerically the full governing equations, are found to be in good agreement with the developed solution based on the scale analysis approach. The resulting convective flows are found to be dependent on the local particle concentration φ and the corresponding solutal to thermal buoyancy ratio N. The induced nanofluid heterogeneity showed a significant heat transfer modification. The heat transfer in natural convection increases with nanoparticle concentration but remains less than the enhancement previously underlined in forced convection case. PMID:21711755

Study of toroidal flow generation by ion cyclotron range of frequency minority heating in the Alcator C-Mod plasma

NASA Astrophysics Data System (ADS)

Murakami, S.; Itoh, K.; Zheng, L. J.; Van Dam, J. W.; Bonoli, P.; Rice, J. E.; Fiore, C. L.; Gao, C.; Fukuyama, A.

2016-01-01

The averaged toroidal flow of energetic minority ions during ICRF (ion cyclotron range of frequencies) heating is investigated in the Alcator C-Mod plasma by applying the GNET code, which can solve the drift kinetic equation with complicated orbits of accelerated energetic particles. It is found that a co-directional toroidal flow of the minority ions is generated in the region outside of the resonance location, and that the toroidal velocity reaches more than 40% of the central ion thermal velocity (Vtor ˜ 300 km/s with PICRF ˜ 2 MW). When we shift the resonance location to the outside of |r /a |˜0.5 , the toroidal flow immediately inside of the resonance location is reduced to 0 or changes to the opposite direction, and the toroidal velocity shear is enhanced at r/a ˜ 0.5. A radial diffusion equation for toroidal flow is solved by assuming a torque profile for the minority ion mean flow, and good agreements with experimental radial toroidal flow profiles are obtained. This suggests that the ICRF driven minority ion flow is related to the experimentally observed toroidal rotation during ICRF heating in the Alcator C-Mod plasma.

Numerical simulation of supersonic water vapor jet impinging on a flat plate

NASA Astrophysics Data System (ADS)

Kuzuu, Kazuto; Aono, Junya; Shima, Eiji

2012-11-01

We investigated supersonic water vapor jet impinging on a flat plate through numerical simulation. This simulation is for estimating heating effect of a reusable sounding rocket during vertical landing. The jet from the rocket bottom is supersonic, M=2 to 3, high temperature, T=2000K, and over-expanded. Atmospheric condition is a stationary standard air. The simulation is base on the full Navier-Stokes equations, and the flow is numerically solved by an unstructured compressible flow solver, in-house code LS-FLOW-RG. In this solver, the transport properties of muti-species gas and mass conservation equations of those species are considered. We employed DDES method as a turbulence model. For verification and validation, we also carried out a simulation under the condition of air, and compared with the experimental data. Agreement between our results and the experimental data are satisfactory. Through this simulation, we calculated the flow under some exit pressure conditions, and discuss the effects of pressure ratio on flow structures, heat transfer and so on. Furthermore, we also investigated diffusion effects of water vapor, and we confirmed that these phenomena are generated by the interaction of atmospheric air and affects the heat transfer to the surrounding environment.

A minimal model of an autonomous thermal motor

NASA Astrophysics Data System (ADS)

Fogedby, Hans C.; Imparato, Alberto

2017-09-01

We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a non-vanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the Büttiker-Landauer model for a single particle diffusing in an environment with position-dependent temperature. By using numerical calculations of the Fokker-Planck equation and simulations of the Langevin equations we study the model for arbitrary coupling, retrieving many features of the strong-coupling limit. In particular, directed transport emerges even for symmetric potentials. For distinct heat reservoirs the heat currents are well-defined quantities allowing a study of the motor efficiency. We show that the optimal working regime occurs for moderate coupling. Finally, we introduce a model with discrete phase space which captures the essential features of the continuous model, can be solved in the limit of weak coupling, and exhibits a larger efficiency than the continuous counterpart.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Non-fragile consensus algorithms for a network of diffusion PDEs with boundary local interaction

NASA Astrophysics Data System (ADS)

Xiong, Jun; Li, Junmin

2017-07-01

In this study, non-fragile consensus algorithm is proposed to solve the average consensus problem of a network of diffusion PDEs, modelled by boundary controlled heat equations. The problem deals with the case where the Neumann-type boundary controllers are corrupted by additive persistent disturbances. To achieve consensus between agents, a linear local interaction rule addressing this requirement is given. The proposed local interaction rules are analysed by applying a Lyapunov-based approach. The multiplicative and additive non-fragile feedback control algorithms are designed and sufficient conditions for the consensus of the multi-agent systems are presented in terms of linear matrix inequalities, respectively. Simulation results are presented to support the effectiveness of the proposed algorithms.

Brownian diffusion and thermophoresis mechanisms in Casson fluid over a moving wedge

NASA Astrophysics Data System (ADS)

Ullah, Imran; Shafie, Sharidan; Khan, Ilyas; Hsiao, Kai Long

2018-06-01

The effect of Brownian diffusion and thermophoresis on electrically conducting mixed convection flow of Casson fluid induced by moving wedge is investigated in this paper. It is assumed that the wedge is saturated in a porous medium and experiences the thermal radiation and chemical reaction effects. The transformed nonlinear governing equations are solved numerically by Keller box scheme. Findings reveal that increase in Casson and magnetic parameters reduced the boundary layer thickness. The effect of Brownian motion and thermophoresis parameters are more pronounced on temperature profile as compared to nanoparticles concentration. The presence of thermal radiation assisted the heat transfer rate significantly. The influence of magnetic parameter is observed less significant on temperature and nanoparticles concentration.

Thermal diffusion effect on MHD mixed convective flow along a vertically inclined plate: A casson fluid flow

NASA Astrophysics Data System (ADS)

Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa

2018-05-01

The nature of Casson fluid on MHD free convective flow of over an impulsively started infinite vertically inclined plate in presence of thermal diffusion (Soret), thermal radiation, heat and mass transfer effects is studied. The basic governing nonlinear coupled partial differential equations are solved numerically using finite element method. The relevant physical parameters appearing in velocity, temperature and concentration profiles are analyzed and discussed through graphs. Finally, the results for velocity profiles and the reduced Nusselt and Sherwood numbers are obtained and compared with previous results in the literature and are found to be in excellent agreement. Applications of the present study would be useful in magnetic material processing and chemical engineering systems.

Variable mass diffusion effects on free convection flow past an impulsively started infinite vertical plate

NASA Astrophysics Data System (ADS)

Rushi Kumar, B.; Jayakar, R.; Vijay Kumar, A. G.

2017-11-01

An exact analysis of the problem of free convection flow of a viscous incompressible chemically reacting fluid past an infinite vertical plate with the flow due to impulsive motion of the plate with Newtonian heating in the presence of thermal radiation and variable mass diffusion is performed. The resulting governing equations were tackled by Laplace transform technique. Finally the effects of pertinent flow parameters such as the radiation parameter, chemical reaction parameter, buoyancy ratio parameter, thermal Grashof number, Schmidt number, Prandtl number and time on the velocity, temperature, concentration and skin friction for both aiding and opposing flows were examined in detail when Pr=0.71(conducting air) and Pr=7.0(water).

An experimental and theoretical evaluation of increased thermal diffusivity phase change devices

NASA Technical Reports Server (NTRS)

White, S. P.; Golden, J. O.; Stermole, F. J.

1972-01-01

This study was to experimentally evaluate and mathematically model the performance of phase change thermal control devices containing high thermal conductivity metal matrices. Three aluminum honeycomb filters were evaluated at five different heat flux levels using n-oct-adecane as the test material. The system was mathematically modeled by approximating the partial differential equations with a three-dimensional implicit alternating direction technique. The mathematical model predicts the system quite well. All of the phase change times are predicted. The heating of solid phase is predicted exactly while there is some variation between theoretical and experimental results in the liquid phase. This variation in the liquid phase could be accounted for by the fact that there are some heat losses in the cell and there could be some convection in the experimental system.

Feasibility of High Energy Lasers for Interdiction Activities

DTIC Science & Technology

2017-12-01

2.3.2 Power in the Bucket Another parameter we will use in this study is the power-in-the-bucket. The “bucket” is defined as the area on the target we...the heat diffusion equation for a one -dimensional case (where the x-direction is into the target) and assuming a semi-infinite slab of material. The... studied and modeled. One of the approaches to describe these interactions is by making a one -dimensional mathematical model assuming [8]: 1. A semi

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

Penetration of Cosmic Rays into Dense Molecular Clouds: Role of Diffuse Envelopes

NASA Astrophysics Data System (ADS)

Ivlev, A. V.; Dogiel, V. A.; Chernyshov, D. O.; Caselli, P.; Ko, C.-M.; Cheng, K. S.

2018-03-01

A flux of cosmic rays (CRs) propagating through a diffuse ionized gas can excite MHD waves, thus generating magnetic disturbances. We propose a generic model of CR penetration into molecular clouds through their diffuse envelopes, and identify the leading physical processes controlling their transport on the way from a highly ionized interstellar medium to the dense interior of the cloud. The model allows us to describe a transition between a free streaming of CRs and their diffusive propagation, determined by the scattering on the self-generated disturbances. A self-consistent set of equations, governing the diffusive transport regime in an envelope and the MHD turbulence generated by the modulated CR flux, is characterized by two dimensionless numbers. We demonstrate a remarkable mutual complementarity of different mechanisms leading to the onset of the diffusive regime, which results in a universal energy spectrum of the modulated CRs. In conclusion, we briefly discuss implications of our results for several fundamental astrophysical problems, such as the spatial distribution of CRs in the Galaxy as well as the ionization, heating, and chemistry in dense molecular clouds. This paper is dedicated to the memory of Prof. Vadim Tsytovich.

Snow Micro-Structure Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Micah Johnson, Andrew Slaughter

PIKA is a MOOSE-based application for modeling micro-structure evolution of seasonal snow. The model will be useful for environmental, atmospheric, and climate scientists. Possible applications include application to energy balance models, ice sheet modeling, and avalanche forecasting. The model implements physics from published, peer-reviewed articles. The main purpose is to foster university and laboratory collaboration to build a larger multi-scale snow model using MOOSE. The main feature of the code is that it is implemented using the MOOSE framework, thus making features such as multiphysics coupling, adaptive mesh refinement, and parallel scalability native to the application. PIKA implements three equations:more » the phase-field equation for tracking the evolution of the ice-air interface within seasonal snow at the grain-scale; the heat equation for computing the temperature of both the ice and air within the snow; and the mass transport equation for monitoring the diffusion of water vapor in the pore space of the snow.« less

Quasiballistic heat removal from small sources studied from first principles

NASA Astrophysics Data System (ADS)

Vermeersch, Bjorn; Mingo, Natalio

2018-01-01

Heat sources whose characteristic dimension R is comparable to phonon mean free paths display thermal resistances that exceed conventional diffusive predictions. This has direct implications to (opto)electronics thermal management and phonon spectroscopy. Theoretical analyses have so far limited themselves to particular experimental configurations. Here, we build upon the multidimensional Boltzmann transport equation (BTE) to derive universal expressions for the apparent conductivity suppression S (R ) =κeff(R ) /κbulk experienced by radially symmetric 2D and 3D sources. In striking analogy to cross-plane heat conduction in thin films, a distinct quasiballistic regime emerges between ballistic (κeff˜R ) and diffusive (κeff≃κbulk ) asymptotes that displays a logarithmic dependence κeff˜ln(R ) in single crystals and fractional power dependence κeff˜R2 -α in alloys (with α the Lévy superdiffusion exponent). Analytical solutions and Monte Carlo simulations for spherical and circular heat sources in Si, GaAs, Si0.99Ge0.01 , and Si0.82Ge0.18 , all carried out from first principles, confirm the predicted generic tendencies. Contrary to the thin film case, common approximations like kinetic theory estimates κeff≃∑Sωgreyκω and modified Fourier temperature curves perform relatively poorly. Up to threefold deviations from the BTE solutions for sub-100 nm sources underline the need for rigorous treatment of multidimensional nondiffusive transport.

An Artificial Neural Networks Method for Solving Partial Differential Equations

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2010-09-01

While there already exists many analytical and numerical techniques for solving PDEs, this paper introduces an approach using artificial neural networks. The approach consists of a technique developed by combining the standard numerical method, finite-difference, with the Hopfield neural network. The method is denoted Hopfield-finite-difference (HFD). The architecture of the nets, energy function, updating equations, and algorithms are developed for the method. The HFD method has been used successfully to approximate the solution of classical PDEs, such as the Wave, Heat, Poisson and the Diffusion equations, and on a system of PDEs. The software Matlab is used to obtain the results in both tabular and graphical form. The results are similar in terms of accuracy to those obtained by standard numerical methods. In terms of speed, the parallel nature of the Hopfield nets methods makes them easier to implement on fast parallel computers while some numerical methods need extra effort for parallelization.

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

NASA Technical Reports Server (NTRS)

Morozov, S. K.; Krasitskiy, O. P.

1978-01-01

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

Comparison of Austenite Decomposition Models During Finite Element Simulation of Water Quenching and Air Cooling of AISI 4140 Steel

NASA Astrophysics Data System (ADS)

Babu, K.; Prasanna Kumar, T. S.

2014-08-01

An indigenous, non-linear, and coupled finite element (FE) program has been developed to predict the temperature field and phase evolution during heat treatment of steels. The diffusional transformations during continuous cooling of steels were modeled using Johnson-Mehl-Avrami-Komogorov equation, and the non-diffusion transformation was modeled using Koistinen-Marburger equation. Cylindrical quench probes made of AISI 4140 steel of 20-mm diameter and 50-mm long were heated to 1123 K (850 °C), quenched in water, and cooled in air. The temperature history during continuous cooling was recorded at the selected interior locations of the quench probes. The probes were then sectioned at the mid plane and resultant microstructures were observed. The process of water quenching and air cooling of AISI 4140 steel probes was simulated with the heat flux boundary condition in the FE program. The heat flux for air cooling process was calculated through the inverse heat conduction method using the cooling curve measured during air cooling of a stainless steel 304L probe as an input. The heat flux for the water quenching process was calculated from a surface heat flux model proposed for quenching simulations. The isothermal transformation start and finish times of different phases were taken from the published TTT data and were also calculated using Kirkaldy model and Li model and used in the FE program. The simulated cooling curves and phases using the published TTT data had a good agreement with the experimentally measured values. The computation results revealed that the use of published TTT data was more reliable in predicting the phase transformation during heat treatment of low alloy steels than the use of the Kirkaldy or Li model.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. III. Cylindrical approximations for heat waves traveling inwards

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, P.O. Box 1207, 3430 BE Nieuwegein

In this paper, a number of new explicit approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on the heat equation in cylindrical geometry using the symmetry (Neumann) boundary condition at the plasma center. This means that the approximations derived here should be used only to estimate transport coefficients between the plasma center and the off-axis perturbative source. If the effect of cylindrical geometry is small, it is also possiblemore » to use semi-infinite domain approximations presented in Part I and Part II of this series. A number of new approximations are derived in this part, Part III, based upon continued fractions of the modified Bessel function of the first kind and the confluent hypergeometric function of the first kind. These approximations together with the approximations based on semi-infinite domains are compared for heat waves traveling towards the center. The relative error for the different derived approximations is presented for different values of the frequency, transport coefficients, and dimensionless radius. Moreover, it is shown how combinations of different explicit formulas can be used to estimate the transport coefficients over a large parameter range for cases without convection and damping, cases with damping only, and cases with convection and damping. The relative error between the approximation and its underlying model is below 2% for the case, where only diffusivity and damping are considered. If also convectivity is considered, the diffusivity can be estimated well in a large region, but there is also a large region in which no suitable approximation is found. This paper is the third part (Part III) of a series of three papers. In Part I, the semi-infinite slab approximations have been treated. In Part II, cylindrical approximations are treated for heat waves traveling towards the plasma edge assuming a semi-infinite domain.« less

Influence of convection on microstructure

NASA Technical Reports Server (NTRS)

Wilcox, William R.; Caram, Rubens; Mohanty, A. P.; Seth, Jayshree

1990-01-01

In eutectic growth, as the solid phases grow they reject atoms to the liquid. This results in a variation of melt composition along the solid/liquid interface. In the past, mass transfer in eutectic solidification, in the absence of convection, was considered to be governed only by the diffusion induced by compositional gradients. However, mass transfer can also be generated by a temperature gradient. This is called thermotransport, thermomigration, thermal diffusion or the Soret effect. A theoretical model of the influence of the Soret effect on the growth of eutectic alloys is presented. A differential equation describing the compositional field near the interface during unidirectional solidification of a binary eutectic alloy was formulated by including the contributions of both compositional and thermal gradients in the liquid. A steady-state solution of the differential equation was obtained by applying appropriate boundary conditions and accounting for heat flow in the melt. Following that, the average interfacial composition was converted to a variation of undercooling at the interface, and consequently to microstructural parameters. The results obtained show that thermotransport can, under certain circumstances, be a parameter of paramount importance.

Thermal Characterization, Using the Photopyroelectric Technique, of Liquids Used in the Automobile Industry

NASA Astrophysics Data System (ADS)

Cervantes-Espinosa, L. M.; Castillo-Alvarado, F. de L.; Lara-Hernández, G.; Cruz-Orea, A.; Mendoza-Alvarez, J. G.; Valcárcel, J. P.; García-Quiroz, A.

2012-11-01

Thermal properties of liquids used in the automobile industry such as engine oil, antifreeze, and a liquid for windshield wipers were obtained using the photopyroelectric (PPE) technique. The inverse PPE configuration was used in order to obtain the thermal effusivity of the liquid samples. The theoretical equation for the PPE signal in this configuration, as a function of the incident light modulation frequency, was fitted to the experimental data in order to obtain the thermal effusivity of these samples. Also, the back PPE configuration was used to obtain the thermal diffusivity of these liquids; this thermal parameter was obtained by fitting the theoretical equation for this configuration, as a function of the sample thickness (called the thermal wave resonator cavity), to the experimental data. All measurements were done at room temperature. A complete thermal characterization of these liquids used in the automobile industry was achieved by the relationship between the obtained thermal diffusivities and thermal effusivities with their thermal conductivities and volumetric heat capacities. The obtained results are compared with the thermal properties of similar liquids.

Large Eddy Simulation of Entropy Generation in a Turbulent Mixing Layer

NASA Astrophysics Data System (ADS)

Sheikhi, Reza H.; Safari, Mehdi; Hadi, Fatemeh

2013-11-01

Entropy transport equation is considered in large eddy simulation (LES) of turbulent flows. The irreversible entropy generation in this equation provides a more general description of subgrid scale (SGS) dissipation due to heat conduction, mass diffusion and viscosity effects. A new methodology is developed, termed the entropy filtered density function (En-FDF), to account for all individual entropy generation effects in turbulent flows. The En-FDF represents the joint probability density function of entropy, frequency, velocity and scalar fields within the SGS. An exact transport equation is developed for the En-FDF, which is modeled by a system of stochastic differential equations, incorporating the second law of thermodynamics. The modeled En-FDF transport equation is solved by a Lagrangian Monte Carlo method. The methodology is employed to simulate a turbulent mixing layer involving transport of passive scalars and entropy. Various modes of entropy generation are obtained from the En-FDF and analyzed. Predictions are assessed against data generated by direct numerical simulation (DNS). The En-FDF predictions are in good agreements with the DNS data.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion.

PubMed

Gowrishankar, T R; Stewart, Donald A; Martin, Gregory T; Weaver, James C

2004-11-17

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

The {sech}( {\\hat{ξ }} ) -Type Profiles: A Swiss-Army Knife for Exact Analytical Modeling of Thermal Diffusion and Wave Propagation in Graded Media

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-07-01

This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, the so-called {sech}( {\\hat{ξ }} ) -type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant to providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more {sech}( {\\hat{ξ }} ) -type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

Hydrodynamic model of temperature change in open ionic channels.

PubMed Central

Chen, D P; Eisenberg, R S; Jerome, J W; Shu, C W

1995-01-01

Most theories of open ionic channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account density changes, temperature changes, and electrical potential gradients. We integrate the equations with an essentially nonoscillatory shock-capturing numerical scheme previously shown to be stable and accurate. Our calculations show that 1) a significant amount of electrical energy is exchanged with the permeating ions; 2) the local temperature of the ions rises some tens of degrees, and this temperature rise significantly alters for ionic flux in a channel 25 A long, such as gramicidin-A; and 3) a critical parameter, called the saturation velocity, determines whether ionic motion is overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel. PMID:8599638

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Collective diffusion and quantum chaos in holography

NASA Astrophysics Data System (ADS)

Wu, Shao-Feng; Wang, Bin; Ge, Xian-Hui; Tian, Yu

2018-05-01

We define a particular combination of charge and heat currents that is decoupled with the heat current. This "heat-decoupled" (HD) current can be transported by diffusion at long distances, when some thermoelectric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z =2 . In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

A model of recovering the parameters of fast nonlocal heat transport in magnetic fusion plasmas

NASA Astrophysics Data System (ADS)

Kukushkin, A. B.; Kulichenko, A. A.; Sdvizhenskii, P. A.; Sokolov, A. V.; Voloshinov, V. V.

2017-12-01

A model is elaborated for interpreting the initial stage of the fast nonlocal transport events, which exhibit immediate response, in the diffusion time scale, of the spatial profile of electron temperature to its local perturbation, while the net heat flux is directed opposite to ordinary diffusion (i.e. along the temperature gradient). We solve the inverse problem of recovering the kernel of the integral equation, which describes nonlocal (superdiffusive) transport of energy due to emission and absorption of electromagnetic (EM) waves with long free path and strong reflection from the vacuum vessel’s wall. To allow for the errors of experimental data, we use the method based on the regularized (in the framework of an ill-posed problem, using the parametric models) approximation of available experimental data. The model is applied to interpreting the data from stellarator LHD and tokamak TFTR. The EM wave transport is considered here in the single-group approximation, however the limitations of the physics model enable us to identify the spectral range of the EM waves which might be responsible for the observed phenomenon.

A quasilinear operator retaining magnetic drift effects in tokamak geometry

NASA Astrophysics Data System (ADS)

Catto, Peter J.; Lee, Jungpyo; Ram, Abhay K.

2017-12-01

The interaction of radio frequency waves with charged particles in a magnetized plasma is usually described by the quasilinear operator that was originally formulated by Kennel & Engelmann (Phys. Fluids, vol. 9, 1966, pp. 2377-2388). In their formulation the plasma is assumed to be homogenous and embedded in a uniform magnetic field. In tokamak plasmas the Kennel-Engelmann operator does not capture the magnetic drifts of the particles that are inherent to the non-uniform magnetic field. To overcome this deficiency a combined drift and gyrokinetic derivation is employed to derive the quasilinear operator for radio frequency heating and current drive in a tokamak with magnetic drifts retained. The derivation requires retaining the magnetic moment to higher order in both the unperturbed and perturbed kinetic equations. The formal prescription for determining the perturbed distribution function then follows a novel procedure in which two non-resonant terms must be evaluated explicitly. The systematic analysis leads to a diffusion equation that is compact and completely expressed in terms of the drift kinetic variables. The equation is not transit averaged, and satisfies the entropy principle, while retaining the full poloidal angle variation without resorting to Fourier decomposition. As the diffusion equation is in physical variables, it can be implemented in any computational code. In the Kennel-Engelmann formalism, the wave-particle resonant delta function is either for the Landau resonance or the Doppler shifted cyclotron resonance. In the combined gyro and drift kinetic approach, a term related to the magnetic drift modifies the resonance condition.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

A stable and accurate partitioned algorithm for conjugate heat transfer

NASA Astrophysics Data System (ADS)

Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.

2017-09-01

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in an implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode theory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized-Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and diffusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. The CHAMP scheme is also developed for general curvilinear grids and CHT examples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.

Specific interface area and self-stirring in a two-liquid system experiencing intense interfacial boiling below the bulk boiling temperatures of both components

NASA Astrophysics Data System (ADS)

Goldobin, Denis S.; Pimenova, Anastasiya V.

2017-04-01

We present an approach to theoretical assessment of the mean specific interface area (δ S/δ V) for a well-stirred system of two immiscible liquids experiencing interfacial boiling. The assessment is based on the balance of transformations of mechanical energy and the laws of the momentum and heat transfer in the turbulent boundary layer. The theory yields relations between the specific interface area and the characteristics of the system state. In particular, this allows us to derive the equations of self-cooling dynamics of the system in the absence of external heat supply. The results provide possibility for constructing a self-contained mathematical description of the process of interfacial boiling. In this study, we assume the volume fractions of two components to be similar as well as the values of their kinematic viscosity and molecular heat diffusivity.

Evaporation for Lithium Bromide Aqueous Solution in a Falling Film Heater under Reduced Pressures

NASA Astrophysics Data System (ADS)

Matsuda, Akira; Ide, Tetsuo; Yukino, Keiji

Experiments on evaporation for water and lithium bromide (LiBr) aqueous solution were made in a externally heated wetted-wall column under reduced pressures. For water, evaporation rate increased slightly as feed rate decreased. The heat transfer coefficients of falling film agreed with those for filmwise condensation. For LiBr solution, evaporation rate decreased and outlet temperature of LiBr solution increased as feed rate decreased. The equations of continuity, diffusion and energy which assume that only water moves to the surface and LiBr doesn't move through falling film of LiBr solution were solved numerically. Calculated values of evaporation rate and outlet temperature of solution agreed with experimental results. The results of this work were compared with pool boiling data reported previously, and it was shown that falling film heater is superior to pool boiling heater concerning heat transfer.

Opposing flow in square porous annulus: Influence of Dufour effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Athani, Abdulgaphur, E-mail: abbu.bec@gmail.com; Al-Rashed, Abdullah A. A. A., E-mail: aa.alrashed@paaet.edu.kw; Khaleed, H. M. T., E-mail: khalid-tan@yahoo.com

Heat and mass transfer in porous medium is very important area of research which is also termed as double diffusive convection or thermo-solutal convection. The buoyancy ratio which is the ratio of thermal to concentration buoyancy can have negative values thus leading to opposing flow. This article is aimed to study the influence of Dufour effect on the opposing flow in a square porous annulus. The partial differential equations that govern the heat and mass transfer behavior inside porous medium are solved using finite element method. A three node triangular element is used to divide the porous domain into smallermore » elements. Results are presented with respect to geometric and physical parameters such as duct diameter ratio, Rayleigh number, radiation parameter etc. It is found that the heat transfer increase with increase in Rayleigh number and radiation parameter. It is observed that Dufour coefficient has more influence on velocity profile.« less

Comparison of Turbulent Thermal Diffusivity and Scalar Variance Models

NASA Technical Reports Server (NTRS)

Yoder, Dennis A.

2016-01-01

In this study, several variable turbulent Prandtl number formulations are examined for boundary layers, pipe flow, and axisymmetric jets. The model formulations include simple algebraic relations between the thermal diffusivity and turbulent viscosity as well as more complex models that solve transport equations for the thermal variance and its dissipation rate. Results are compared with available data for wall heat transfer and profile measurements of mean temperature, the root-mean-square (RMS) fluctuating temperature, turbulent heat flux and turbulent Prandtl number. For wall-bounded problems, the algebraic models are found to best predict the rise in turbulent Prandtl number near the wall as well as the log-layer temperature profile, while the thermal variance models provide a good representation of the RMS temperature fluctuations. In jet flows, the algebraic models provide no benefit over a constant turbulent Prandtl number approach. Application of the thermal variance models finds that some significantly overpredict the temperature variance in the plume and most underpredict the thermal growth rate of the jet. The models yield very similar fluctuating temperature intensities in jets from straight pipes and smooth contraction nozzles, in contrast to data that indicate the latter should have noticeably higher values. For the particular low subsonic heated jet cases examined, changes in the turbulent Prandtl number had no effect on the centerline velocity decay.

Reconciling estimates of the ratio of heat and salt fluxes at the ice-ocean interface

NASA Astrophysics Data System (ADS)

Keitzl, T.; Mellado, J. P.; Notz, D.

2016-12-01

The heat exchange between floating ice and the underlying ocean is determined by the interplay of diffusive fluxes directly at the ice-ocean interface and turbulent fluxes away from it. In this study, we examine this interplay through direct numerical simulations of free convection. Our results show that an estimation of the interface flux ratio based on direct measurements of the turbulent fluxes can be difficult because the flux ratio varies with depth. As an alternative, we present a consistent evaluation of the flux ratio based on the total heat and salt fluxes across the boundary layer. This approach allows us to reconcile previous estimates of the ice-ocean interface conditions. We find that the ratio of heat and salt fluxes directly at the interface is 83-100 rather than 33 as determined by previous turbulence measurements in the outer layer. This can cause errors in the estimated ice-ablation rate from field measurements of up to 40% if they are based on the three-equation formulation.

The exit-time problem for a Markov jump process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Phonon cross-plane transport and thermal boundary resistance: effect of heat source size and thermal boundary resistance on phonon characteristics

NASA Astrophysics Data System (ADS)

Ali, H.; Yilbas, B. S.

2016-09-01

Phonon cross-plane transport across silicon and diamond thin films pair is considered, and thermal boundary resistance across the films pair interface is examined incorporating the cut-off mismatch and diffusive mismatch models. In the cut-off mismatch model, phonon frequency mismatch for each acoustic branch is incorporated across the interface of the silicon and diamond films pair in line with the dispersion relations of both films. The frequency-dependent and transient solution of the Boltzmann transport equation is presented, and the equilibrium phonon intensity ratios at the silicon and diamond film edges are predicted across the interface for each phonon acoustic branch. Temperature disturbance across the edges of the films pair is incorporated to assess the phonon transport characteristics due to cut-off and diffusive mismatch models across the interface. The effect of heat source size, which is allocated at high-temperature (301 K) edge of the silicon film, on the phonon transport characteristics at the films pair interface is also investigated. It is found that cut-off mismatch model predicts higher values of the thermal boundary resistance across the films pair interface as compared to that of the diffusive mismatch model. The ratio of equilibrium phonon intensity due to the cut-off mismatch over the diffusive mismatch models remains >1 at the silicon edge, while it becomes <1 at the diamond edge for all acoustic branches.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Manipulation and simulations of thermal field profiles in laser heat-mode lithography

NASA Astrophysics Data System (ADS)

Wei, Tao; Wei, Jingsong; Wang, Yang; Zhang, Long

2017-12-01

Laser heat-mode lithography is a very useful method for high-speed fabrication of large-area micro/nanostructures. To obtain nanoscale pattern structures, one needs to manipulate the thermal diffusion channels. This work reports the manipulation of the thermal diffusion in laser heat-mode lithography and provides methods to restrain the in-plane thermal diffusion and improve the out-of-plane thermal diffusion. The thermal field profiles in heat-mode resist thin films have been given. It is found that the size of the heat-spot can be decreased by decreasing the thickness of the heat-mode resist thin films, inserting the thermal conduction layers, and shortening the laser irradiation time. The optimized laser writing strategy is also given, where the in-plane thermal diffusion is completely restrained and the out-of-plane thermal diffusion is improved. The heat-spot size is almost equal to that of the laser spot, accordingly. This work provides a very important guide to laser heat-mode lithography.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Radiant exchange in partially specular architectural environments

NASA Astrophysics Data System (ADS)

Beamer, C. Walter; Muehleisen, Ralph T.

2003-10-01

The radiant exchange method, also known as radiosity, was originally developed for thermal radiative heat transfer applications. Later it was used to model architectural lighting systems, and more recently it has been extended to model acoustic systems. While there are subtle differences in these applications, the basic method is based on solving a system of energy balance equations, and it is best applied to spaces with mainly diffuse reflecting surfaces. The obvious drawback to this method is that it is based around the assumption that all surfaces in the system are diffuse reflectors. Because almost all architectural systems have at least some partially specular reflecting surfaces in the system it is important to extend the radiant exchange method to deal with this type of surface reflection. [Work supported by NSF.

Small particle transport across turbulent nonisothermal boundary layers

NASA Technical Reports Server (NTRS)

Rosner, D. E.; Fernandez De La Mora, J.

1982-01-01

The interaction between turbulent diffusion, Brownian diffusion, and particle thermophoresis in the limit of vanishing particle inertial effects is quantitatively modeled for applications in gas turbines. The model is initiated with consideration of the particle phase mass conservation equation for a two-dimensional boundary layer, including the thermophoretic flux term directed toward the cold wall. A formalism of a turbulent flow near a flat plate in a heat transfer problem is adopted, and variable property effects are neglected. Attention is given to the limit of very large Schmidt numbers and the particle concentration depletion outside of the Brownian sublayer. It is concluded that, in the parameter range of interest, thermophoresis augments the high Schmidt number mass-transfer coefficient by a factor equal to the product of the outer sink and the thermophoretic suction.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Study of Cold Heat Energy Release Characteristics of Flowing Ice Water Slurry in a Pipe

NASA Astrophysics Data System (ADS)

Inaba, Hideo; Horibe, Akihiko; Ozaki, Koichi; Yokota, Maki

This paper has dealt with melting heat transfer characteristics of ice water slurry in an inside tube of horizontal double tube heat exchanger in which a hot water circulated in an annular gap between the inside and outside tubes. Two kinds of heat exchangers were used; one is made of acrylic resin tube for flow visualization and the other is made of stainless steel tube for melting heat transfer measurement. The result of flow visualization revealed that ice particles flowed along the top of inside tube in the ranges of small ice packing factor and low ice water slurry velocity, while ice particles diffused into the whole of tube and flowed like a plug built up by ice particles for large ice packing factor and high velocity. Moreover, it was found that the flowing ice plug was separated into numbers of small ice clusters by melting phenomenon. Experiments of melting heat transfer were carried out under some parameters of ice packing factor, ice water slurry flow rate and hot water temperature. Consequently, the correlation equation of melting heat transfer was derived as a function of those experimental parameters.

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

NASA Technical Reports Server (NTRS)

Bune, Andris V.; Gillies, Donald C.; Lehoczky, Sandor L.

1997-01-01

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Uniform tissue lesion formation induced by high-intensity focused ultrasound along a spiral pathway.

PubMed

Qian, Kui; Li, Chenghai; Ni, Zhengyang; Tu, Juan; Guo, Xiasheng; Zhang, Dong

2017-05-01

Both theoretical and experimental studies were performed here to investigate the lesion formation induced by high-intensity focused ultrasound (HIFU) operating in continuous scanning mode along a spiral pathway. The Khokhlov-Zabolotskaya-Kuznetsov equation and bio-heat equation were combined in the current model to predict HIFU-induced temperature distribution and lesion formation. The shape of lesion and treatment efficiency were assessed for a given scanning speed at two different grid spacing (3mm and 4mm) in the gel phantom studies and further researched in ex vivo studies. The results show that uniform lesions can be generated with continuous HIFU scanning along a spiral pathway. The complete coverage of the entire treated volume can be achieved as long as the spacing grid of the spiral pathway is small enough for heat to diffuse and deposit, and the treatment efficiency can be optimized by selecting an appropriate scanning speed. This study can provide guidance for further optimization of the treatment efficiency and safety of HIFU therapy. Copyright © 2017 Elsevier B.V. All rights reserved.

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1977-01-01

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

Scaling for the SOL/separatrix χ ⊥ following from the heuristic drift model for the power scrape-off layer width

NASA Astrophysics Data System (ADS)

Huber, A.; Chankin, A. V.

2017-06-01

A simple two-point representation of the tokamak scrape-off layer (SOL) in the conduction limited regime, based on the parallel and perpendicular energy balance equations in combination with the heat flux width predicted by a heuristic drift-based model, was used to derive a scaling for the cross-field thermal diffusivity {χ }\\perp . For fixed plasma shape and neglecting weak power dependence indexes 1/8, the scaling {χ }\\perp \\propto {P}{{S}{{O}}{{L}}}/(n{B}θ {R}2) is derived.

Investigation of parabolic computational techniques for internal high-speed viscous flows

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Power, G. D.

1985-01-01

A feasibility study was conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves were present. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Non-equilibrium radiation from viscous chemically reacting two-phase exhaust plumes

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Mikatarian, R. R.; Ring, L. R.; Anderson, P. G.

1976-01-01

A knowledge of the structure of the rocket exhaust plumes is necessary to solve problems involving plume signatures, base heating, plume/surface interactions, etc. An algorithm is presented which treats the viscous flow of multiphase chemically reacting fluids in a two-dimensional or axisymmetric supersonic flow field. The gas-particle flow solution is fully coupled with the chemical kinetics calculated using an implicit scheme to calculate chemical production rates. Viscous effects include chemical species diffusion with the viscosity coefficient calculated using a two-equation turbulent kinetic energy model.

Fundamental Thermal and Mechanical Properties of Boride Ceramics

DTIC Science & Technology

2014-02-28

Zr ,Y)B2 ( Zr ,Hf)B2 ( Zr ,Ti)B2 ZrB2 El ec tri ca l R es is tiv ity (µ Ω -c m ) Temperature (°C) Figure 17. Electrical resistivity as a function...family as Zr , namely Ti and Hf, had minimal effect on thermal conductivity, while others such as Nb , Ta, and W had an increasing impact based on their...diffusivity (α), heat capacity (Cp) from the NIST-JANAF tables, and bulk density (ρ) using Equation 6. (5) (6) Electrical resistivity

CFD-ACE+: a CAD system for simulation and modeling of MEMS

NASA Astrophysics Data System (ADS)

Stout, Phillip J.; Yang, H. Q.; Dionne, Paul; Leonard, Andy; Tan, Zhiqiang; Przekwas, Andrzej J.; Krishnan, Anantha

1999-03-01

Computer aided design (CAD) systems are a key to designing and manufacturing MEMS with higher performance/reliability, reduced costs, shorter prototyping cycles and improved time- to-market. One such system is CFD-ACE+MEMS, a modeling and simulation environment for MEMS which includes grid generation, data visualization, graphical problem setup, and coupled fluidic, thermal, mechanical, electrostatic, and magnetic physical models. The fluid model is a 3D multi- block, structured/unstructured/hybrid, pressure-based, implicit Navier-Stokes code with capabilities for multi- component diffusion, multi-species transport, multi-step gas phase chemical reactions, surface reactions, and multi-media conjugate heat transfer. The thermal model solves the total enthalpy from of the energy equation. The energy equation includes unsteady, convective, conductive, species energy, viscous dissipation, work, and radiation terms. The electrostatic model solves Poisson's equation. Both the finite volume method and the boundary element method (BEM) are available for solving Poisson's equation. The BEM method is useful for unbounded problems. The magnetic model solves for the vector magnetic potential from Maxwell's equations including eddy currents but neglecting displacement currents. The mechanical model is a finite element stress/deformation solver which has been coupled to the flow, heat, electrostatic, and magnetic calculations to study flow, thermal electrostatically, and magnetically included deformations of structures. The mechanical or structural model can accommodate elastic and plastic materials, can handle large non-linear displacements, and can model isotropic and anisotropic materials. The thermal- mechanical coupling involves the solution of the steady state Navier equation with thermoelastic deformation. The electrostatic-mechanical coupling is a calculation of the pressure force due to surface charge on the mechanical structure. Results of CFD-ACE+MEMS modeling of MEMS such as cantilever beams, accelerometers, and comb drives are discussed.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Modern aspects of homogeneous-heterogeneous reactions and variable thickness in nanofluids through carbon nanotubes

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Ahmed, Sohail; Muhammad, Taseer; Alsaedi, Ahmed

2017-10-01

This article examines homogeneous-heterogeneous reactions and internal heat generation in Darcy-Forchheimer flow of nanofluids with different base fluids. Flow is generated due to a nonlinear stretchable surface of variable thickness. The characteristics of nanofluid are explored using CNTs (single and multi walled carbon nanotubes). Equal diffusion coefficients are considered for both reactants and auto catalyst. The conversion of partial differential equations (PDEs) to ordinary differential equations (ODEs) is done via appropriate transformations. Optimal homotopy approach is implemented for solutions development of governing problems. Averaged square residual errors are computed. The optimal solution expressions of velocity, temperature and concentration are explored through plots by using several values of physical parameters. Further the coefficient of skin friction and local Nusselt number are examined through graphs.

The effect of water on thermal stresses in polymer composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

1994-01-01

The fundamentals of the thermodynamic theory of mixtures and continuum thermochemistry are reviewed for a mixture of condensed water and polymer. A specific mixture which is mechanically elastic with temperature and water concentration gradients present is considered. An expression for the partial pressure of water in the mixture is obtained based on certain assumptions regarding the thermodynamic state of the water in the mixture. Along with a simple diffusion equation, this partial pressure expression may be used to simulate the thermostructural behavior of polymer composite materials due to water in the free volumes of the polymer. These equations are applied to a specific polymer composite material during isothermal heating conditions. The thermal stresses obtained by the application of the theory are compared to measured results to verify the accuracy of the approach.

Geophysical aspects of underground fluid dynamics and mineral transformation process

NASA Astrophysics Data System (ADS)

Khramchenkov, Maxim; Khramchenkov, Eduard

2014-05-01

The description of processes of mass exchange between fluid and poly-minerals material in porous media from various kinds of rocks (primarily, sedimentary rocks) have been examined. It was shown that in some important cases there is a storage equation of non-linear diffusion equation type. In addition, process of filtration in un-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and particles material were considered. In the latter case equations of physical-chemical mechanics of conservation of mass for fluid and particles material were used. As it is well known, the mechanics of porous media is theoretical basis of such branches of science as rock mechanics, soil physics and so on. But at the same moment some complex processes in the geosystems lacks full theoretical description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The process of rocks consolidation which happens due to filtration of underground fluids is described from the position of rock mechanics. As an additional impact, let us consider the porous media consolidating under the weight of overlying rock with coupled complex geological processes, as a continuous porous medium of variable mass. Problems of obtaining of correct storage equations for coupled processes of consolidation and mass exchange between underground fluid and skeleton material are often met in catagenesi processes description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The present work is dedicated to the retrieval of new ways to formulate and construct such models. It was shown that in some important cases there is a governing equation of non-linear diffusion equation type (well-known Fisher equation). In addition, some geophysical aspects of filtration process in usual non-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and skeleton material, including earth quakes, are considered.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Air cycle machine for an aircraft environmental control system

NASA Technical Reports Server (NTRS)

Decrisantis, Angelo A. (Inventor); O'Coin, James R. (Inventor); Taddey, Edmund P. (Inventor)

2010-01-01

An ECS system includes an ACM mounted adjacent an air-liquid heat exchanger through a diffuser that contains a diffuser plate. The diffuser plate receives airflow from the ACM which strikes the diffuser plate and flows radially outward and around the diffuser plate and into the air-liquid heat exchanger to provide minimal pressure loss and proper flow distribution into the air-liquid heat exchanger with significantly less packaging space.

A local heat transfer analysis of lava cooling in the atmosphere: application to thermal diffusion-dominated lava flows

NASA Astrophysics Data System (ADS)

Neri, Augusto

1998-05-01

The local cooling process of thermal diffusion-dominated lava flows in the atmosphere was studied by a transient, one-dimensional heat transfer model taking into account the most relevant processes governing its behavior. Thermal diffusion-dominated lava flows include any type of flow in which the conductive-diffusive contribution in the energy equation largely overcomes the convective terms. This type of condition is supposed to be satisfied, during more or less extended periods of time, for a wide range of lava flows characterized by very low flow-rates, such as slabby and toothpaste pahoehoe, spongy pahoehoe, flow at the transition pahoehoe-aa, and flows from ephemeral vents. The analysis can be useful for the understanding of the effect of crust formation on the thermal insulation of the lava interior and, if integrated with adequate flow models, for the explanation of local features and morphologies of lava flows. The study is particularly aimed at a better knowledge of the complex non-linear heat transfer mechanisms that control lava cooling in the atmosphere and at the estimation of the most important parameters affecting the global heat transfer coefficient during the solidification process. The three fundamental heat transfer mechanisms with the atmosphere, that is radiation, natural convection, and forced convection by the wind, were modeled, whereas conduction and heat generation due to crystallization were considered within the lava. The magma was represented as a vesiculated binary melt with a given liquidus and solidus temperature and with the possible presence of a eutectic. The effects of different morphological features of the surface were investigated through a simplified description of their geometry. Model results allow both study of the formation in time of the crust and the thermal mushy layer underlying it, and a description of the behavior of the temperature distribution inside the lava as well as radiative and convective fluxes to the atmosphere. The analysis, performed by using parameters typical of Etnean lavas, particularly focuses on the non-intuitive relations between superficial cooling effects and inner temperature distribution as a function of the major variables involved in the cooling process. Results integrate recent modelings and measurements of the cooling process of Hawaiian pahoehoe flow lobes by Hon et al. (1994) and Keszthelyi and Denlinger (1996) and highlight the critical role played by surface morphology, lava thermal properties, and crystallization dynamics. Furthermore, the reported description of the various heat fluxes between lava and atmosphere can be extended to any other type of lava flows in which atmospheric cooling is involved.

Characterization of supersonic radiation diffusion waves

DOE PAGES

Moore, Alastair S.; Guymer, Thomas M.; Morton, John; ...

2015-02-27

Supersonic and diffusive radiation flow is an important test problem for the radiative transfer models used in radiation-hydrodynamics computer codes owing to solutions being accessible via analytic and numeric methods. We present experimental results with which we compare these solutions by studying supersonic and diffusive flow in the laboratory. Here, we present results of higher-accuracy experiments than previously possible studying radiation flow through up to 7 high-temperature mean free paths of low-density, chlorine-doped polystyrene foam and silicon dioxide aerogel contained by an Au tube. Measurements of the heat front position and absolute measurements of the x-ray emission arrival at themore » end of the tube are used to test numerical and analytical models. We find excellent absolute agreement with simulations provided that the opacity and the equation of state are adjusted within expected uncertainties; analytical models provide a good phenomenological match to measurements but are not in quantitative agreement due to their limited scope.« less

Characterization of supersonic radiation diffusion waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moore, Alastair S.; Guymer, Thomas M.; Morton, John

Supersonic and diffusive radiation flow is an important test problem for the radiative transfer models used in radiation-hydrodynamics computer codes owing to solutions being accessible via analytic and numeric methods. We present experimental results with which we compare these solutions by studying supersonic and diffusive flow in the laboratory. Here, we present results of higher-accuracy experiments than previously possible studying radiation flow through up to 7 high-temperature mean free paths of low-density, chlorine-doped polystyrene foam and silicon dioxide aerogel contained by an Au tube. Measurements of the heat front position and absolute measurements of the x-ray emission arrival at themore » end of the tube are used to test numerical and analytical models. We find excellent absolute agreement with simulations provided that the opacity and the equation of state are adjusted within expected uncertainties; analytical models provide a good phenomenological match to measurements but are not in quantitative agreement due to their limited scope.« less

Anisotropic Thermal Diffusion

NASA Astrophysics Data System (ADS)

Gardiner, Thomas

2013-10-01

Anisotropic thermal diffusion in magnetized plasmas is an important physical phenomena for a diverse set of physical conditions ranging from astrophysical plasmas to MFE and ICF. Yet numerically simulating this phenomenon accurately poses significant challenges when the computational mesh is misaligned with respect to the magnetic field. Particularly when the temperature gradients are unresolved, one frequently finds entropy violating solutions with heat flowing from cold to hot zones for χ∥ /χ⊥ >=102 which is substantially smaller than the range of interest which can reach 1010 or higher. In this talk we present a new implicit algorithm for solving the anisotropic thermal diffusion equations and demonstrate its characteristics on what has become a fairly standard set of test problems in the literature. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. SAND2013-5687A.

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

Multi-step cure kinetic model of ultra-thin glass fiber epoxy prepreg exhibiting both autocatalytic and diffusion-controlled regimes under isothermal and dynamic-heating conditions

NASA Astrophysics Data System (ADS)

Kim, Ye Chan; Min, Hyunsung; Hong, Sungyong; Wang, Mei; Sun, Hanna; Park, In-Kyung; Choi, Hyouk Ryeol; Koo, Ja Choon; Moon, Hyungpil; Kim, Kwang J.; Suhr, Jonghwan; Nam, Jae-Do

2017-08-01

As packaging technologies are demanded that reduce the assembly area of substrate, thin composite laminate substrates require the utmost high performance in such material properties as the coefficient of thermal expansion (CTE), and stiffness. Accordingly, thermosetting resin systems, which consist of multiple fillers, monomers and/or catalysts in thermoset-based glass fiber prepregs, are extremely complicated and closely associated with rheological properties, which depend on the temperature cycles for cure. For the process control of these complex systems, it is usually required to obtain a reliable kinetic model that could be used for the complex thermal cycles, which usually includes both the isothermal and dynamic-heating segments. In this study, an ultra-thin prepreg with highly loaded silica beads and glass fibers in the epoxy/amine resin system was investigated as a model system by isothermal/dynamic heating experiments. The maximum degree of cure was obtained as a function of temperature. The curing kinetics of the model prepreg system exhibited a multi-step reaction and a limited conversion as a function of isothermal curing temperatures, which are often observed in epoxy cure system because of the rate-determining diffusion of polymer chain growth. The modified kinetic equation accurately described the isothermal behavior and the beginning of the dynamic-heating behavior by integrating the obtained maximum degree of cure into the kinetic model development.

Onset of fractional-order thermal convection in porous media

NASA Astrophysics Data System (ADS)

Karani, Hamid; Rashtbehesht, Majid; Huber, Christian; Magin, Richard L.

2017-12-01

The macroscopic description of buoyancy-driven thermal convection in porous media is governed by advection-diffusion processes, which in the presence of thermophysical heterogeneities fail to predict the onset of thermal convection and the average rate of heat transfer. This work extends the classical model of heat transfer in porous media by including a fractional-order advective-dispersive term to account for the role of thermophysical heterogeneities in shifting the thermal instability point. The proposed fractional-order model overcomes limitations of the common closure approaches for the thermal dispersion term by replacing the diffusive assumption with a fractional-order model. Through a linear stability analysis and Galerkin procedure, we derive an analytical formula for the critical Rayleigh number as a function of the fractional model parameters. The resulting critical Rayleigh number reduces to the classical value in the absence of thermophysical heterogeneities when solid and fluid phases have similar thermal conductivities. Numerical simulations of the coupled flow equation with the fractional-order energy model near the primary bifurcation point confirm our analytical results. Moreover, data from pore-scale simulations are used to examine the potential of the proposed fractional-order model in predicting the amount of heat transfer across the porous enclosure. The linear stability and numerical results show that, unlike the classical thermal advection-dispersion models, the fractional-order model captures the advance and delay in the onset of convection in porous media and provides correct scalings for the average heat transfer in a thermophysically heterogeneous medium.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Studies on free stream turbulence as related to gas turbine heat transfer. A review of authors' past work and future implications.

PubMed

Yavuzkurt, S; Iyer, G R

2001-05-01

A review of the past work done on free stream turbulence (FST) as applied to gas turbine heat transfer and its implications for future studies are presented. It is a comprehensive approach to the results of many individual studies in order to derive the general conclusions that could be inferred from all rather than discussing the results of each individual study. Three experimental and four modeling studies are reviewed. The first study was on prediction of heat transfer for film cooled gas turbine blades. An injection model was devised and used along with a 2-D low Reynolds number k-epsilon model of turbulence for the calculations. Reasonable predictions of heat transfer coefficients were obtained for turbulence intensity levels up to 7%. Following this modeling study a series of experimental studies were undertaken. The objective of these studies was to gain a fundamental understanding of mechanisms through which FST augments the surface heat transfer. Experiments were carried out in the boundary layer and in the free stream downstream of a gas turbine combustor simulator, which produced initial FST levels of 25.7% and large length scales (About 5-10 cm for a boundary layer 4-5 cm thick). This result showed that one possible mechanism through which FST caused an increase in heat transfer is by increasing the number of ejection events. In a number of modeling studies several well-known k-epsilon models were compared for their predictive capability of heat transfer and skin friction coefficients under moderate and high FST. Two data sets, one with moderate levels of FST (about 7%) and one with high levels of FST (about 25%) were used for this purpose. Although the models did fine in their predictions of cases with no FST (baseline cases) they failed one by one as FST levels were increased. Under high FST (25.7% initial intensity) predictions of Stanton number were between 35-100% in error compared to the measured values. Later a new additional production term indicating the interaction between the turbulent kinetic energy (TKE) and mean velocity gradients was introduced into the TKE equation. The predicted results of skin friction coefficient and Stanton number were excellent both in moderate and high FST cases. In fact these model also gave good predictions of TKE profiles whereas earlier unmodified models did not predict the correct TKE profiles even under moderate turbulence intensities. Although this new production term seems to achieve the purpose, it is the authors' belief that it is diffusion term of the TKE equation, which needs to be modified in order to fit the physical events in high FST boundary layer flows. The results of these studies are currently being used to come up with new diffusion model for the TKE equation.

Convective thinning of the lithosphere - A mechanism for the initiation of continental rifting

NASA Technical Reports Server (NTRS)

Spohn, T.; Schubert, G.

1982-01-01

A model of lithospheric thinning, in which heat is convected to the base and conducted within the lithosphere, is presented. An analytical equation for determinining the amount of thinning attainable on increasing the heat flux from the asthenosphere is derived, and a formula for lithosphere thickness approximations as a function of time is given. Initial and final equilibrium thicknesses, thermal diffusivity, transition temperature profile, and plume temperature profile are all factors considered for performing rate of thinning determinations. In addition, between initial and final equilibrium states, lithospheric thinning occurs at a rate which is inversely proportional to the square root of the time. Finally, uplift resulting from thermal expansion upon lithospheric thinning is on the order of 10 to the 2nd to 10 to the 3rd m.

Experimental study of the thermal-acoustic efficiency in a long turbulent diffusion-flame burner

NASA Technical Reports Server (NTRS)

Mahan, J. R.

1983-01-01

An acoustic source/propagation model is used to interpret measured noise spectra from a long turbulent burner. The acoustic model is based on the perturbation solution of the equations describing the unsteady one-dimensional flow of an inviscid ideal gas with a distributed heat source. The model assumes that the measured noise spectra are due uniquely to the unsteady component of combustion heat release. The model was applied to a long cylindrical hydrogen burner operating over a range of power levels between 4.5 kW and 22.3 kW. Acoustic impedances at the inlet to the burner and at the exit of the tube downstream of the burner were measured and are used as boundary conditions for the model. These measured impedances are also presented.

Porosity Measurement in Laminated Composites by Thermography and FEA

NASA Technical Reports Server (NTRS)

Chu, Tsuchin Philip; Russell, Samuel S.; Walker, James L.; Munafo, Paul M. (Technical Monitor)

2001-01-01

This paper presents the correlation between the through-thickness thermal diffusivity and the porosity of composites. Finite element analysis (FEA) was used to determine the transient thermal response of composites that were subjected to laser heating. A series of finite element models were built and thermal responses for isotropic and orthographic materials with various thermal diffusivities subjected to different heating conditions were investigated. Experiments were conducted to verify the models and to estimate the unknown parameters such as the amount of heat flux. The analysis and experimental results show good correlation between thermal diffusivity and porosity in the composite materials. They also show that both laser and flash heating can be used effectively to obtain thermal diffusivity. The current infrared thermography system is developed for use with flash heating. The laser heating models and the FEA results can provide useful tools to develop practical thermal diffusivity measurement scheme using laser heat.

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

NASA Astrophysics Data System (ADS)

Shamshuddin, MD.; Anwar Bég, O.; Sunder Ram, M.; Kadir, A.

2018-02-01

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic, incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Modelling wildland fire propagation by tracking random fronts

NASA Astrophysics Data System (ADS)

Pagnini, G.; Mentrelli, A.

2013-11-01

Wildland fire propagation is studied in literature by two alternative approaches, namely the reaction-diffusion equation and the level-set method. These two approaches are considered alternative each other because the solution of the reaction-diffusion equation is generally a continuous smooth function that has an exponential decay and an infinite support, while the level-set method, which is a front tracking technique, generates a sharp function with a finite support. However, these two approaches can indeed be considered complementary and reconciled. Turbulent hot-air transport and fire spotting are phenomena with a random character that are extremely important in wildland fire propagation. As a consequence the fire front gets a random character, too. Hence a tracking method for random fronts is needed. In particular, the level-set contourn is here randomized accordingly to the probability density function of the interface particle displacement. Actually, when the level-set method is developed for tracking a front interface with a random motion, the resulting averaged process emerges to be governed by an evolution equation of the reaction-diffusion type. In this reconciled approach, the rate of spread of the fire keeps the same key and characterizing role proper to the level-set approach. The resulting model emerges to be suitable to simulate effects due to turbulent convection as fire flank and backing fire, the faster fire spread because of the actions by hot air pre-heating and by ember landing, and also the fire overcoming a firebreak zone that is a case not resolved by models based on the level-set method. Moreover, from the proposed formulation it follows a correction for the rate of spread formula due to the mean jump-length of firebrands in the downwind direction for the leeward sector of the fireline contour.

A new thermal model for bone drilling with applications to orthopaedic surgery.

PubMed

Lee, JuEun; Rabin, Yoed; Ozdoganlar, O Burak

2011-12-01

This paper presents a new thermal model for bone drilling with applications to orthopaedic surgery. The new model combines a unique heat-balance equation for the system of the drill bit and the chip stream, an ordinary heat diffusion equation for the bone, and heat generation at the drill tip, arising from the cutting process and friction. Modeling of the drill bit-chip stream system assumes an axial temperature distribution and a lumped heat capacity effect in the transverse cross-section. The new model is solved numerically using a tailor-made finite-difference scheme for the drill bit-chip stream system, coupled with a classic finite-difference method for the bone. The theoretical investigation addresses the significance of heat transfer between the drill bit and the bone, heat convection from the drill bit to the surroundings, and the effect of the initial temperature of the drill bit on the developing thermal field. Using the new model, a parametric study on the effects of machining conditions and drill-bit geometries on the resulting temperature field in the bone and the drill bit is presented. Results of this study indicate that: (1) the maximum temperature in the bone decreases with increased chip flow; (2) the transient temperature distribution is strongly influenced by the initial temperature; (3) the continued cooling (irrigation) of the drill bit reduces the maximum temperature even when the tip is distant from the cooled portion of the drill bit; and (4) the maximum temperature increases with increasing spindle speed, increasing feed rate, decreasing drill-bit diameter, increasing point angle, and decreasing helix angle. The model is expected to be useful in determination of optimum drilling conditions and drill-bit geometries. Copyright © 2011. Published by Elsevier Ltd.

Diffusion of chemically reactive species in MHD oscillatory flow with thermal radiation in the presence of constant suction and injection

NASA Astrophysics Data System (ADS)

Sasikumar, J.; Bhuvaneshwari, S.; Govindarajan, A.

2018-04-01

In this project, it is proposed to investigate the effect of suction/injection on the unsteady oscillatory flow of an incompressible viscous electrically conducting fluid through a channel filled with porous medium and non-uniform wall temperature. The fluid is subjected to a uniform magnetic field normal to the channel and the velocity slip at the cold plate is taken into consideration. With the assumption of magnetic Reynolds number to be very small, the induced magnetic field is neglected. Assuming pressure gradient to be oscillatory across the ends of the channel, resulting flow as unsteady oscillatory flow. Under the usual Bousinessq approximation, a mathematical model representing this fluid flow consisting of governing equations with boundary conditions will be developed. Closed form solutions of the dimensionless governing equations of the fluid flow, namely momentum equation, energy equation and species concentration can be obtained . The effects of heat radiation and chemical reaction with suction and injection on temperature, velocity and species concentration profiles will be analysed with tables and graphs.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames. Volume 4

NASA Technical Reports Server (NTRS)

Ku, Jerry C.; Tong, Li; Greenberg, Paul S.

1996-01-01

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

New approaches in the indirect quantification of thermal rock properties in sedimentary basins: the well-log perspective

NASA Astrophysics Data System (ADS)

Fuchs, Sven; Balling, Niels; Förster, Andrea

2016-04-01

Numerical temperature models generated for geodynamic studies as well as for geothermal energy solutions heavily depend on rock thermal properties. Best practice for the determination of those parameters is the measurement of rock samples in the laboratory. Given the necessity to enlarge databases of subsurface rock parameters beyond drill core measurements an approach for the indirect determination of these parameters is developed, for rocks as well a for geological formations. We present new and universally applicable prediction equations for thermal conductivity, thermal diffusivity and specific heat capacity in sedimentary rocks derived from data provided by standard geophysical well logs. The approach is based on a data set of synthetic sedimentary rocks (clastic rocks, carbonates and evaporates) composed of mineral assemblages with variable contents of 15 major rock-forming minerals and porosities varying between 0 and 30%. Petrophysical properties are assigned to both the rock-forming minerals and the pore-filling fluids. Using multivariate statistics, relationships then were explored between each thermal property and well-logged petrophysical parameters (density, sonic interval transit time, hydrogen index, volume fraction of shale and photoelectric absorption index) on a regression sub set of data (70% of data) (Fuchs et al., 2015). Prediction quality was quantified on the remaining test sub set (30% of data). The combination of three to five well-log parameters results in predictions on the order of <15% for thermal conductivity and thermal diffusivity, and of <10% for specific heat capacity. Comparison of predicted and benchmark laboratory thermal conductivity from deep boreholes of the Norwegian-Danish Basin, the North German Basin, and the Molasse Basin results in 3 to 5% larger uncertainties with regard to the test data set. With regard to temperature models, the use of calculated TC borehole profiles approximate measured temperature logs with an error of <3°C along a 4 km deep profile. A benchmark comparison for thermal diffusivity and specific heat capacity is pending. Fuchs, Sven; Balling, Niels; Förster, Andrea (2015): Calculation of thermal conductivity, thermal diffusivity and specific heat capacity of sedimentary rocks using petrophysical well logs, Geophysical Journal International 203, 1977-2000, doi: 10.1093/gji/ggv403

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

On Diffusive Climatological Models.

NASA Astrophysics Data System (ADS)

Griffel, D. H.; Drazin, P. G.

1981-11-01

A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.

Symmetry methods for option pricing

NASA Astrophysics Data System (ADS)

Davison, A. H.; Mamba, S.

2017-06-01

We obtain a solution of the Black-Scholes equation with a non-smooth boundary condition using symmetry methods. The Black-Scholes equation along with its boundary condition are first transformed into the one dimensional heat equation and an initial condition respectively. We then find an appropriate general symmetry generator of the heat equation using symmetries and the fundamental solution of the heat equation. The symmetry generator is chosen such that the boundary condition is left invariant; the symmetry can be used to solve the heat equation and hence the Black-Scholes equation.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

A theoretically based determination of bowen-ratio fetch requirements

USGS Publications Warehouse

Stannard, D.I.

1997-01-01

Determination of fetch requirements for accurate Bowen-ratio measurements of latent- and sensible-heat fluxes is more involved than for eddy-correlation measurements because Bowen-ratio sensors are located at two heights, rather than just one. A simple solution to the diffusion equation is used to derive an expression for Bowen-ratio fetch requirements, downwind of a step change in surface fluxes. These requirements are then compared to eddy-correlation fetch requirements based on the same diffusion equation solution. When the eddy-correlation and upper Bowen-ratio sensor heights are equal, and the available energy upwind and downwind of the step change is constant, the Bowen-ratio method requires less fetch than does eddy correlation. Differences in fetch requirements between the two methods are greatest over relatively smooth surfaces. Bowen-ratio fetch can be reduced significantly by lowering the lower sensor, as well as the upper sensor. The Bowen-ratio fetch model was tested using data from a field experiment where multiple Bowen-ratio systems were deployed simultaneously at various fetches and heights above a field of bermudagrass. Initial comparisons were poor, but improved greatly when the model was modified (and operated numerically) to account for the large roughness of the upwind cotton field.

G-Jitter Induced Magnetohydrodynamics Flow of Nanofluid with Constant Convective Thermal and Solutal Boundary Conditions

PubMed Central

Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmad Izani Md.

2015-01-01

Taking into account the effect of constant convective thermal and mass boundary conditions, we present numerical solution of the 2-D laminar g-jitter mixed convective boundary layer flow of water-based nanofluids. The governing transport equations are converted into non-similar equations using suitable transformations, before being solved numerically by an implicit finite difference method with quasi-linearization technique. The skin friction decreases with time, buoyancy ratio, and thermophoresis parameters while it increases with frequency, mixed convection and Brownian motion parameters. Heat transfer rate decreases with time, Brownian motion, thermophoresis and diffusion-convection parameters while it increases with the Reynolds number, frequency, mixed convection, buoyancy ratio and conduction-convection parameters. Mass transfer rate decreases with time, frequency, thermophoresis, conduction-convection parameters while it increases with mixed convection, buoyancy ratio, diffusion-convection and Brownian motion parameters. To the best of our knowledge, this is the first paper on this topic and hence the results are new. We believe that the results will be useful in designing and operating thermal fluids systems for space materials processing. Special cases of the results have been compared with published results and an excellent agreement is found. PMID:25933066

Verification and Validation of a Coordinate Transformation Method in Axisymmetric Transient Magnetics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ashcraft, C. Chace; Niederhaus, John Henry; Robinson, Allen C.

We present a verification and validation analysis of a coordinate-transformation-based numerical solution method for the two-dimensional axisymmetric magnetic diffusion equation, implemented in the finite-element simulation code ALEGRA. The transformation, suggested by Melissen and Simkin, yields an equation set perfectly suited for linear finite elements and for problems with large jumps in material conductivity near the axis. The verification analysis examines transient magnetic diffusion in a rod or wire in a very low conductivity background by first deriving an approximate analytic solution using perturbation theory. This approach for generating a reference solution is shown to be not fully satisfactory. A specializedmore » approach for manufacturing an exact solution is then used to demonstrate second-order convergence under spatial refinement and tem- poral refinement. For this new implementation, a significant improvement relative to previously available formulations is observed. Benefits in accuracy for computed current density and Joule heating are also demonstrated. The validation analysis examines the circuit-driven explosion of a copper wire using resistive magnetohydrodynamics modeling, in comparison to experimental tests. The new implementation matches the accuracy of the existing formulation, with both formulations capturing the experimental burst time and action to within approximately 2%.« less

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter systems

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1990-01-01

The convergence of solutions to the discrete or sampled time linear quadratic regulator problem and associated Riccati equation for infinite dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero (infinity) is established. Both the finite and infinite time horizon problems are studied. In the finite time horizon case, strong continuity of the operators which define the control system and performance index together with a stability and consistency condition on the sampling scheme are required. For the infinite time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary of delay system, and a flexible beam are presented and discussed.

1/f Noise Inside a Faraday Cage

NASA Astrophysics Data System (ADS)

Handel, Peter H.; George, Thomas F.

2009-04-01

We show that quantum 1/f noise does not have a lower frequency limit given by the lowest free electromagnetic field mode in a Faraday cage, even in an ideal cage. Indeed, quantum 1/f noise comes from the infrared-divergent coupling of the field with the charges, in their joint nonlinear system, where the charges cause the field that reacts back on the charges, and so on. This low-frequency limitation is thus not applicable for the nonlinear system of matter and field in interaction. Indeed, this nonlinear system is governed by Newton's laws, Maxwell's equations, in general also by the diffusion equations for particles and heat, or reaction kinetics given by quantum matrix elements. Nevertheless, all the other quantities can be eliminated in principle, resulting in highly nonlinear integro-differential equations for the electromagnetic field only, which no longer yield a fundamental frequency. Alternatively, we may describe this through the presence of an infinite system of subharmonics. We show how this was proven early in the classical and quantum domains, adding new insight.

On the continuous dependence with respect to sampling of the linear quadratic regulator problem for distributed parameter system

NASA Technical Reports Server (NTRS)

Rosen, I. G.; Wang, C.

1992-01-01

The convergence of solutions to the discrete- or sampled-time linear quadratic regulator problem and associated Riccati equation for infinite-dimensional systems to the solutions to the corresponding continuous time problem and equation, as the length of the sampling interval (the sampling rate) tends toward zero(infinity) is established. Both the finite-and infinite-time horizon problems are studied. In the finite-time horizon case, strong continuity of the operators that define the control system and performance index, together with a stability and consistency condition on the sampling scheme are required. For the infinite-time horizon problem, in addition, the sampled systems must be stabilizable and detectable, uniformly with respect to the sampling rate. Classes of systems for which this condition can be verified are discussed. Results of numerical studies involving the control of a heat/diffusion equation, a hereditary or delay system, and a flexible beam are presented and discussed.

Projecting diffusion along the normal bundle of a plane curve

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Transient Numerical Modeling of Catalytic Channels

NASA Technical Reports Server (NTRS)

Struk, Peter M.; Dietrich, Daniel L.; Miller, Fletcher J.; T'ien, James S.

2007-01-01

This paper presents a transient model of catalytic combustion suitable for isolated channels and monolith reactors. The model is a lumped two-phase (gas and solid) model where the gas phase is quasi-steady relative to the transient solid. Axial diffusion is neglected in the gas phase; lateral diffusion, however, is accounted for using transfer coefficients. The solid phase includes axial heat conduction and external heat loss due to convection and radiation. The combustion process utilizes detailed gas and surface reaction models. The gas-phase model becomes a system of stiff ordinary differential equations while the solid phase reduces, after discretization, into a system of stiff ordinary differential-algebraic equations. The time evolution of the system came from alternating integrations of the quasi-steady gas and transient solid. This work outlines the numerical model and presents some sensitivity studies on important parameters including internal transfer coefficients, catalytic surface site density, and external heat-loss (if applicable). The model is compared to two experiments using CO fuel: (1) steady-state conversion through an isothermal platinum (Pt) tube and (2) transient propagation of a catalytic reaction inside a small Pt tube. The model requires internal mass-transfer resistance to match the experiments at lower residence times. Under mass-transport limited conditions, the model reasonably predicted exit conversion using global mass-transfer coefficients. Near light-off, the model results did not match the experiment precisely even after adjustment of mass-transfer coefficients. Agreement improved for the first case after adjusting the surface kinetics such that the net rate of CO adsorption increased compared to O2. The CO / O2 surface mechanism came from a sub-set of reactions in a popular CH4 / O2 mechanism. For the second case, predictions improved for lean conditions with increased external heat loss or adjustment of the kinetics as in the first case. Finally, the results show that different initial surface-species distribution leads to different steady-states under certain conditions. These results demonstrate the utility of a lumped two-phase model of a transient catalytic combustor with detailed chemistry.

A Finite-Orbit-Width Fokker-Planck solver for modeling of energetic particle interactions with waves, with application to Helicons in ITER

NASA Astrophysics Data System (ADS)

Petrov, Yuri V.; Harvey, R. W.

2017-10-01

The bounce-average (BA) finite-difference Fokker-Planck (FP) code CQL3D [1,2] now includes the essential physics to describe the RF heating of Finite-Orbit-Width (FOW) ions in tokamaks. The FP equation is reformulated in terms of Constants-Of-Motion coordinates, which we select to be particle speed, pitch angle, and major radius on the equatorial plane thus obtaining the distribution function directly at this location. Full-orbit, low collisionality neoclassical radial transport emerges from averaging the local friction and diffusion coefficients along guiding center orbits. Similarly, the BA of local quasilinear RF diffusion terms gives rise to additional radial transport. The local RF electric field components needed for the BA operator are usually obtained by a ray-tracing code, such as GENRAY, or in conjunction with full-wave codes. As a new, practical application, the CQL3D-FOW version is used for simulation of alpha-particle heating by high-harmonic waves in ITER. Coupling of high harmonic or helicon fast waves power to electrons is a promising current drive (CD) scenario for high beta plasmas. However, the efficiency of current drive can be diminished by parasitic channeling of RF power into fast ions, such as alphas, through finite Larmor-radius effects. We investigate possibilities to reduce the fast ion heating in CD scenarios.

Applications of a time-dependent polar ionosphere model for radio modification experiments

NASA Astrophysics Data System (ADS)

Fallen, Christopher Thomas

A time-dependent self-consistent ionosphere model (SLIM) has been developed to study the response of the polar ionosphere to radio modification experiments, similar to those conducted at the High-Frequency Active Auroral Research Program (HAARP) facility in Gakona, Alaska. SCIM solves the ion continuity and momentum equations, coupled with average electron and ion gas energy equations; it is validated by reproducing the diurnal variation of the daytime ionosphere critical frequency, as measured with an ionosonde. Powerful high-frequency (HF) electromagnetic waves can drive naturally occurring electrostatic plasma waves, enhancing the ionospheric reflectivity to ultra-high frequency (UHF) radar near the HF-interaction region as well as heating the electron gas. Measurements made during active experiments are compared with model calculations to clarify fundamental altitude-dependent physical processes governing the vertical composition and temperature of the polar ionosphere. The modular UHF ionosphere radar (MUIR), co-located with HAARP, measured HF-enhanced ion-line (HFIL) reflection height and observed that it ascended above its original altitude after the ionosphere had been HF-heated for several minutes. The HFIL ascent is found to follow from HF-induced depletion of plasma surrounding the F-region peak density layer, due to temperature-enhanced transport of atomic oxygen ions along the geomagnetic field line. The lower F-region and topside ionosphere also respond to HF heating. Model results show that electron temperature increases will lead to suppression of molecular ion recombination rates in the lower F region and enhancements of ambipolar diffusion in the topside ionosphere, resulting in a net enhancement of slant total electron content (TEC); these results have been confirmed by experiment. Additional evidence for the model-predicted topside ionosphere density enhancements via ambipolar diffusion is provided by in-situ measurements of ion density and vertical velocity over HAARP made by a Defense Meteorological Satellite Program (DMSP) satellite.

A Harmonic Solution for the Hyperbolic Heat Conduction Equation and Its Relationship to the Guyer-Krumhansl Equation

NASA Astrophysics Data System (ADS)

Zhukovsky, K. V.

2018-01-01

A particular solution of the hyperbolic heat-conduction equation was constructed using the method of operators. The evolution of a harmonic solution is studied, which simulates the propagation of electric signals in long wire transmission lines. The structures of the solutions of the telegraph equation and of the Guyer-Krumhansl equation are compared. The influence of the phonon heat-transfer mechanism in the environment is considered from the point of view of heat conductivity. The fulfillment of the maximum principle for the obtained solutions is considered. The frequency dependences of heat conductivity in the telegraph equation and in an equation of the Guyer-Krumhansl type are studied and compared with each other. The influence of the Knudsen number on heat conductivity in the model of thin films is studied.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion

PubMed Central

Gowrishankar, TR; Stewart, Donald A; Martin, Gregory T; Weaver, James C

2004-01-01

Background Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. Methods We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42°C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. Results The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45°C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. Conclusions The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue. PMID:15548324

Heat Fluxes and Evaporation Measurements by Multi-Function Heat Pulse Probe: a Laboratory Experiment

NASA Astrophysics Data System (ADS)

Sharma, V.; Ciocca, F.; Hopmans, J. W.; Kamai, T.; Lunati, I.; Parlange, M. B.

2012-04-01

Multi Functional Heat Pulse Probes (MFHPP) are multi-needles probes developed in the last years able to measure temperature, thermal properties such as thermal diffusivity and volumetric heat capacity, from which soil moisture is directly retrieved, and electric conductivity (through a Wenner array). They allow the simultaneous measurement of coupled heat, water and solute transport in porous media, then. The use of only one instrument to estimate different quantities in the same volume and almost at the same time significantly reduces the need to interpolate different measurement types in space and time, increasing the ability to study the interdependencies characterizing the coupled transports, especially of water and heat, and water and solute. A three steps laboratory experiment is realized at EPFL to investigate the effectiveness and reliability of the MFHPP responses in a loamy soil from Conthey, Switzerland. In the first step specific calibration curves of volumetric heat capacity and thermal conductivity as function of known volumetric water content are obtained placing the MFHPP in small samplers filled with the soil homogeneously packed at different saturation degrees. The results are compared with literature values. In the second stage the ability of the MFHPP to measure heat fluxes is tested within a homemade thermally insulated calibration box and results are matched with those by two self-calibrating Heatflux plates (from Huxseflux), placed in the same box. In the last step the MFHPP are used to estimate the cumulative subsurface evaporation inside a small column (30 centimeters height per 8 centimeters inner diameter), placed on a scale, filled with the same loamy soil (homogeneously packed and then saturated) and equipped with a vertical array of four MFHPP inserted close to the surface. The subsurface evaporation is calculated from the difference between the net sensible heat and the net heat storage in the volume scanned by the probes, and the values obtained are matched with the overall evaporation, estimated through the scale in terms of weight loss. A numerical model able to solve the coupled heat-moisture diffusive equations is used to interpolate the obtained measures in the second and third step.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

A Non Local Electron Heat Transport Model for Multi-Dimensional Fluid Codes

NASA Astrophysics Data System (ADS)

Schurtz, Guy

2000-10-01

Apparent inhibition of thermal heat flow is one of the most ancient problems in computational Inertial Fusion and flux-limited Spitzer-Harm conduction has been a mainstay in multi-dimensional hydrodynamic codes for more than 25 years. Theoretical investigation of the problem indicates that heat transport in laser produced plasmas has to be considered as a non local process. Various authors contributed to the non local theory and proposed convolution formulas designed for practical implementation in one-dimensional fluid codes. Though the theory, confirmed by kinetic calculations, actually predicts a reduced heat flux, it fails to explain the very small limiters required in two-dimensional simulations. Fokker-Planck simulations by Epperlein, Rickard and Bell [PRL 61, 2453 (1988)] demonstrated that non local effects could lead to a strong reduction of heat flow in two dimensions, even in situations where a one-dimensional analysis suggests that the heat flow is nearly classical. We developed at CEA/DAM a non local electron heat transport model suitable for implementation in our two-dimensional radiation hydrodynamic code FCI2. This model may be envisionned as the first step of an iterative solution of the Fokker-Planck equations; it takes the mathematical form of multigroup diffusion equations, the solution of which yields both the heat flux and the departure of the electron distribution function to the Maxwellian. Although direct implementation of the model is straightforward, formal solutions of it can be expressed in convolution form, exhibiting a three-dimensional tensor propagator. Reduction to one dimension retrieves the original formula of Luciani, Mora and Virmont [PRL 51, 1664 (1983)]. Intense magnetic fields may be generated by thermal effects in laser targets; these fields, as well as non local effects, will inhibit electron conduction. We present simulations where both effects are taken into account and shortly discuss the coupling strategy between them.

Thermal coupling effect on the vortex dynamics of superconducting thin films: time-dependent Ginzburg–Landau simulations

NASA Astrophysics Data System (ADS)

Jing, Ze; Yong, Huadong; Zhou, Youhe

2018-05-01

In this paper, vortex dynamics of superconducting thin films are numerically investigated by the generalized time-dependent Ginzburg–Landau (TDGL) theory. Interactions between vortex motion and the motion induced energy dissipation is considered by solving the coupled TDGL equation and the heat diffusion equation. It is found that thermal coupling has significant effects on the vortex dynamics of superconducting thin films. Branching in the vortex penetration path originates from the coupling between vortex motion and the motion induced energy dissipation. In addition, the environment temperature, the magnetic field ramp rate and the geometry of the superconducting film also greatly influence the vortex dynamic behaviors. Our results provide new insights into the dynamics of superconducting vortices, and give a mesoscopic understanding on the channeling and branching of vortex penetration paths during flux avalanches.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.

2014-09-01

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less

Magnetic pumping of the solar wind

NASA Astrophysics Data System (ADS)

Egedal, Jan; Lichko, Emily; Daughton, William

2015-11-01

The transport of matter and radiation in the solar wind and terrestrial magnetosphere is a complicated problem involving competing processes of charged particles interacting with electric and magnetic fields. Given the rapid expansion of the solar wind, it would be expected that superthermal electrons originating in the corona would cool rapidly as a function of distance to the Sun. However, this is not observed, and various models have been proposed as candidates for heating the solar wind. In the compressional pumping mechanism explored by Fisk and Gloeckler particles are accelerated by random compressions by the interplanetary wave turbulence. This theory explores diffusion due to spatial non-uniformities and provides a mechanism for redistributing particle. For investigation of a related but different heating mechanism, magnetic pumping, in our work we include diffusion of anisotropic features that develops in velocity space. The mechanism allows energy to be transferred to the particles directly from the turbulence. Guided by kinetic simulations a theory is derived for magnetic pumping. At the heart of this work is a generalization of the Parker Equation to capture the role of the pressure anisotropy during the pumping process. Supported by NASA grant NNX15AJ73G.

A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion

NASA Astrophysics Data System (ADS)

Lee, Seungjoon; Kevrekidis, Ioannis G.; Karniadakis, George Em

2017-09-01

Exascale-level simulations require fault-resilient algorithms that are robust against repeated and expected software and/or hardware failures during computations, which may render the simulation results unsatisfactory. If each processor can share some global information about the simulation from a coarse, limited accuracy but relatively costless auxiliary simulator we can effectively fill-in the missing spatial data at the required times by a statistical learning technique - multi-level Gaussian process regression, on the fly; this has been demonstrated in previous work [1]. Based on the previous work, we also employ another (nonlinear) statistical learning technique, Diffusion Maps, that detects computational redundancy in time and hence accelerate the simulation by projective time integration, giving the overall computation a "patch dynamics" flavor. Furthermore, we are now able to perform information fusion with multi-fidelity and heterogeneous data (including stochastic data). Finally, we set the foundations of a new framework in CFD, called patch simulation, that combines information fusion techniques from, in principle, multiple fidelity and resolution simulations (and even experiments) with a new adaptive timestep refinement technique. We present two benchmark problems (the heat equation and the Navier-Stokes equations) to demonstrate the new capability that statistical learning tools can bring to traditional scientific computing algorithms. For each problem, we rely on heterogeneous and multi-fidelity data, either from a coarse simulation of the same equation or from a stochastic, particle-based, more "microscopic" simulation. We consider, as such "auxiliary" models, a Monte Carlo random walk for the heat equation and a dissipative particle dynamics (DPD) model for the Navier-Stokes equations. More broadly, in this paper we demonstrate the symbiotic and synergistic combination of statistical learning, domain decomposition, and scientific computing in exascale simulations.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM- FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

Generation and Sustainment of Plasma Rotation by ICRF Heating

NASA Astrophysics Data System (ADS)

Perkins, F. W.

2000-10-01

When tokamak plasmas are heated by the fundamental minority ion-cyclotron process, they are observed to rotate toroidally, even though this heating process introduces negligable angular momentum. This work proposes and evaluates a physics mechanism which resolves this apparent conflict. The argument has two elements. First, it is assumed that angular momentum transport is governed by a diffusion equation with a v_tor = 0 boundary condition at the plasma surface and a torque-density source. When the source consists of separated regions of positive and negative torque density, a finite central rotation velocity results, even though the volume integrated torque density - the angular momentum input - vanishes. Secondly, ions energized by the ICRF process can generate separated regions of positive and negative torque density. Heating increases their banana widths which leads to radial energetic-particle transport that must be balanced by neutralizing radial currents and a j_rB_pR torque density in the bulk plasma. Additional, comparable torque density results from collisional transfer of mechanical angular momentum from energetic particles to the bulk plasma and particle loss through banana particles impacting the wall. Monte-Carlo calculations utilizing the ORBIT code evaluate all sources of torque density and rigorously assure that no net angular momentum is introduced. Two models of ICRF heating, diffusive and instantaneous, give similar results. When the resonance location is on the LFS, the calculated rotation has the magnitude, profile, and co-current sense of Alcator C-Mod observations. For HFS resonance locations, the model predicts counter-current rotation. Scans of rotational profiles vs. resonance location, initial energy, particle loss, pitch, and qm will be presented as will the location of the velocity shear layer its scaling to a reactor.

Bessel Fourier Orientation Reconstruction (BFOR): An Analytical Diffusion Propagator Reconstruction for Hybrid Diffusion Imaging and Computation of q-Space Indices

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.

2012-01-01

The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853

Closed Form Equations for the Preliminary Design of a Heat-Pipe-Cooled Leading Edge

NASA Technical Reports Server (NTRS)

Glass, David E.

1998-01-01

A set of closed form equations for the preliminary evaluation and design of a heat-pipe-cooled leading edge is presented. The set of equations can provide a leading-edge designer with a quick evaluation of the feasibility of using heat-pipe cooling. The heat pipes can be embedded in a metallic or composite structure. The maximum heat flux, total integrated heat load, and thermal properties of the structure and heat-pipe container are required input. The heat-pipe operating temperature, maximum surface temperature, heat-pipe length, and heat pipe-spacing can be estimated. Results using the design equations compared well with those from a 3-D finite element analysis for both a large and small radius leading edge.

Simulation of chemical-vapor-deposited silicon carbide for a cold wall vertical reactor

NASA Astrophysics Data System (ADS)

Lee, Y. L.; Sanchez, J. M.

1997-07-01

The growth rate of silicon carbide obtained by low-pressure chemical vapor deposition from tetramethylsilane is numerically simulated for a cold wall vertical reactor. The transport equations for momentum, heat, and mass transfer are simultaneously solved by employing the finite volume method. A model for reaction rate is also proposed in order to predict the measured growth rates [A. Figueras, S. Garelik, J. Santiso, R. Rodroguez-Clemente, B. Armas, C. Combescure, R. Berjoan, J.M. Saurel and R. Caplain, Mater. Sci. Eng. B 11 (1992) 83]. Finally, the effects of thermal diffusion on the growth rate are investigated.

Controlled Hydrogen Peroxide Decomposition for a Solid Oxide Fuel Cell (SOFC) Oxidant Source with a Microreactor Model

DTIC Science & Technology

2007-10-01

established assuming first order kinetics weighted via an inputted catalyst mass, Mcat (equation 2). catrxn MCk *−=22OHr (2) The...H2O2 (0-50%w/w) solution heat capacity(J/kg*K) M cat Mcat 0.03 Mass of Catalyst (g) Deffhh2o 7.85E-10 Average effective diffusivity of H2O2 into... Mcat *c Rate Law for Elementary 1st Order Irreversible Reaction (mol/((s*m^3)) r H2O rtb -rt Rate Law for Elementary 1st Order Irreversible Reaction

Boundary conditions for a one-sided numerical model of evaporative instabilities in sessile drops of ethanol on heated substrates

NASA Astrophysics Data System (ADS)

Semenov, Sergey; Carle, Florian; Medale, Marc; Brutin, David

2017-12-01

The work is focused on obtaining boundary conditions for a one-sided numerical model of thermoconvective instabilities in evaporating pinned sessile droplets of ethanol on heated substrates. In the one-sided model, appropriate boundary conditions for heat and mass transfer equations are required at the droplet surface. Such boundary conditions are obtained in the present work based on a derived semiempirical theoretical formula for the total droplet's evaporation rate, and on a two-parametric nonisothermal approximation of the local evaporation flux. The main purpose of these boundary conditions is to be applied in future three-dimensional (3D) one-sided numerical models in order to save a lot of computational time and resources by solving equations only in the droplet domain. Two parameters, needed for the nonisothermal approximation of the local evaporation flux, are obtained by fitting computational results of a 2D two-sided numerical model. Such model is validated here against parabolic flight experiments and the theoretical value of the total evaporation rate. This study combines theoretical, experimental, and computational approaches in convective evaporation of sessile droplets. The influence of the gravity level on evaporation rate and contributions of different mechanisms of vapor transport (diffusion, Stefan flow, natural convection) are shown. The qualitative difference (in terms of developing thermoconvective instabilities) between steady-state and unsteady numerical approaches is demonstrated.

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

A time-dependent model to determine the thermal conductivity of a nanofluid

NASA Astrophysics Data System (ADS)

Myers, T. G.; MacDevette, M. M.; Ribera, H.

2013-07-01

In this paper, we analyse the time-dependent heat equations over a finite domain to determine expressions for the thermal diffusivity and conductivity of a nanofluid (where a nanofluid is a fluid containing nanoparticles with average size below 100 nm). Due to the complexity of the standard mathematical analysis of this problem, we employ a well-known approximate solution technique known as the heat balance integral method. This allows us to derive simple analytical expressions for the thermal properties, which appear to depend primarily on the volume fraction and liquid properties. The model is shown to compare well with experimental data taken from the literature even up to relatively high concentrations and predicts significantly higher values than the Maxwell model for volume fractions approximately >1 %. The results suggest that the difficulty in reproducing the high values of conductivity observed experimentally may stem from the use of a static heat flow model applied over an infinite domain rather than applying a dynamic model over a finite domain.

Electron heating in quasi-perpendicular shocks - A Monte Carlo simulation

NASA Technical Reports Server (NTRS)

Veltri, Pierluigi; Mangeney, Andre; Scudder, Jack D.

1990-01-01

To study the problem of electron heating in quasi-perpendicular shocks, under the combined effects of 'reversible' motion, in the shock electric potential and magnetic field, and wave-particle interactions a diffusion equation was derived, in the drift (adiabatic) approximation and it was solved by using a Monte Carlo method. The results show that most of the observations can be explained within this framework. The simulation has also definitively shown that the electron parallel temperature is determined by the dc electromagnetic field and not by any wave particle induced heating. Wave-particle interactions are effective in smoothing out the large gradients in phase space produced by the 'reversible' motion of the electrons, thus producing a 'cooling' of the electrons. Some constraints on the wave-particle interaction process may be obtained from a detailed comparison between the simulation and observations. In particular, it appears that the adiabatic approximation must be violated in order to explain the observed evolution of the perpendicular temperature.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE PAGES

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; ...

2017-02-21

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Worst case prediction of additives migration from polystyrene for food safety purposes: a model update.

PubMed

Martínez-López, Brais; Gontard, Nathalie; Peyron, Stéphane

2018-03-01

A reliable prediction of migration levels of plastic additives into food requires a robust estimation of diffusivity. Predictive modelling of diffusivity as recommended by the EU commission is carried out using a semi-empirical equation that relies on two polymer-dependent parameters. These parameters were determined for the polymers most used by packaging industry (LLDPE, HDPE, PP, PET, PS, HIPS) from the diffusivity data available at that time. In the specific case of general purpose polystyrene, the diffusivity data published since then shows that the use of the equation with the original parameters results in systematic underestimation of diffusivity. The goal of this study was therefore, to propose an update of the aforementioned parameters for PS on the basis of up to date diffusivity data, so the equation can be used for a reasoned overestimation of diffusivity.

The drag of airplane radiators with special reference to air heating : comparison of theory and experiment

NASA Technical Reports Server (NTRS)

Gothert, B

1939-01-01

This report contains a survey of past radiator research. This report also is intended as a systematic comparison of theoretical and experimental radiator drag, with the object of ascertaining the most important loss sources and their interaction in different cases of installation, and to separate the radiator systems which are amenable to calculation, both as regards axial flow and drag. The sources of loss due to the diffuser are to be looked into closely as in many cases they can be of preeminent magnitude and their customary appraisal, according to Fliegner's formula, does not meet actual conditions. Besides, generally applicable equations and charts are developed for the rapid determination of the heating effect of radiators as regards flow and drag, and then checked by routine tests on hot radiators.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

Characteristic time scales for diffusion processes through layers and across interfaces

NASA Astrophysics Data System (ADS)

Carr, Elliot J.

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Characteristic time scales for diffusion processes through layers and across interfaces.

PubMed

Carr, Elliot J

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Exergy optimization in a steady moving bed heat exchanger.

PubMed

Soria-Verdugo, A; Almendros-Ibáñez, J A; Ruiz-Rivas, U; Santana, D

2009-04-01

This work provides an energy and exergy optimization analysis of a moving bed heat exchanger (MBHE). The exchanger is studied as a cross-flow heat exchanger where one of the phases is a moving granular medium. The optimal MBHE dimensions and the optimal particle diameter are obtained for a range of incoming fluid flow rates. The analyses are carried out over operation data of the exchanger obtained in two ways: a numerical simulation of the steady-state problem and an analytical solution of the simplified equations, neglecting the conduction terms. The numerical simulation considers, for the solid, the convection heat transfer to the fluid and the diffusion term in both directions, and for the fluid only the convection heat transfer to the solid. The results are compared with a well-known analytical solution (neglecting conduction effects) for the temperature distribution in the exchanger. Next, the analytical solution is used to derive an expression for the exergy destruction. The optimal length of the MBHE depends mainly on the flow rate and does not depend on particle diameter unless they become very small (thus increasing sharply the pressure drop). The exergy optimal length is always smaller than the thermal one, although the difference is itself small.

Behaviors and kinetics of toluene adsorption-desorption on activated carbons with varying pore structure.

PubMed

Yang, Xi; Yi, Honghong; Tang, Xiaolong; Zhao, Shunzheng; Yang, Zhongyu; Ma, Yueqiang; Feng, Tiecheng; Cui, Xiaoxu

2018-05-01

This work was undertaken to investigate the behaviors and kinetics of toluene adsorption and desorption on activated carbons with varying pore structure. Five kinds of activated carbon from different raw materials were selected. Adsorption isotherms and breakthrough curves for toluene were measured. Langmuir and Freundlich equations were fitted to the equilibrium data, and the Freundlich equation was more suitable for simulating toluene adsorption. The process consisted of monolayer, multilayer and partial active site adsorption types. The effect of the pore structure of the activated carbons on toluene adsorption capacity was investigated. The quasi-first-order model was more suitable for describing the process than the quasi-second-order model. The adsorption data was also modeled by the internal particle diffusion model and it was found that the adsorption process could be divided into three stages. In the external surface adsorption process, the rate depended on the specific surface area. During the particle diffusion stage, pore structure and volume were the main factors affecting adsorption rate. In the final equilibrium stage, the rate was determined by the ratio of meso- and macro-pores to total pore volume. The rate over the whole adsorption process was dominated by the toluene concentration. The desorption behavior of toluene on activated carbons was investigated, and the process was divided into heat and mass transfer parts corresponding to emission and diffusion mechanisms, respectively. Physical adsorption played the main role during the adsorption process. Copyright © 2017. Published by Elsevier B.V.

The Martian climate and energy balance models with CO2/H2O atmospheres

NASA Technical Reports Server (NTRS)

Hoffert, M. I.

1986-01-01

The analysis begins with a seasonal energy balance model (EBM) for Mars. This is used to compute surface temperature versus x = sin(latitude) and time over the seasonal cycle. The core model also computes the evolving boundaries of the CO2 icecaps, net sublimational/condensation rates, and the resulting seasonal pressure wave. Model results are compared with surface temperature and pressure history data at Viking lander sites, indicating fairly good agreement when meridional heat transport is represented by a thermal diffusion coefficient D approx. 0.015 W/sq. m/K. Condensational wind distributions are also computed. An analytic model of Martian wind circulation is then proposed, as an extension of the EMB, which incorporates vertical wind profiles containing an x-dependent function evaluated by substitution in the equation defining the diffusion coefficient. This leads to a parameterization of D(x) and of the meridional circulation which recovers the high surface winds predicted by dynamic Mars atmosphere models (approx. 10 m/sec). Peak diffusion coefficients, D approx. 0.6 w/sq m/K, are found over strong Hadley zones - some 40 times larger than those of high-latitude baroclinic eddies. When the wind parameterization is used to find streamline patterns over Martian seasons, the resulting picture shows overturning hemispheric Hadley cells crossing the equator during solstices, and attaining peak intensities during the south summer dust storm season, while condensational winds are most important near the polar caps.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer.

PubMed

Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-02-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized " n -diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

PubMed Central

Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-01-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized “n-diffusion theory,” which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system. PMID:28344433

Harmonic Chain with Velocity Flips: Thermalization and Kinetic Theory

NASA Astrophysics Data System (ADS)

Lukkarinen, Jani; Marcozzi, Matteo; Nota, Alessia

2016-12-01

We consider the detailed structure of correlations in harmonic chains with pinning and a bulk velocity flip noise during the heat relaxation phase which occurs on diffusive time scales, for t=O(L^2) where L is the chain length. It has been shown earlier that for non-degenerate harmonic interactions these systems thermalize, and the dominant part of the correlations is given by local thermal equilibrium determined by a temperature profile which satisfies a linear heat equation. Here we are concerned with two new aspects about the thermalization process: the first order corrections in 1 / L to the local equilibrium correlations and the applicability of kinetic theory to study the relaxation process. Employing previously derived explicit uniform estimates for the temperature profile, we first derive an explicit form for the first order corrections to the particle position-momentum correlations. By suitably revising the definition of the Wigner transform and the kinetic scaling limit we derive a phonon Boltzmann equation whose predictions agree with the explicit computation. Comparing the two results, the corrections can be understood as arising from two different sources: a current-related term and a correction to the position-position correlations related to spatial changes in the phonon eigenbasis.

Initial Coupling of the RELAP-7 and PRONGHORN Applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

J. Ortensi; D. Andrs; A.A. Bingham

2012-10-01

Modern nuclear reactor safety codes require the ability to solve detailed coupled neutronic- thermal fluids problems. For larger cores, this implies fully coupled higher dimensionality spatial dynamics with appropriate feedback models that can provide enough resolution to accurately compute core heat generation and removal during steady and unsteady conditions. The reactor analysis code PRONGHORN is being coupled to RELAP-7 as a first step to extend RELAP’s current capabilities. This report details the mathematical models, the type of coupling, and the testing results from the integrated system. RELAP-7 is a MOOSE-based application that solves the continuity, momentum, and energy equations inmore » 1-D for a compressible fluid. The pipe and joint capabilities enable it to model parts of the power conversion unit. The PRONGHORN application, also developed on the MOOSE infrastructure, solves the coupled equations that define the neutron diffusion, fluid flow, and heat transfer in a full core model. The two systems are loosely coupled to simplify the transition towards a more complex infrastructure. The integration is tested on a simplified version of the OECD/NEA MHTGR-350 Coupled Neutronics-Thermal Fluids benchmark model.« less

Level set immersed boundary method for gas-liquid-solid interactions with phase-change

NASA Astrophysics Data System (ADS)

Dhruv, Akash; Balaras, Elias; Riaz, Amir; Kim, Jungho

2017-11-01

We will discuss an approach to simulate the interaction between two-phase flows with phase changes and stationary/moving structures. In our formulation, the Navier-Stokes and heat advection-diffusion equations are solved on a block-structured grid using adaptive mesh refinement (AMR) along with sharp jump in pressure, velocity and temperature across the interface separating the different phases. The jumps are implemented using a modified Ghost Fluid Method (Lee et al., J. Comput. Physics, 344:381-418, 2017), and the interface is tracked with a level set approach. Phase transition is achieved by calculating mass flux near the interface and extrapolating it to the rest of the domain using a Hamilton-Jacobi equation. Stationary/moving structures are simulated with an immersed boundary formulation based on moving least squares (Vanella & Balaras, J. Comput. Physics, 228:6617-6628, 2009). A variety of canonical problems involving vaporization, film boiling and nucleate boiling is presented to validate the method and demonstrate the its formal accuracy. The robustness of the solver in complex problems, which are crucial in efficient design of heat transfer mechanisms for various applications, will also be demonstrated. Work supported by NASA, Grant NNX16AQ77G.

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

GRIZZLY Model of Multi-Reactive Species Diffusion, Moisture/Heat Transfer and Alkali-Silica Reaction for Simulating Concrete Aging and Degradation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Hai; Spencer, Benjamin W.; Cai, Guowei

Concrete is widely used in the construction of nuclear facilities because of its structural strength and its ability to shield radiation. The use of concrete in nuclear power plants for containment and shielding of radiation and radioactive materials has made its performance crucial for the safe operation of the facility. As such, when life extension is considered for nuclear power plants, it is critical to have accurate and reliable predictive tools to address concerns related to various aging processes of concrete structures and the capacity of structures subjected to age-related degradation. The goal of this report is to document themore » progress of the development and implementation of a fully coupled thermo-hydro-mechanical-chemical model in GRIZZLY code with the ultimate goal to reliably simulate and predict long-term performance and response of aged NPP concrete structures subjected to a number of aging mechanisms including external chemical attacks and volume-changing chemical reactions within concrete structures induced by alkali-silica reactions and long-term exposure to irradiation. Based on a number of survey reports of concrete aging mechanisms relevant to nuclear power plants and recommendations from researchers in concrete community, we’ve implemented three modules during FY15 in GRIZZLY code, (1) multi-species reactive diffusion model within cement materials; (2) coupled moisture and heat transfer model in concrete; and (3) anisotropic, stress-dependent, alkali-silica reaction induced swelling model. The multi-species reactive diffusion model was implemented with the objective to model aging of concrete structures subjected to aggressive external chemical attacks (e.g., chloride attack, sulfate attack, etc.). It considers multiple processes relevant to external chemical attacks such as diffusion of ions in aqueous phase within pore spaces, equilibrium chemical speciation reactions and kinetic mineral dissolution/precipitation. The moisture/heat transfer module was implemented to simulate long-term spatial and temporal evolutions of the moisture and temperature fields within concrete structures at both room and elevated temperatures. The ASR swelling model implemented in GRIZZLY code can simulate anisotropic expansions of ASR gel under either uniaxial, biaxial and triaxial stress states, and can be run simultaneously with the moisture/heat transfer model and coupled with various elastic/inelastic solid mechanics models that were implemented in GRIZZLY code previously. This report provides detailed descriptions of the governing equations, constitutive equations and numerical algorithms of the three modules implemented in GRIZZLY during FY15, simulation results of example problems and model validation results by comparing simulations with available experimental data reported in the literature. The close match between the experiments and simulations clearly demonstrate the potential of GRIZZLY code for reliable evaluation and prediction of long-term performance and response of aged concrete structures in nuclear power plants.« less

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

NASA Astrophysics Data System (ADS)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; Birkholzer, Jens T.

2017-11-01

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1-D, 2-D, and 3-D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, td. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, td0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the first two terms for high-accuracy approximations (with less than 10-7 relative error) for 1-D isotropic (spheres, cylinders, slabs) and 2-D/3-D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1-D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2-D/3-D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Revisiting the Fundamental Analytical Solutions of Heat and Mass Transfer: The Kernel of Multirate and Multidimensional Diffusion

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Rutqvist, Jonny; ...

2017-10-24

There are two types of analytical solutions of temperature/concentration in and heat/mass transfer through boundaries of regularly shaped 1D, 2D, and 3D blocks. These infinite-series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times, t d0. In this paper, approximate solutions were developed by combining the error-function-series solutions for early times and the exponential-series solutions for late times and by using time partitioning at the switchover time, t d0. The combined solutions contain either the leading term of both series for normal-accuracy approximations (with less than 0.003 relative error) or the firstmore » two terms for high-accuracy approximations (with less than 10-7 relative error) for 1D isotropic (spheres, cylinders, slabs) and 2D/3D rectangular blocks (squares, cubes, rectangles, and rectangular parallelepipeds). This rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1D slab solutions. The switchover dimensionless time was determined to minimize the maximum approximation errors. Furthermore, the analytical solutions of first-order heat/mass flux for 2D/3D rectangular blocks were derived for normal-accuracy approximations. These flux equations contain the early-time solution with a three-term polynomial in √td and the late-time solution with the limited-term exponentials for rectangular blocks. The heat/mass flux equations and the combined temperature/concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat/mass transfer in porous/fractured media with millions of low-permeability blocks of varying shapes and sizes.« less

Control of reaction-diffusion equations on time-evolving manifolds.

PubMed

Rossi, Francesco; Duteil, Nastassia Pouradier; Yakoby, Nir; Piccoli, Benedetto

2016-12-01

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

A Novel Method for Modeling Neumann and Robin Boundary Conditions in Smoothed Particle Hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryan, Emily M.; Tartakovsky, Alexandre M.; Amon, Cristina

2010-08-26

In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries.more » The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.« less

Improved image reconstruction of low-resolution multichannel phase contrast angiography

PubMed Central

P. Krishnan, Akshara; Joy, Ajin; Paul, Joseph Suresh

2016-01-01

Abstract. In low-resolution phase contrast magnetic resonance angiography, the maximum intensity projected channel images will be blurred with consequent loss of vascular details. The channel images are enhanced using a stabilized deblurring filter, applied to each channel prior to combining the individual channel images. The stabilized deblurring is obtained by the addition of a nonlocal regularization term to the reverse heat equation, referred to as nonlocally stabilized reverse diffusion filter. Unlike reverse diffusion filter, which is highly unstable and blows up noise, nonlocal stabilization enhances intensity projected parallel images uniformly. Application to multichannel vessel enhancement is illustrated using both volunteer data and simulated multichannel angiograms. Robustness of the filter applied to volunteer datasets is shown using statistically validated improvement in flow quantification. Improved performance in terms of preserving vascular structures and phased array reconstruction in both simulated and real data is demonstrated using structureness measure and contrast ratio. PMID:26835501

Photoacoustic design parameter optimization for deep tissue imaging by numerical simulation

NASA Astrophysics Data System (ADS)

Wang, Zhaohui; Ha, Seunghan; Kim, Kang

2012-02-01

A new design of light illumination scheme for deep tissue photoacoustic (PA) imaging, a light catcher, is proposed and evaluated by in silico simulation. Finite element (FE)-based numerical simulation model was developed for photoacoustic (PA) imaging in soft tissues. In this in silico simulation using a commercially available FE simulation package (COMSOL MultiphysicsTM, COMSOL Inc., USA), a short-pulsed laser point source (pulse length of 5 ns) was placed in water on the tissue surface. Overall, four sets of simulation models were integrated together to describe the physical principles of PA imaging. Light energy transmission through background tissues from the laser source to the target tissue or contrast agent was described by diffusion equation. The absorption of light energy and its conversion to heat by target tissue or contrast agent was modeled using bio-heat equation. The heat then causes the stress and strain change, and the resulting displacement of the target surface produces acoustic pressure. The created wide-band acoustic pressure will propagate through background tissues to the ultrasound detector, which is governed by acoustic wave equation. Both optical and acoustical parameters in soft tissues such as scattering, absorption, and attenuation are incorporated in tissue models. PA imaging performance with different design parameters of the laser source and energy delivery scheme was investigated. The laser light illumination into the deep tissues can be significantly improved by up to 134.8% increase of fluence rate by introducing a designed compact light catcher with highly reflecting inner surface surrounding the light source. The optimized parameters through this simulation will guide the design of PA system for deep tissue imaging, and help to form the base protocols of experimental evaluations in vitro and in vivo.

Geochemistry of Dissolved Gases in the Hypersaline Orca Basin.

DTIC Science & Technology

1980-12-01

brine (",250%/o) is internally well mixed due to convective overturning, but transfer across the brine-sea water interface is controlled by- molecular ...diffusion. With a molecular diffusivity of l0-cm . sec- , it will take 10 years for all salts to diffuse fro’i-te-basin. Heat diffuses faster than salt...trolled by molecular diffusion. With a molecular diffusivity of 10 cm sec , it will take 10 years for all salts to diffuse from the basin. Heat diffuses

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels.

PubMed

Li, Baowen; Wang, Jiao; Wang, Lei; Zhang, Gang

2005-03-01

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is sigma(2)(t)=2Dt(alpha) (01) implies an anomalous heat conduction with a divergent thermal conductivity (beta>0), and more interestingly, a subdiffusion (alpha<1) implies an anomalous heat conduction with a convergent thermal conductivity (beta<0), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Stress, deformation and diffusion interactions in solids - A simulation study

NASA Astrophysics Data System (ADS)

Fischer, F. D.; Svoboda, J.

2015-05-01

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain-stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.