GFSSP Training Course Lectures

NASA Technical Reports Server (NTRS)

Majumdar, Alok K.

2008-01-01

GFSSP has been extended to model conjugate heat transfer Fluid Solid Network Elements include: a) Fluid nodes and Flow Branches; b) Solid Nodes and Ambient Nodes; c) Conductors connecting Fluid-Solid, Solid-Solid and Solid-Ambient Nodes. Heat Conduction Equations are solved simultaneously with Fluid Conservation Equations for Mass, Momentum, Energy and Equation of State. The extended code was verified by comparing with analytical solution for simple conduction-convection problem The code was applied to model: a) Pressurization of Cryogenic Tank; b) Freezing and Thawing of Metal; c) Chilldown of Cryogenic Transfer Line; d) Boil-off from Cryogenic Tank.

Importance of Ambipolar Electric Field in the Ion Loss from Mars- Results from a Multi-fluid MHD Model with the Electron Pressure Equation Included

NASA Astrophysics Data System (ADS)

Ma, Y.; Dong, C.; van der Holst, B.; Nagy, A. F.; Bougher, S. W.; Toth, G.; Cravens, T.; Yelle, R. V.; Jakosky, B. M.

2017-12-01

The multi-fluid (MF) magnetohydrodynamic (MHD) model of Mars is further improved by solving an additional electron pressure equation. Through the electron pressure equation, the electron temperature is calculated based on the effects from various electrons related heating and cooling processes (e.g. photo-electron heating, electron-neutral collision and electron-ion collision), and thus the improved model is able to calculate the electron temperature and the electron pressure force self-consistently. Electron thermal conductivity is also considered in the calculation. Model results of a normal case with electron pressure equation included (MFPe) are compared in detail to an identical case using the regular MF model to identify the effect of the improved physics. We found that when the electron pressure equation is included, the general interaction patterns are similar to that of the case with no electron pressure equation. The model with electron pressure equation predicts that electron temperature is much larger than the ion temperature in the ionosphere, consistent with both Viking and MAVEN observations. The inclusion of electron pressure equation significantly increases the total escape fluxes predicted by the model, indicating the importance of the ambipolar electric field(electron pressure gradient) in driving the ion loss from Mars.

HST3D; a computer code for simulation of heat and solute transport in three-dimensional ground-water flow systems

USGS Publications Warehouse

Kipp, K.L.

1987-01-01

The Heat- and Soil-Transport Program (HST3D) simulates groundwater flow and associated heat and solute transport in three dimensions. The three governing equations are coupled through the interstitial pore velocity, the dependence of the fluid density on pressure, temperature, the solute-mass fraction , and the dependence of the fluid viscosity on temperature and solute-mass fraction. The solute transport equation is for only a single, solute species with possible linear equilibrium sorption and linear decay. Finite difference techniques are used to discretize the governing equations using a point-distributed grid. The flow-, heat- and solute-transport equations are solved , in turn, after a particle Gauss-reduction scheme is used to modify them. The modified equations are more tightly coupled and have better stability for the numerical solutions. The basic source-sink term represents wells. A complex well flow model may be used to simulate specified flow rate and pressure conditions at the land surface or within the aquifer, with or without pressure and flow rate constraints. Boundary condition types offered include specified value, specified flux, leakage, heat conduction, and approximate free surface, and two types of aquifer influence functions. All boundary conditions can be functions of time. Two techniques are available for solution of the finite difference matrix equations. One technique is a direct-elimination solver, using equations reordered by alternating diagonal planes. The other technique is an iterative solver, using two-line successive over-relaxation. A restart option is available for storing intermediate results and restarting the simulation at an intermediate time with modified boundary conditions. This feature also can be used as protection against computer system failure. Data input and output may be in metric (SI) units or inch-pound units. Output may include tables of dependent variables and parameters, zoned-contour maps, and plots of the dependent variables versus time. (Lantz-PTT)

Incompressible Navier-Stokes Computations with Heat Transfer

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan; Rogers, Stuart; Kutler, Paul (Technical Monitor)

1994-01-01

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Determination of thermophysical characteristics of solid materials by electrical modelling of the solutions to the inverse problems in nonsteady heat conduction

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Krivoshei, F. A.

1985-01-01

The solution of the inverse problem of nonsteady heat conduction is discussed, based on finding the coefficient of the heat conduction and the coefficient of specific volumetric heat capacity. These findings are included in the equation used for the electrical model of this phenomenon.

Numerical study on characteristics of radio-frequency discharge at atmospheric pressure in argon with small admixtures of oxygen

NASA Astrophysics Data System (ADS)

Wang, Yinan; Liu, Yue

2017-07-01

In this paper, a 1D fluid model is developed to study the characteristics of a discharge in argon with small admixtures of oxygen at atmospheric pressure. This model consists of a series of equations, including continuity equations for electrons, positive ions, negative ions and neutral particles, the energy equation, and the Poisson equation for electric potential. Special attention has been paid to the electron energy dissipation and the mechanisms of electron heating, while the admixture of oxygen is in the range of 0.1%-0.6%. It is found that when the oxygen-to-argon ratio grows, the discharge is obviously divided into three stages: electron growth, electron reduction and the electron remaining unchanged. Furthermore, the cycle-averaged electric field, electron temperature, electron Ohmic heating, electron collisionless heating, electron energy dissipation and the net electron production are also studied in detail, and when the oxygen-to-argon ratio is relatively larger (R = 0.6%), double value peaks of electron Ohmic heating appear in the sheath. According to the results of the numerical simulation, various oxygen-to-argon ratios result in different amounts of electron energy dissipation and electron heating.

Generalized approach to cooling charge-coupled devices using thermoelectric coolers

NASA Technical Reports Server (NTRS)

Petrick, S. Walter

1987-01-01

This paper is concerned with the use of thermoelectric coolers (TECs) to cool charge-coupled devices (CCDs). Heat inputs to the CCD from the warmer environment are identified, and generalized graphs are used to approximate the major heat inputs. A method of choosing and estimating the power consumption of the TEC is discussed. This method includes the use of TEC performance information supplied by the manufacturer and equations derived from this information. Parameters of the equations are tabulated to enable the reader to use the TEC performance equations for choosing and estimating the power needed for specific TEC applications.

Modeling of the heat transfer in bypass transitional boundary-layer flows

NASA Technical Reports Server (NTRS)

Simon, Frederick F.; Stephens, Craig A.

1991-01-01

A low Reynolds number k-epsilon turbulence model and conditioned momentum, energy and turbulence equations were used to predict bypass transition heat transfer on a flat plate in a high-disturbance environment with zero pressure gradient. The use of conditioned equations was demonstrated to be an improvement over the use of the global-time-averaged equations for the calculation of velocity profiles and turbulence intensity profiles in the transition region of a boundary layer. The approach of conditioned equations is extended to include heat transfer and a modeling of transition events is used to predict transition onset and the extent of transition on a flat plate. The events, which describe the boundary layer at the leading edge, result in boundary-layer regions consisting of: (1) the laminar, (2) pseudolaminar, (3) transitional, and (4) turbulent boundary layers. The modeled transition events were incorporated into the TEXSTAN 2-D boundary-layer code which is used to numerically predict the heat transfer. The numerical predictions in general compared well with the experimental data and revealed areas where additional experimental information is needed.

Kinetic modeling of Nernst effect in magnetized hohlraums.

PubMed

Joglekar, A S; Ridgers, C P; Kingham, R J; Thomas, A G R

2016-04-01

We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in flux would suggest. Nonlocality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling.

User Guide for Compressible Flow Toolbox Version 2.1 for Use With MATLAB(Registered Trademark); Version 7

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

This report provides a user guide for the Compressible Flow Toolbox, a collection of algorithms that solve almost 300 linear and nonlinear classical compressible flow relations. The algorithms, implemented in the popular MATLAB programming language, are useful for analysis of one-dimensional steady flow with constant entropy, friction, heat transfer, or shock discontinuities. The solutions do not include any gas dissociative effects. The toolbox also contains functions for comparing and validating the equation-solving algorithms against solutions previously published in the open literature. The classical equations solved by the Compressible Flow Toolbox are: isentropic-flow equations, Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section.), normal-shock equations, oblique-shock equations, and Prandtl-Meyer expansion equations. At the time this report was published, the Compressible Flow Toolbox was available without cost from the NASA Software Repository.

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.

A numerical model on thermodynamic analysis of free piston Stirling engines

NASA Astrophysics Data System (ADS)

Mou, Jian; Hong, Guotong

2017-02-01

In this paper, a new numerical thermodynamic model which bases on the energy conservation law has been used to analyze the free piston Stirling engine. In the model all data was taken from a real free piston Stirling engine which has been built in our laboratory. The energy conservation equations have been applied to expansion space and compression space of the engine. The equation includes internal energy, input power, output power, enthalpy and the heat losses. The heat losses include regenerative heat conduction loss, shuttle heat loss, seal leakage loss and the cavity wall heat conduction loss. The numerical results show that the temperature of expansion space and the temperature of compression space vary with the time. The higher regeneration effectiveness, the higher efficiency and bigger output work. It is also found that under different initial pressures, the heat source temperature, phase angle and engine work frequency pose different effects on the engine’s efficiency and power. As a result, the model is expected to be a useful tool for simulation, design and optimization of Stirling engines.

Kinetic: A system code for analyzing nuclear thermal propulsion rocket engine transients

NASA Astrophysics Data System (ADS)

Schmidt, Eldon; Lazareth, Otto; Ludewig, Hans

The topics are presented in viewgraph form and include the following: outline of kinetic code; a kinetic information flow diagram; kinetic neutronic equations; turbopump/nozzle algorithm; kinetic heat transfer equations per node; and test problem diagram.

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.

Effect of Ponderomotive Terms on Heat Flux in Laser-Produced Plasmas

NASA Astrophysics Data System (ADS)

Li, G.

2005-10-01

A laser electromagnetic field introduces ponderomotive termsootnotetextV. N. Goncharov and G. Li, Phys. Plasmas 11, 5680 (2004). in the heat flux in a plasma. To account for the nonlocal effects in the ponderomotive terms, first, the kinetic equation coupled with the Maxwell equations is numerically solved for the isotropic part of the electron distribution function. Such an equation includes self-consistent electromagnetic fields and laser absorption through the inverse bremsstrahlung. Then, the anisotropic part is found by solving a simplified Fokker--Planck equation. Using the distribution function, the electric current and heat flux are obtained and substituted into the hydrocode LILAC to simulate ICF implosions. The simulation results are compared against the existing nonlocal electron conduction modelsootnotetextG. P. Schurtz, P. D. Nicola"i, and M. Busquet, Phys. Plasmas 9, 4238 (2000). and Fokker--Planck simulations. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-92SF19460.

A computer program for the simulation of heat and moisture flow in soils

NASA Technical Reports Server (NTRS)

Camillo, P.; Schmugge, T. J.

1981-01-01

A computer program that simulates the flow of heat and moisture in soils is described. The space-time dependence of temperature and moisture content is described by a set of diffusion-type partial differential equations. The simulator uses a predictor/corrector to numerically integrate them, giving wetness and temperature profiles as a function of time. The simulator was used to generate solutions to diffusion-type partial differential equations for which analytical solutions are known. These equations include both constant and variable diffusivities, and both flux and constant concentration boundary conditions. In all cases, the simulated and analytic solutions agreed to within the error bounds which were imposed on the integrator. Simulations of heat and moisture flow under actual field conditions were also performed. Ground truth data were used for the boundary conditions and soil transport properties. The qualitative agreement between simulated and measured profiles is an indication that the model equations are reasonably accurate representations of the physical processes involved.

Analysis of the transient behavior of rubbing components

NASA Technical Reports Server (NTRS)

Quezdou, M. B.; Mullen, R. L.

1986-01-01

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

Thermal protection for hypervelocity flight in earth's atmosphere by use of radiation backscattering ablating materials

NASA Technical Reports Server (NTRS)

Howe, John T.; Yang, Lily

1991-01-01

A heat-shield-material response code predicting the transient performance of a material subject to the combined convective and radiative heating associated with the hypervelocity flight is developed. The code is dynamically interactive to the heating from a transient flow field, including the effects of material ablation on flow field behavior. It accomodates finite time variable material thickness, internal material phase change, wavelength-dependent radiative properties, and temperature-dependent thermal, physical, and radiative properties. The equations of radiative transfer are solved with the material and are coupled to the transfer energy equation containing the radiative flux divergence in addition to the usual energy terms.

Numerical Modeling of Conjugate Heat Transfer in Fluid Network

NASA Technical Reports Server (NTRS)

Majumdar, Alok

2004-01-01

Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.

Effect of heat flux on differential rotation in turbulent convection.

PubMed

Kleeorin, Nathan; Rogachevskii, Igor

2006-04-01

We studied the effect of the turbulent heat flux on the Reynolds stresses in a rotating turbulent convection. To this end we solved a coupled system of dynamical equations which includes the equations for the Reynolds stresses, the entropy fluctuations, and the turbulent heat flux. We used a spectral tau approximation in order to close the system of dynamical equations. We found that the ratio of the contributions to the Reynolds stresses caused by the turbulent heat flux and the anisotropic eddy viscosity is of the order of approximately 10(L rho/l0)2, where l0 is the maximum scale of turbulent motions and L rho is the fluid density variation scale. This effect is crucial for the formation of the differential rotation and should be taken into account in the theories of the differential rotation of the Sun, stars, and planets. In particular, we demonstrated that this effect may cause the differential rotation which is comparable with the typical solar differential rotation.

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.

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

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.

Diffusion, Fluxes, Friction Forces, and Joule Heating in Two-Temperature Multicomponent Magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Chang, C. H.

1999-01-01

The relationship between Joule heating, diffusion fluxes, and friction forces has been studied for both total and electron thermal energy equations, using general expressions for multicomponent diffusion in two-temperature plasmas with the velocity dependent Lorentz force acting on charged species in a magnetic field. It is shown that the derivation of Joule heating terms requires both diffusion fluxes and friction between species which represents the resistance experienced by the species moving at different relative velocities. It is also shown that the familiar Joule heating term in the electron thermal energy equation includes artificial effects produced by switching the convective velocity from the species velocity to the mass-weighted velocity, and thus should not be ignored even when there is no net energy dissipation.

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

NASA Astrophysics Data System (ADS)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

Selection, Evaluation, and Rating of Compact Heat Exchangers v. 1.006

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

Carlson, Matthew D.

2016-11-09

SEARCH determines and optimizes the design of a compact heat exchanger for specified process conditions. The user specifies process boundary conditions including the fluid state and flow rate and SEARCH will determine the optimum flow arrangement, channel geometry, and mechanical design for the unit. Fluids are modeled using NIST Refprop or tabulated values. A variety of thermal-hydraulic correlations are available including user-defined equations to accurately capture the heat transfer and pressure drop behavior of the process flows.

A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

NASA Technical Reports Server (NTRS)

Radhadrishnan, Krishnan

1993-01-01

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

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.

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

NASA Astrophysics Data System (ADS)

Muldoon, F. H.

2018-04-01

Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.

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.

Modeling and Simulation of Radiative Compressible Flows in Aerodynamic Heating Arc-Jet Facility

NASA Technical Reports Server (NTRS)

Bensassi, Khalil; Laguna, Alejandro A.; Lani, Andrea; Mansour, Nagi N.

2016-01-01

Numerical simulations of an arc heated flow inside NASA's 20 [MW] Aerodynamics heating facility (AHF) are performed in order to investigate the three-dimensional swirling flow and the current distribution inside the wind tunnel. The plasma is considered in Local Thermodynamics Equilibrium(LTE) and is composed of Air-Argon gas mixture. The governing equations are the Navier-Stokes equations that include source terms corresponding to Joule heating and radiative cooling. The former is obtained by solving an electric potential equation, while the latter is calculated using an innovative massively parallel ray-tracing algorithm. The fully coupled system is closed by the thermodynamics relations and transport properties which are obtained from Chapman-Enskog method. A novel strategy was developed in order to enable the flow solver and the radiation calculation to be preformed independently and simultaneously using a different number of processors. Drastic reduction in the computational cost was achieved using this strategy. Details on the numerical methods used for space discretization, time integration and ray-tracing algorithm will be presented. The effect of the radiative cooling on the dynamics of the flow will be investigated. The complete set of equations were implemented within the COOLFluiD Framework. Fig. 1 shows the geometry of the Anode and part of the constrictor of the Aerodynamics heating facility (AHF). Fig. 2 shows the velocity field distribution along (x-y) plane and the streamline in (z-y) plane.

TACT1- TRANSIENT THERMAL ANALYSIS OF A COOLED TURBINE BLADE OR VANE EQUIPPED WITH A COOLANT INSERT

NASA Technical Reports Server (NTRS)

Gaugler, R. E.

1994-01-01

As turbine-engine core operating conditions become more severe, designers must develop more effective means of cooling blades and vanes. In order to design reliable, cooled turbine blades, advanced transient thermal calculation techniques are required. The TACT1 computer program was developed to perform transient and steady-state heat-transfer and coolant-flow analyses for cooled blades, given the outside hot-gas boundary condition, the coolant inlet conditions, the geometry of the blade shell, and the cooling configuration. TACT1 can analyze turbine blades, or vanes, equipped with a central coolant-plenum insert from which coolant-air impinges on the inner surface of the blade shell. Coolant-side heat-transfer coefficients are calculated with the heat transfer mode at each station being user specified as either impingement with crossflow, forced convection channel flow, or forced convection over pin fins. A limited capability to handle film cooling is also available in the program. The TACT1 program solves for the blade temperature distribution using a transient energy equation for each node. The nodal energy balances are linearized, one-dimensional, heat-conduction equations which are applied at the wall-outer-surface node, at the junction of the cladding and the metal node, and at the wall-inner-surface node. At the mid-metal node a linear, three-dimensional, heat-conduction equation is used. Similarly, the coolant pressure distribution is determined by solving the set of transfer momentum equations for the one-dimensional flow between adjacent fluid nodes. In the coolant channel, energy and momentum equations for one-dimensional compressible flow, including friction and heat transfer, are used for the elemental channel length between two coolant nodes. The TACT1 program first obtains a steady-state solution using iterative calculations to obtain convergence of stable temperatures, pressures, coolant-flow split, and overall coolant mass balance. Transient calculations are based on the steady-state solutions obtained. Input to the TACT1 program includes a geometrical description of the blade and insert, the nodal spacing to be used, and the boundary conditions describing the outside hot-gas and the coolant-inlet conditions. The program output includes the value of nodal temperatures and pressures at each iteration. The final solution output includes the temperature at each coolant node, and the coolant flow rates and Reynolds numbers. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 360 computer with a central memory requirement of approximately 480K of 8 bit bytes. The TACT1 program was developed in 1978.

Latent Heating Retrieval from TRMM Observations Using a Simplified Thermodynamic Model

NASA Technical Reports Server (NTRS)

Grecu, Mircea; Olson, William S.

2003-01-01

A procedure for the retrieval of hydrometeor latent heating from TRMM active and passive observations is presented. The procedure is based on current methods for estimating multiple-species hydrometeor profiles from TRMM observations. The species include: cloud water, cloud ice, rain, and graupel (or snow). A three-dimensional wind field is prescribed based on the retrieved hydrometeor profiles, and, assuming a steady-state, the sources and sinks in the hydrometeor conservation equations are determined. Then, the momentum and thermodynamic equations, in which the heating and cooling are derived from the hydrometeor sources and sinks, are integrated one step forward in time. The hydrometeor sources and sinks are reevaluated based on the new wind field, and the momentum and thermodynamic equations are integrated one more step. The reevalution-integration process is repeated until a steady state is reached. The procedure is tested using cloud model simulations. Cloud-model derived fields are used to synthesize TRMM observations, from which hydrometeor profiles are derived. The procedure is applied to the retrieved hydrometeor profiles, and the latent heating estimates are compared to the actual latent heating produced by the cloud model. Examples of procedure's applications to real TRMM data are also provided.

The nature of the sunspot phenomenon. I - Solutions of the heat transport equation

NASA Technical Reports Server (NTRS)

Parker, E. N.

1974-01-01

It is pointed out that sunspots represent a disruption in the uniform flow of heat through the convective zone. The basic sunspot structure is, therefore, determined by the energy transport equation. The solutions of this equation for the case of stochastic heat transport are examined. It is concluded that a sunspot is basically a region of enhanced, rather than inhibited, energy transport and emissivity. The heat flow equations are discussed and attention is given to the shallow depth of the sunspot phenomenon. The sunspot is seen as a heat engine of high efficiency which converts most of the heat flux into hydromagnetic waves.

Effect of partial heating at mid of vertical plate adjacent to porous medium

NASA Astrophysics Data System (ADS)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

Dynamics of charged bulk viscous collapsing cylindrical source with heat flux

NASA Astrophysics Data System (ADS)

Shah, S. M.; Abbas, G.

2017-04-01

In this paper, we have explored the effects of dissipation on the dynamics of charged bulk viscous collapsing cylindrical source which allows the out-flow of heat flux in the form of radiations. The Misner-Sharp formalism has been implemented to drive the dynamical equation in terms of proper time and radial derivatives. We have investigated the effects of charge and bulk viscosity on the dynamics of collapsing cylinder. To determine the effects of radial heat flux, we have formulated the heat transport equations in the context of Müller-Israel-Stewart theory by assuming that thermodynamics viscous/heat coupling coefficients can be neglected within some approximations. In our discussion, we have introduced the viscosity by the standard (non-causal) thermodynamics approach. The dynamical equations have been coupled with the heat transport equation; the consequences of the resulting coupled heat equation have been analyzed in detail.

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.

Effects from equation of state and rheology in dissipative heating in compressible mantle convection

NASA Technical Reports Server (NTRS)

Yuen, David A.; Quareni, Francesca; Hong, H.-J.

1987-01-01

The effects of compressibility on mantle convection are considered, incorporating the effects of equations of state and rheology in the dissipative heating term of the energy equation. The ways in which compression may raise the interior mantle temperature are explicitly demonstrated, and it is shown how this effect can be used to constrain some of the intrinsic parameters associated with the equation of state in the mantle. It is concluded that the coupling between variable viscosity and equation of state in dissipative heating is potentially an important mechanism in mantle convection. These findings emphasize that rheology, equation of state, and radiogenic heating are all linked to each other by nonlinear thermomechanical couplings.

A method to model latent heat for transient analysis using NASTRAN

NASA Technical Reports Server (NTRS)

Harder, R. L.

1982-01-01

A sample heat transfer analysis is demonstrated which includes the heat of fusion. The method can be used to analyze a system with nonconstant specific heat. The enthalpy is introduced as an independent degree of freedom at each node. The user input consists of a curve of temperature as a function of enthalpy, which may include a constant temperature phase change. The basic NASTRAN heat transfer capability is used to model the effects of latent heat with existing direct matrix output and nonlinear load data cards. Although some user care is required, the numerical stability of the integration is quite good when the given recommendations are followed. The theoretical equations used and the NASTRAN techniques are shown.

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

The Heat Is on: An Inquiry-Based Investigation for Specific Heat

ERIC Educational Resources Information Center

Herrington, Deborah G.

2011-01-01

A substantial number of upper-level science students and practicing physical science teachers demonstrate confusion about thermal equilibrium, heat transfer, heat capacity, and specific heat capacity. The traditional method of instruction, which involves learning the related definitions and equations, using equations to solve 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.

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

NASA Technical Reports Server (NTRS)

Goldstein, M. L.; Usmanov, A. V.; Matthaeus, W. H.; Breech, B.

2009-01-01

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

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

Heat Stress Equation Development and Usage for Dryden Flight Research Center (DFRC)

NASA Technical Reports Server (NTRS)

Houtas, Franzeska; Teets, Edward H., Jr.

2012-01-01

Heat Stress Indices are equations that integrate some or all variables (e.g. temperature, relative humidity, wind speed), directly or indirectly, to produce a number for thermal stress on humans for a particular environment. There are a large number of equations that have been developed which range from simple equations that may ignore basic factors (e.g. wind effects on thermal loading, fixed contribution from solar heating) to complex equations that attempt to incorporate all variables. Each equation is evaluated for a particular use, as well as considering the ease of use and reliability of the results. The meteorology group at the Dryden Flight Research Center has utilized and enhanced the American College of Sports Medicine equation to represent the specific environment of the Mojave Desert. The Dryden WBGT Heat Stress equation has been vetted and implemented as an automated notification to the entire facility for the safety of all personnel and visitors.

Turbulent Fluid Motion 5: Fourier Analysis, the Spectral Form of the Continuum Equations, and Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Background material on Fourier analysis and on the spectral form of the continuum equations, both averaged and unaveraged, are given. The equations are applied to a number of cases of homogeneous turbulence with and without mean gradients. Spectral transfer of turbulent activity between scales of motion is studied in some detail. The effects of mean shear, heat transfer, normal strain, and buoyancy are included in the analyses.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

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.

Modelling crystal growth: Convection in an asymmetrically heated ampoule

NASA Technical Reports Server (NTRS)

Alexander, J. Iwan D.; Rosenberger, Franz; Pulicani, J. P.; Krukowski, S.; Ouazzani, Jalil

1990-01-01

The objective was to develop and implement a numerical method capable of solving the nonlinear partial differential equations governing heat, mass, and momentum transfer in a 3-D cylindrical geometry in order to examine the character of convection in an asymmetrically heated cylindrical ampoule. The details of the numerical method, including verification tests involving comparison with results obtained from other methods, are presented. The results of the study of 3-D convection in an asymmetrically heated cylinder are described.

Analytical study of the liquid phase transient behavior of a high temperature heat pipe. M.S. Thesis

NASA Technical Reports Server (NTRS)

Roche, Gregory Lawrence

1988-01-01

The transient operation of the liquid phase of a high temperature heat pipe is studied. The study was conducted in support of advanced heat pipe applications that require reliable transport of high temperature drops and significant distances under a broad spectrum of operating conditions. The heat pipe configuration studied consists of a sealed cylindrical enclosure containing a capillary wick structure and sodium working fluid. The wick is an annular flow channel configuration formed between the enclosure interior wall and a concentric cylindrical tube of fine pore screen. The study approach is analytical through the solution of the governing equations. The energy equation is solved over the pipe wall and liquid region using the finite difference Peaceman-Rachford alternating direction implicit numerical method. The continuity and momentum equations are solved over the liquid region by the integral method. The energy equation and liquid dynamics equation are tightly coupled due to the phase change process at the liquid-vapor interface. A kinetic theory model is used to define the phase change process in terms of the temperature jump between the liquid-vapor surface and the bulk vapor. Extensive auxiliary relations, including sodium properties as functions of temperature, are used to close the analytical system. The solution procedure is implemented in a FORTRAN algorithm with some optimization features to take advantage of the IBM System/370 Model 3090 vectorization facility. The code was intended for coupling to a vapor phase algorithm so that the entire heat pipe problem could be solved. As a test of code capabilities, the vapor phase was approximated in a simple manner.

VS2DI: Model use, calibration, and validation

USGS Publications Warehouse

Healy, Richard W.; Essaid, Hedeff I.

2012-01-01

VS2DI is a software package for simulating water, solute, and heat transport through soils or other porous media under conditions of variable saturation. The package contains a graphical preprocessor for constructing simulations, a postprocessor for displaying simulation results, and numerical models that solve for flow and solute transport (VS2DT) and flow and heat transport (VS2DH). Flow is described by the Richards equation, and solute and heat transport are described by advection-dispersion equations; the finite-difference method is used to solve these equations. Problems can be simulated in one, two, or three (assuming radial symmetry) dimensions. This article provides an overview of calibration techniques that have been used with VS2DI; included is a detailed description of calibration procedures used in simulating the interaction between groundwater and a stream fed by drainage from agricultural fields in central Indiana. Brief descriptions of VS2DI and the various types of problems that have been addressed with the software package are also presented.

Thermal electron heating rate: A derivation

NASA Technical Reports Server (NTRS)

Hoegy, W. R.

1983-01-01

The thermal electron heating rate is an important heat source term in the ionospheric electron energy balance equation, representing heating by photoelectrons or by precipitating higher energy electrons. A formula for the thermal electron heating rate is derived from the kinetic equation using the electron-electron collision operator as given by the unified theory of Kihara and Aono. This collision operator includes collective interactions to produce a finite collision operator with an exact Coulomb logarithm term. The derived heating rate O(e) is the sum of three terms, O(e) = O(p) + S + O(int), which are respectively: (1) primary electron production term giving the heating from newly created electrons that have not yet suffered collisions with the ambient electrons; (2) a heating term evaluated on the energy surface m(e)/2 = E(T) at the transition between Maxwellian and tail electrons at E(T); and (3) the integral term representing heating of Maxwellian electrons by energetic tail electrons at energies ET. Published ionospheric electron temperature studies used only the integral term O(int) with differing lower integration limits. Use of the incomplete heating rate could lead to erroneous conclusions regarding electron heat balance, since O(e) is greater than O(int) by as much as a factor of two.

Geometry, Heat Equation and Path Integrals on the Poincaré Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincaré upper half-plane. The fundamental solution to the heat equation partial f/partial t = Delta_{H} f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrödinger equation is also valid for our case.

Asymptotic problems for stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Salins, Michael

Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

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.

An analysis of the vapor flow and the heat conduction through the liquid-wick and pipe wall in a heat pipe with single or multiple heat sources

NASA Technical Reports Server (NTRS)

Chen, Ming-Ming; Faghri, Amir

1990-01-01

A numerical analysis is presented for the overall performance of heat pipes with single or multiple heat sources. The analysis includes the heat conduction in the wall and liquid-wick regions as well as the compressibility effect of the vapor inside the heat pipe. The two-dimensional elliptic governing equations in conjunction with the thermodynamic equilibrium relation and appropriate boundary conditions are solved numerically. The solutions are in agreement with existing experimental data for the vapor and wall temperatures at both low and high operating temperatures.

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

ERIC Educational Resources Information Center

Spayd, Kimberly; Puckett, James

2016-01-01

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

Numerical Analysis of Microwave Heating on Saponification Reaction

NASA Astrophysics Data System (ADS)

Huang, Kama; Jia, Kun

2005-01-01

Currently, microwave is widely used in chemical industry to accelerate chemical reactions. Saponification reaction has important applications in industry; some research results have shown that microwave heating can significantly accelerate the reaction [1]. But so far, no efficient method has been reported for the analysis of the heating process and design of an efficient reactor powered by microwave. In this paper, we present a method to study the microwave heating process on saponification reaction, where the reactant in a test tube is considered as a mixture of dilute solution. According to the preliminary measurement results, the effective permittivity of the mixture is approximately the permittivity of water, but the conductivity, which could change with the reaction, is derived from the reaction equation (RE). The electromagnetic field equation and reaction equation are coupled by the conductivity. Following that, the whole heating processes, which is described by Maxwell's equations, the reaction equation and heat transport equation (HTE), is analyzed by finite difference time domain (FDTD) method. The temperature rising in the test tube are measured and compared with the computational results. Good agreement can be seen between the measured and calculated results.

Prediction of rectal temperature using non-invasive physiologic variable measurements in hair pregnant ewes subjected to natural conditions of heat stress.

PubMed

Vicente-Pérez, Ricardo; Avendaño-Reyes, Leonel; Mejía-Vázquez, Ángel; Álvarez-Valenzuela, F Daniel; Correa-Calderón, Abelardo; Mellado, Miguel; Meza-Herrera, Cesar A; Guerra-Liera, Juan E; Robinson, P H; Macías-Cruz, Ulises

2016-01-01

Rectal temperature (RT) is the foremost physiological variable indicating if an animal is suffering hyperthermia. However, this variable is traditionally measured by invasive methods, which may compromise animal welfare. Models to predict RT have been developed for growing pigs and lactating dairy cows, but not for pregnant heat-stressed ewes. Our aim was to develop a prediction equation for RT using non-invasive physiological variables in pregnant ewes under heat stress. A total of 192 records of respiratory frequency (RF) and hair coat temperature in various body regions (i.e., head, rump, flank, shoulder, and belly) obtained from 24 Katahdin × Pelibuey pregnant multiparous ewes were collected during the last third of gestation (i.e., d 100 to lambing) with a 15 d sampling interval. Hair coat temperatures were taken using infrared thermal imaging technology. Initially, a Pearson correlation analysis examined the relationship among variables, and then multiple linear regression analysis was used to develop the prediction equations. All predictor variables were positively correlated (P<0.01; r=0.59-0.67) with RT. The adjusted equation which best predicted RT (P<0.01; Radj(2)=56.15%; CV=0.65%) included as predictors RF and head and belly temperatures. Comparison of predicted and observed values for RT indicates a suitable agreement (P<0.01) between them with moderate accuracy (Radj(2)=56.15%) when RT was calculated with the adjusted equation. In general, the final equation does not violate any assumption of multiple regression analysis. The RT in heat-stressed pregnant ewes can be predicted with an adequate accuracy using non-invasive physiologic variables, and the final equation was: RT=35.57+0.004 (RF)+0.067 (heat temperature)+0.028 (belly temperature). Copyright © 2015 Elsevier Ltd. All rights reserved.

Statistical Contact Model for Confined Molecules

NASA Astrophysics Data System (ADS)

Santamaria, Ruben; de la Paz, Antonio Alvarez; Roskop, Luke; Adamowicz, Ludwik

2016-08-01

A theory that describes in a realistic form a system of atoms under the effects of temperature and confinement is presented. The theory departs from a Lagrangian of the Zwanzig type and contains the main ingredients for describing a system of atoms immersed in a heat bath that is also formed by atoms. The equations of motion are derived according to Lagrangian mechanics. The application of statistical mechanics to describe the bulk effects greatly reduces the complexity of the equations. The resultant equations of motion are of the Langevin type with the viscosity and the temperature of the heat reservoir able to influence the trajectories of the particles. The pressure effects are introduced mechanically by using a container with an atomic structure immersed in the heat bath. The relevant variables that determine the equation of state are included in the formulation. The theory is illustrated by the derivation of the equation of state for a system with 76 atoms confined inside of a 180-atom fullerene-like cage that is immersed in fluid forming the heat bath at a temperature of 350 K and with the friction coefficient of 3.0 {ps}^{-1}. The atoms are of the type believed to form the cores of the Uranus and Neptune planets. The dynamic and the static pressures of the confined system are varied in the 3-5 KBar and 2-30 MBar ranges, respectively. The formulation can be equally used to analyze chemical reactions under specific conditions of pressure and temperature, determine the structure of clusters with their corresponding equation of state, the conditions for hydrogen storage, etc. The theory is consistent with the principles of thermodynamics and it is intrinsically ergodic, of general use, and the first of this kind.

Theoretical study on a Miniature Joule-Thomson & Bernoulli Cryocooler

NASA Astrophysics Data System (ADS)

Xiong, L. Y.; Kaiser, G.; Binneberg, A.

2004-11-01

In this paper, a microchannel-based cryocooler consisting of a compressor, a recuperator and a cold heat exchanger has been developed to study the feasibility of cryogenic cooling by the use of Joule-Thomson effect and Bernoulli effect. A set of governing equations including Bernoulli equations and energy equations are introduced and the performance of the cooler is calculated. The influences of some working conditions and structure parameters on the performance of coolers are discussed in details.

Stochastic modeling of stock price process induced from the conjugate heat equation

NASA Astrophysics Data System (ADS)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Three-Fluid Magnetohydrodynamic Modeling of the Solar Wind in the Outer Heliosphere

NASA Technical Reports Server (NTRS)

Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

2011-01-01

We have developed a three-fluid, fully three-dimensional magnetohydrodynamic model of the solar wind plasma in the outer heliosphere as a co-moving system of solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Our approach takes into account the effects of electron heat conduction and dissipation of Alfvenic turbulence on the spatial evolution of the solar wind plasma and interplanetary magnetic fields. The turbulence transport model is based on the Reynolds decomposition of physical variables into mean and fluctuating components and uses the turbulent phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. We solve the coupled set of the three-fluid equations for the mean-field solar wind and the turbulence equations for the turbulence energy, cross helicity, and correlation length. The equations are written in the rotating frame of reference and include heating by turbulent dissipation, energy transfer from interstellar pickup protons to solar wind protons, and solar wind deceleration due to the interaction with the interstellar hydrogen. The numerical solution is constructed by the time relaxation method in the region from 0.3 to 100 AU. Initial results from the novel model are presented.

Trajectory characteristics and heating of hypervelocity projectiles having large ballistic coefficients

NASA Technical Reports Server (NTRS)

Tauber, Michael E.

1986-01-01

A simple, approximate equation describing the velocity-density relationship (or velocity-altitude) has been derived from the flight of large ballistic coefficient projectiles launched at high speeds. The calculations obtained by using the approximate equation compared well with results for numerical integrations of the exact equations of motion. The flightpath equation was used to parametrically calculate maximum body decelerations and stagnation pressures for initial velocities from 2 to 6 km/s. Expressions were derived for the stagnation-point convective heating rates and total heat loads. The stagnation-point heating was parametrically calculated for a nonablating wall and an ablating carbon surface. Although the heating rates were very high, the pulse decayed quickly. The total nose-region heat shield weight was conservatively estimated to be only about 1 percent of the body mass.

Bio-heat transfer model of electroconvulsive therapy: Effect of biological properties on induced temperature variation.

PubMed

de Oliveira, Marilia M; Wen, Paul; Ahfock, Tony

2016-08-01

A realistic human head model consisting of six tissue layers was modelled to investigate the behavior of temperature profile and magnitude when applying electroconvulsive therapy stimulation and different biological properties. The thermo-electrical model was constructed with the use of bio-heat transfer equation and Laplace equation. Three different electrode montages were analyzed as well as the influence of blood perfusion, metabolic heat and electric and thermal conductivity in the scalp. Also, the effect of including the fat layer was investigated. The results showed that temperature increase is inversely proportional to electrical and thermal conductivity increase. Furthermore, the inclusion of blood perfusion slightly drops the peak temperature. Finally, the inclusion of fat is highly recommended in order to acquire more realistic results from the thermo-electrical models.

Experimental Study of Heat Transfer Performance of Polysilicon Slurry Drying Process

NASA Astrophysics Data System (ADS)

Wang, Xiaojing; Ma, Dongyun; Liu, Yaqian; Wang, Zhimin; Yan, Yangyang; Li, Yuankui

2016-12-01

In recent years, the growth of the solar energy photovoltaic industry has greatly promoted the development of polysilicon. However, there has been little research into the slurry by-products of polysilicon production. In this paper the thermal performance of polysilicon slurry was studied in an industrial drying process with a twin-screw horizontal intermittent dryer. By dividing the drying process into several subunits, the parameters of each unit could be regarded as constant in that period. The time-dependent changes in parameters including temperature, specific heat and evaporation enthalpy were plotted. An equation for the change in the heat transfer coefficient over time was calculated based on heat transfer equations. The concept of a distribution coefficient was introduced to reflect the influence of stirring on the heat transfer area. The distribution coefficient ranged from 1.2 to 1.7 and was obtained with the fluid simulation software FLUENT, which simplified the calculation of heat transfer area during the drying process. These experimental data can be used to guide the study of polysilicon slurry drying and optimize the design of dryers for industrial processes.

User's Guide of TOUGH2-EGS. A Coupled Geomechanical and Reactive Geochemical Simulator for Fluid and Heat Flow in Enhanced Geothermal Systems Version 1.0

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

Fakcharoenphol, Perapon; Xiong, Yi; Hu, Litang

TOUGH2-EGS is a numerical simulation program coupling geomechanics and chemical reactions for fluid and heat flows in porous media and fractured reservoirs of enhanced geothermal systems. The simulator includes the fully-coupled geomechanical (THM) module, the fully-coupled geochemical (THC) module, and the sequentially coupled reactive geochemistry (THMC) module. The fully-coupled flow-geomechanics model is developed from the linear elastic theory for the thermo-poro-elastic system and is formulated with the mean normal stress as well as pore pressure and temperature. The chemical reaction is sequentially coupled after solution of flow equations, which provides the flow velocity and phase saturation for the solute transportmore » calculation at each time step. In addition, reservoir rock properties, such as porosity and permeability, are subjected to change due to rock deformation and chemical reactions. The relationships between rock properties and geomechanical and chemical effects from poro-elasticity theories and empirical correlations are incorporated into the simulator. This report provides the user with detailed information on both mathematical models and instructions for using TOUGH2-EGS for THM, THC or THMC simulations. The mathematical models include the fluid and heat flow equations, geomechanical equation, reactive geochemistry equations, and discretization methods. Although TOUGH2-EGS has the capability for simulating fluid and heat flows coupled with both geomechanical and chemical effects, it is up to the users to select the specific coupling process, such as THM, THC, or THMC in a simulation. There are several example problems illustrating the applications of this program. These example problems are described in details and their input data are presented. The results demonstrate that this program can be used for field-scale geothermal reservoir simulation with fluid and heat flow, geomechanical effect, and chemical reaction in porous and fractured media.« less

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

PubMed

Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

2011-01-01

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

NASA Astrophysics Data System (ADS)

Gavrilov, S. N.; Krivtsov, A. M.; Tsvetkov, D. V.

2018-05-01

We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.

Influence of heat conducting substrates on explosive crystallization in thin layers

NASA Astrophysics Data System (ADS)

Schneider, Wilhelm

2017-09-01

Crystallization in a thin, initially amorphous layer is considered. The layer is in thermal contact with a substrate of very large dimensions. The energy equation of the layer contains source and sink terms. The source term is due to liberation of latent heat in the crystallization process, while the sink term is due to conduction of heat into the substrate. To determine the latter, the heat diffusion equation for the substrate is solved by applying Duhamel's integral. Thus, the energy equation of the layer becomes a heat diffusion equation with a time integral as an additional term. The latter term indicates that the heat loss due to the substrate depends on the history of the process. To complete the set of equations, the crystallization process is described by a rate equation for the degree of crystallization. The governing equations are then transformed to a moving co-ordinate system in order to analyze crystallization waves that propagate with invariant properties. Dual solutions are found by an asymptotic expansion for large activation energies of molecular diffusion. By introducing suitable variables, the results can be presented in a universal form that comprises the influence of all non-dimensional parameters that govern the process. Of particular interest for applications is the prediction of a critical heat loss parameter for the existence of crystallization waves with invariant properties.

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.

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

NASA Astrophysics Data System (ADS)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

Fem Formulation of Heat Transfer in Cylindrical Porous Medium

NASA Astrophysics Data System (ADS)

Azeem; Khaleed, H. M. T.; Soudagar, Manzoor Elahi M.

2017-08-01

Heat transfer in porous medium can be derived from the fundamental laws of flow in porous region ass given by Henry Darcy. The fluid flow and energy transport inside the porous medium can be described with the help of momentum and energy equations. The heat transfer in cylindrical porous medium differs from its counterpart in radial and axial coordinates. The present work is focused to discuss the finite element formulation of heat transfer in cylindrical porous medium. The basic partial differential equations are derived using Darcy law which is the converted into a set of algebraic equations with the help of finite element method. The resulting equations are solved by matrix method for two solution variables involved in the coupled equations.

An algorithm for the kinetics of tire pyrolysis under different heating rates.

PubMed

Quek, Augustine; Balasubramanian, Rajashekhar

2009-07-15

Tires exhibit different kinetic behaviors when pyrolyzed under different heating rates. A new algorithm has been developed to investigate pyrolysis behavior of scrap tires. The algorithm includes heat and mass transfer equations to account for the different extents of thermal lag as the tire is heated at different heating rates. The algorithm uses an iterative approach to fit model equations to experimental data to obtain quantitative values of kinetic parameters. These parameters describe the pyrolysis process well, with good agreement (r(2)>0.96) between the model and experimental data when the model is applied to three different brands of automobile tires heated under five different heating rates in a pure nitrogen atmosphere. The model agrees with other researchers' results that frequencies factors increased and time constants decreased with increasing heating rates. The model also shows the change in the behavior of individual tire components when the heating rates are increased above 30 K min(-1). This result indicates that heating rates, rather than temperature, can significantly affect pyrolysis reactions. This algorithm is simple in structure and yet accurate in describing tire pyrolysis under a wide range of heating rates (10-50 K min(-1)). It improves our understanding of the tire pyrolysis process by showing the relationship between the heating rate and the many components in a tire that depolymerize as parallel reactions.

Three-Dimensional Magnetohydrodynamic Modeling of the Solar Wind Including Pickup Protons and Turbulence Transport

NASA Technical Reports Server (NTRS)

Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

2012-01-01

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

NASA Astrophysics Data System (ADS)

Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

2018-04-01

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

Polymer Fluid Dynamics.

ERIC Educational Resources Information Center

Bird, R. Byron

1980-01-01

Problems in polymer fluid dynamics are described, including development of constitutive equations, rheometry, kinetic theory, flow visualization, heat transfer studies, flows with phase change, two-phase flow, polymer unit operations, and drag reduction. (JN)

Unstructured Adaptive Meshes: Bad for Your Memory?

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Feng, Hui-Yu; VanderWijngaart, Rob

2003-01-01

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Hall effects on peristalsis of boron nitride-ethylene glycol nanofluid with temperature dependent thermal conductivity

NASA Astrophysics Data System (ADS)

Abbasi, F. M.; Gul, Maimoona; Shehzad, S. A.

2018-05-01

Current study provides a comprehensive numerical investigation of the peristaltic transport of boron nitride-ethylene glycol nanofluid through a symmetric channel in presence of magnetic field. Significant effects of Brownian motion and thermophoresis have been included in the energy equation. Hall and Ohmic heating effects are also taken into consideration. Resulting system of non-linear equations is solved numerically using NDSolve in Mathematica. Expressions for velocity, temperature, concentration and streamlines are derived and plotted under the assumption of long wavelength and low Reynolds number. Influence of various parameters on heat and mass transfer rates have been discussed with the help of bar charts.

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.

Experimental and numerical studies on the treatment of wet astronaut trash by forced-convection drying

NASA Astrophysics Data System (ADS)

Arquiza, J. M. R. Apollo; Morrow, Robert; Remiker, Ross; Hunter, Jean B.

2017-09-01

During long-term space missions, astronauts generate wet trash, including food containers with uneaten portions, moist hygiene wipes and wet paper towels. This waste produces two problems: the loss of water and the generation of odors and health hazards by microbial growth. These problems are solved by a closed-loop, forced-convection, heat-pump drying system which stops microbial activity by both pasteurization and desiccation, and recovers water in a gravity-independent porous media condensing heat exchanger. A transient, pseudo-homogeneous continuum model for the drying of wet ersatz trash was formulated for this system. The model is based on the conservation equations for energy and moisture applied to the air and solid phases and includes the unique trash characteristic of having both dry and wet solids. Experimentally determined heat and mass transfer coefficients, together with the moisture sorption equilibrium relationship for the wet material are used in the model. The resulting system of differential equations is solved by the finite-volume method as implemented by the commercial software COMSOL. Model simulations agreed well with experimental data under certain conditions. The validated model will be used in the optimization of the entire closed-loop system consisting of fan, air heater, dryer vessel, heat-pump condenser, and heat-recovery modules.

Symposium on Numerical and Physical Aspects of Aerodynamic Flows

DTIC Science & Technology

1992-01-15

ReT/R. -1 wide range of Mach numbers including pressure gradient, a = - (a*) (10) surface roughness. surface heating and cooling . and surface 9 I + ReT...and specific heat at constant pressure, respectively. Favre equation is then obtained by contracting the Reynolds-stress decomposition is applied to...their near- wall behavior. In other words, if highly cooled -wall flows are to be predicted correctly, heat fluxes should be modeled e = 2ak + 4bky

Gradient estimates on the weighted p-Laplace heat equation

NASA Astrophysics Data System (ADS)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

An investigation of the accuracy of the Merkel equation for evaporative cooling tower calculations. Waste heat management

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

Yadigaroglu, G.; Pastor, E.J.

1974-01-01

The exact differential equations governing heat and mass transfer and air flow in an evaporative, natural-draft cooling tower are presented. The Merkel equation is then derived starting from this exact formulation and showing all the approximations involved. The Merkel formulation lumps the sensible and the latent heat transfer together and considers a single enthalpy-difference driving force for the total heat transfer. The effect of the approximations inherent in the Merkel equation is investigated and analyzed by a series of parametric numerical calculations of cooling tower performance under various ambient conditions and load conditions.

Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating.

PubMed

Qasim, Muhammad; Khan, Ilyas; Shafie, Sharidan

2013-01-01

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involved parameters on dimensionless velocity, microrotation and temperature is examined. An excellent agreement is found between the present and previous limiting results.

Double diffusive conjugate heat transfer: Part III

NASA Astrophysics Data System (ADS)

Soudagar, Manzoor Elahi M.; Azeem

2018-05-01

The placement of a small solid wall towards cold surface of square porous cavity affects the heat transfer behavior of porous region due to restriction of fluid motion in the region occupied by solid wall. An investigation of heat transfer is carried out to understand the fluid flow and heat transfer behavior in porous cavity by solving the governing partial differential equations. Galerkin's approach is used to convert the partial differential equations into algebraic form of equations by applying finite element method. The heat transfer increases for solid towards right surface as compared to the case of solid at center of cavity.

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.

Self-consistent electro-opto-thermal model of quantum cascade lasers with coupled electron and phonon interactions far from equilibrium

NASA Astrophysics Data System (ADS)

Yousefvand, Hossein Reza

2017-12-01

A self-consistent model of quantum cascade lasers (QCLs) is presented here for the study of the QCL's behavior in the far from equilibrium conditions. The approach is developed by employing a number of physics-based models such as the carrier and photon rate equations, the energy balance equation, the heat transfer equation and a simplified rate equation for the creation and annihilation of nonequilibrium optical phonons. The temperature dependency of the relevant physical effects such as stimulated gain cross section, longitudinal optical (LO) phonons and hot-phonon generation rates are included in the model. Using the presented model, the static and transient device characteristics are calculated and analyzed for a wide range of heat sink temperatures. Besides the output characteristics, this model also provides a way to study the hot-phonon dynamics in the device, and to explore the electron temperature and thermal roll-over in the QCLs.

Slip effect on stagnation point flow past a stretching surface with the presence of heat generation/absorption and Newtonian heating

NASA Astrophysics Data System (ADS)

Mohamed, Muhammad Khairul Anuar; Noar, Nor Aida Zuraimi Md; Ismail, Zulkhibri; Kasim, Abdul Rahman Mohd; Sarif, Norhafizah Md; Salleh, Mohd Zuki; Ishak, Anuar

2017-08-01

Present study solved numerically the velocity slip effect on stagnation point flow past a stretching surface with the presence of heat generation/absorption and Newtonian heating. The governing equations which in the form of partial differential equations are transformed to ordinary differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the surface temperature, heat transfer coefficient, reduced skin friction coefficient as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the pertinent parameter such as Prandtl number, stretching parameter, heat generation/absorption parameter, velocity slip parameter and conjugate parameter are analyzed and discussed.

Simulations of Turbine Cooling Flows Using a Multiblock-Multigrid Scheme

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Ameri, Ali A.; Rigby, David L.

1996-01-01

Results from numerical simulations of air flow and heat transfer in a 'branched duct' geometry are presented. The geometry contains features, including pins and a partition, as are found in coolant passages of turbine blades. The simulations were performed using a multi-block structured grid system and a finite volume discretization of the governing equations (the compressible Navier-Stokes equations). The effects of turbulence on the mean flow and heat transfer were modeled using the Baldwin-Lomax turbulence model. The computed results are compared to experimental data. It was found that the extent of some regions of high heat transfer was somewhat under predicted. It is conjectured that the underlying reason is the local nature of the turbulence model which cannot account for upstream influence on the turbulence field. In general, however, the comparison with the experimental data is favorable.

User's guide of TOUGH2-EGS-MP: A Massively Parallel Simulator with Coupled Geomechanics for Fluid and Heat Flow in Enhanced Geothermal Systems VERSION 1.0

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

Xiong, Yi; Fakcharoenphol, Perapon; Wang, Shihao

2013-12-01

TOUGH2-EGS-MP is a parallel numerical simulation program coupling geomechanics with fluid and heat flow in fractured and porous media, and is applicable for simulation of enhanced geothermal systems (EGS). TOUGH2-EGS-MP is based on the TOUGH2-MP code, the massively parallel version of TOUGH2. In TOUGH2-EGS-MP, the fully-coupled flow-geomechanics model is developed from linear elastic theory for thermo-poro-elastic systems and is formulated in terms of mean normal stress as well as pore pressure and temperature. Reservoir rock properties such as porosity and permeability depend on rock deformation, and the relationships between these two, obtained from poro-elasticity theories and empirical correlations, are incorporatedmore » into the simulation. This report provides the user with detailed information on the TOUGH2-EGS-MP mathematical model and instructions for using it for Thermal-Hydrological-Mechanical (THM) simulations. The mathematical model includes the fluid and heat flow equations, geomechanical equation, and discretization of those equations. In addition, the parallel aspects of the code, such as domain partitioning and communication between processors, are also included. Although TOUGH2-EGS-MP has the capability for simulating fluid and heat flows coupled with geomechanical effects, it is up to the user to select the specific coupling process, such as THM or only TH, in a simulation. There are several example problems illustrating applications of this program. These example problems are described in detail and their input data are presented. Their results demonstrate that this program can be used for field-scale geothermal reservoir simulation in porous and fractured media with fluid and heat flow coupled with geomechanical effects.« less

Research and application of surface heat treatment for multipulse laser ablation of materials

NASA Astrophysics Data System (ADS)

Cai, Song; Chen, Genyu; Zhou, Cong

2015-11-01

This study analysed a laser ablation platform and built heat transfer equations for multipulse laser ablation of materials. The equations include three parts: laser emission after the material melt and gasification; end of laser emission after the material melts and there is the presence of a super-hot layer and solid-phase heat transfer changes during material ablation. For each of the three parts, the effects of evaporation, plasma shielding and energy accumulation under the pulse interval were considered. The equations are reasonable, and all the required parameters are only related to the laser parameters and material properties, allowing the model to have a certain versatility and practicability. The model was applied for numerical simulation of the heat transfer characteristics in the multipulse laser ablation of bronze and diamond. Next, experiments were conducted to analyse the topography of a bronze-bonded diamond grinding wheel after multipulse laser ablation. The theoretical analysis and experimental results showed that multipulse laser can merge the truing and dressing on a bronze-bonded diamond grinding wheel. This study provides theoretical guidance for optimising the process parameters in the laser ablation of a bronze-bonded diamond grinding wheel. A comparative analysis showed that the numerical solution to the model is in good agreement with the experimental data, thus verifying the correctness and feasibility of the heat transfer model.

Heat pipe dynamic behavior

NASA Technical Reports Server (NTRS)

Issacci, F.; Roche, G. L.; Klein, D. B.; Catton, I.

1988-01-01

The vapor flow in a heat pipe was mathematically modeled and the equations governing the transient behavior of the core were solved numerically. The modeled vapor flow is transient, axisymmetric (or two-dimensional) compressible viscous flow in a closed chamber. The two methods of solution are described. The more promising method failed (a mixed Galerkin finite difference method) whereas a more common finite difference method was successful. Preliminary results are presented showing that multi-dimensional flows need to be treated. A model of the liquid phase of a high temperature heat pipe was developed. The model is intended to be coupled to a vapor phase model for the complete solution of the heat pipe problem. The mathematical equations are formulated consistent with physical processes while allowing a computationally efficient solution. The model simulates time dependent characteristics of concern to the liquid phase including input phase change, output heat fluxes, liquid temperatures, container temperatures, liquid velocities, and liquid pressure. Preliminary results were obtained for two heat pipe startup cases. The heat pipe studied used lithium as the working fluid and an annular wick configuration. Recommendations for implementation based on the results obtained are presented. Experimental studies were initiated using a rectangular heat pipe. Both twin beam laser holography and laser Doppler anemometry were investigated. Preliminary experiments were completed and results are reported.

The thermodynamic properties of oxygen and nitrogen

NASA Technical Reports Server (NTRS)

Stewart, R. B.; Jacobsen, R. T.; Myers, A. F.

1972-01-01

The development of a single equation of state for oxygen and nitrogen based on the thermodynamic properties of the gases is described. The coefficients of the equation of state were determined by simultaneous least squares fits to values of isochoric heat capacity and saturation density values used to define the criteria for phase equilibrium. Tables of data for the conditions of both gases are included.

Analytic Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings

NASA Technical Reports Server (NTRS)

Bruckner, Robert J.; DellaCorte, Christopher; Prahl, Joseph M.

2005-01-01

A simulation and modeling effort is conducted on gas foil thrust bearings. A foil bearing is a self acting hydrodynamic device capable of separating stationary and rotating components of rotating machinery by a film of air or other gaseous lubricant. Although simple in appearance these bearings have proven to be complicated devices in analysis. They are sensitive to fluid structure interaction, use a compressible gas as a lubricant, may not be in the fully continuum range of fluid mechanics, and operate in the range where viscous heat generation is significant. These factors provide a challenge to the simulation and modeling task. The Reynolds equation with the addition of Knudsen number effects due to thin film thicknesses is used to simulate the hydrodynamics. The energy equation is manipulated to simulate the temperature field of the lubricant film and combined with the ideal gas relationship, provides density field input to the Reynolds equation. Heat transfer between the lubricant and the surroundings is also modeled. The structural deformations of the bearing are modeled with a single partial differential equation. The equation models the top foil as a thin, bending dominated membrane whose deflections are governed by the biharmonic equation. A linear superposition of hydrodynamic load and compliant foundation reaction is included. The stiffness of the compliant foundation is modeled as a distributed stiffness that supports the top foil. The system of governing equations is solved numerically by a computer program written in the Mathematica computing environment. Representative calculations and comparisons with experimental results are included for a generation I gas foil thrust bearing.

Thermodynamic analysis of journal bearings operating under steady state loading in laminar regime. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Khonsari, M. M.

1983-01-01

Thermohydrodynamic effects in journal bearings operating under steady load in laminar regime are investigated. An analytical model for the finite and infinitely long journal bearings is formulated. The model includes correction factors for the cavitation effects in the unloaded region of the bearing and the mixing of the recirculating oil and supply oil at the oil inlet. A finite difference computer program is developed to numerically solve the governing equations of the continuity, Reynolds, energy, Laplace heat conduction, and a viscosity-temperature relation simultaneously. The program includes a numerical technique for obtaining an isothermal shaft temperature. The numerical results of temperature distribution and the heat effects on the bearing load carrying capacity agree closely with those of experimental findings. Several different sets of simpler boundary conditions for the energy equation are studied.

Numerical analysis on interactions between fluid flow and structure deformation in plate-fin heat exchanger by Galerkin method

NASA Astrophysics Data System (ADS)

Liu, Jing-cheng; Wei, Xiu-ting; Zhou, Zhi-yong; Wei, Zhen-wen

2018-03-01

The fluid-structure interaction performance of plate-fin heat exchanger (PFHE) with serrated fins in large scale air-separation equipment was investigated in this paper. The stress and deformation of fins were analyzed, besides, the interaction equations were deduced by Galerkin method. The governing equations of fluid flow and heat transfer in PFHE were deduced by finite volume method (FVM). The distribution of strain and stress were calculated in large scale air separation equipment and the coupling situation of serrated fins under laminar situation was analyzed. The results indicated that the interactions between fins and fluid flow in the exchanger have significant impacts on heat transfer enhancement, meanwhile, the strain and stress of fins includes dynamic pressure of the sealing head and flow impact with the increase of flow velocity. The impacts are especially significant at the conjunction of two fins because of the non-alignment fins. It can be concluded that the soldering process and channel width led to structure deformation of fins in the exchanger, and degraded heat transfer efficiency.

Modeling of the WSTF frictional heating apparatus in high pressure systems

NASA Technical Reports Server (NTRS)

Skowlund, Christopher T.

1992-01-01

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

Study on Heat Transfer Agent Models of Transmission Line and Transformer

NASA Astrophysics Data System (ADS)

Wang, B.; Zhang, P. P.

2018-04-01

When using heat transfer simulation to study the dynamic overload of transmission line and transformer, it needs to establish the mathematical expression of heat transfer. However, the formula is a nonlinear differential equation or equation set and it is not easy to get general solutions. Aiming at this problem, some different temperature change processes caused by different initial conditions are calculated by differential equation and equation set. New agent models are developed according to the characteristics of different temperature change processes. The results show that the agent models have high precision and can solve the problem that the original equation cannot be directly applied in some practical engineers.

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

NASA Technical Reports Server (NTRS)

Hou, Gene

2000-01-01

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

Selection of Oil Coolers to Avoid Congealing

DTIC Science & Technology

1943-07-01

from one fluid to another, there is a resistance to heat transfer l/ htSt . The total resistance to the flow of heat is the sum of the...total thermal resistance equation is, htst hasa hoso n v \\hasa Vo/ (W The generally accepted equations for correlating heat...1 -. 1 htSt n v Da jS u Do Ho •a°l|.ki (5i2jLS 8oc3lc0/ W^ V \\SAafa; ^ fa^Z/yfij tM: (7) The heat-balance equation is. H

Heat transfer in a conical porous medium due to inner and top surface heating: Effect of radius ratio

NASA Astrophysics Data System (ADS)

Ahamad, N. Ameer; Khan, T. M. Yunus

2018-05-01

The present study investigates the effect of radius ratio and Rayleigh number on beat transfer characteristics of an annular cone subjected to two side heating and one side cooling. Finite element method is used to convert the partial differential equations into algebraic equations. The resulting equations are solved with the help of in-house computer code developed for specific purpose of heat transfer in conical porous medium. The results are discussed with respect to the radius ratio and Rayleigh number.

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.

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

NASA Technical Reports Server (NTRS)

Garrett, L. B.; Smith, G. L.; Perkins, J. N.

1972-01-01

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Numerical simulations of drainage flows on Mars

NASA Technical Reports Server (NTRS)

Parish, Thomas R.; Howard, Alan D.

1992-01-01

Data collected by Viking Landers have shown that the meteorology of the near surface Martian environment is analogous to desertlike terrestrial conditions. Geological evidence such as dunes and frost streaks indicate that the surface wind is a potentially important factor in scouring of the martian landscape. In particular, the north polar basin shows erosional features that suggest katabatic wind convergence into broad valleys near the margin of the polar cap. The pattern of katabatic wind drainage off the north polar cap is similar to that observed on Earth over Antarctica or Greenland. The sensitivity is explored of Martian drainage flows to variations in terrain slope and diurnal heating using a numerical modeling approach. The model used is a 2-D sigma coordinate primitive equation system that has been used for simulations of Antarctic drainage flows. Prognostic equations include the flux forms of the horizontal scalar momentum equations, temperature, and continuity. Parameterization of both longwave (terrestrial) and shortwave (solar) radiation is included. Turbulent transfer of heat and momentum in the Martian atmosphere remains uncertain since relevant measurements are essentially nonexistent.

TWO-PHASE (GAS-LIQUID) SYSTEM: HEAT TRANSFER AND HYDRAULICS. An Annotated Bibliography

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

Kepple, R.R.; Tung, T.V.

1963-07-01

A bibliography of 2843 references in abstracted form is presented which covers the period l950 to 1962. The references are arranged under the following headings: books and review articles, boiling, bubble, condensation, evaporation, equations of state, interfacial characteristics, mass transfer across phase boundaries, measurement techniques, nuclear reactor heat removal, and twophase flow. An author index is included. (D.L.C.)

Electrohydrodynamic heat pipe research

NASA Technical Reports Server (NTRS)

Jones, T. B.; Perry, M. P.

1973-01-01

Experimental and theoretical applications to electrohydrodynamic heat pipe (EHDHP) research are presented. Two problems in the research which are discussed are the prediction of the effective thermal conductance of an EHDHP with threaded grooves for fluid distribution to the evaporator of an EHDHP. Hydrodynamic equations are included along with a discussion of boundary conditions and burn-out conditions. A discussion of the theoretical and experimental results is presented.

THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC MODELING OF THE SOLAR WIND INCLUDING PICKUP PROTONS AND TURBULENCE TRANSPORT

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

Usmanov, Arcadi V.; Matthaeus, William H.; Goldstein, Melvyn L., E-mail: arcadi.usmanov@nasa.gov

2012-07-20

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfermore » from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons. We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 Degree-Sign -90 Degree-Sign and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.« less

Heat loss and hypothermia in free diving: Estimation of survival time under water

NASA Astrophysics Data System (ADS)

Aguilella-Arzo, Marcel; Alcaraz, Antonio; Aguilella, Vicente M.

2003-04-01

The heat exchange between a diver and the colder surrounding water is analyzed on the basis of the fundamental equations of thermal transport. To estimate the decrease in the diver's body temperature as a function of time, we discuss the complex interplay of several factors including the body heat production rate, the role of the diver's wet suit, and the way different heat exchange mechanisms (conduction, convection, and radiation) contribute to thermal transport. This knowledge could be useful to prevent physiological disorders that occur when the human body temperature drops below 35 °C.

Arc-driven rail gun research

NASA Technical Reports Server (NTRS)

Ray, P. K.

1984-01-01

The equations describing the performance of an inductively-driven rail gun are analyzed numerically. Friction between the projectile and rails is included through an empirical formulation. The equations are applied to the experiment of Rashleigh and Marshall to obtain an estimate of energy distribution in rail guns as a function of time. The effect of frictional heat dissipation on the bore of the gun is calculated. The mechanism of plasma and projectile acceleration in a dc rail gun is described from a microscopic point of view through the establishment of the Hall field. The plasma conductivity is shown to be a tensor indicating that there is a small component of current parallel to the direction of acceleration. The plasma characteristics are evaluated as a function of plasma mass through a simple fluid mechanical analysis of the plasma. By equating the energy dissipated in the plasma with the radiation heat loss, the properties of the plasma are determined.

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

Tissue and external insulation estimates and their effects on prediction of energy requirements and of heat stress.

PubMed

Berman, A

2004-05-01

Published data were used to develop improved equations to predict tissue insulation (TI) and external insulation (EI) and their effects on maintenance requirements of Holstein cattle. These are used to calculate lower critical temperature (LCT), energy cost of exposure to temperatures below LCT, and excess heat accumulating in the body at temperatures above LCT. The National Research Council classifies TI by age groups and body condition score; and in the EI equation air velocity effects are linear and coat insulation values are derived from beef animals in cold climates. These lead to low LCT values, which are not compatible with known effects of environment on the performance of Holsteins in warm climates. Equations were developed to present TI as a function of body weight, improving prediction of TI for animals of similar age but differing in body weight. An equation was developed to predict rate of decrease of TI at ambient temperatures above LCT. Nonlinear equations were developed that account for wind effects as boundary layer insulation effects dependent on body weight and air velocity. Published data were used to develop adjustments for hair coat effects on EI in Holstein cows. While by NRC equations, wind has negligible effects on heat loss, the recalculated effects of air velocity on heat loss were consistent with published effects of forced ventilation on the responses of the Holstein cow. The derived LCT was higher by 10 to 20 degrees C than that calculated by NRC (2001) and accounted for known Holstein performance in temperate and warm climates. These equations pointed to tentative significant effects of cold (-10 degrees C) on energy requirements (7 Mcal/d) further increased by 1 m/s wind (15 Mcal/d), even in high-producing cows. Needs for increased heat dissipation and estimating heat stress development at ambient temperatures above the LCT are predicted. These equations can be used to revise NRC equations for heat exchange.

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Relationships of models of the inner magnetosphere to the Rice Convection Model

NASA Astrophysics Data System (ADS)

Heinemann, M.; Wolf, R. A.

2001-08-01

Ideal magnetohydrodynamics is known to be inaccurate for the Earth's inner magnetosphere, where transport by gradient-curvature drift is nonnegligible compared to E×B drift. Most theoretical treatments of the inner plasma sheet and ring current, including the Rice Convection Model (RCM), treat the inner magnetospheric plasma in terms of guiding center drifts. The RCM assumes that the distribution function is isotropic, but particles with different energy invariants are treated as separate guiding center fluids. However, Peymirat and Fontaine [1994] developed a two-fluid picture of the inner magnetosphere, which utilizes modified forms of the conventional fluid equations, not guiding center drift equations. Heinemann [1999] argued theoretically that for inner magnetospheric conditions the fluid energy equation should include a heat flux term, which, in the case of Maxwellian plasma, was derived by Braginskii [1965]. We have now reconciled the Heinemann [1999] fluid approach with the RCM. The fluid equations, including the Braginskii heat flux, can be derived by taking appropriate moments of the RCM equations for the case of the Maxwellian distribution. The physical difference between the RCM formalism and the Heinemann [1999] fluid approach is that the RCM pretends that particles suffer elastic collisions that maintain the isotropy of the distribution function but do not change particle energies. The Heinemann [1999] fluid treatment makes a different physical approximation, namely that the collisions maintain local thermal equilibrium among the ions and separately among the electrons. For some simple cases, numerical results are presented that illustrate the differences in the predictions of the two formalisms, along with those of MHD, guiding center theory, and Peymirat and Fontaine [1994].

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.

Thermal Model of a Current-Carrying Wire in a Vacuum

NASA Technical Reports Server (NTRS)

Border, James

2006-01-01

A computer program implements a thermal model of an insulated wire carrying electric current and surrounded by a vacuum. The model includes the effects of Joule heating, conduction of heat along the wire, and radiation of heat from the outer surface of the insulation on the wire. The model takes account of the temperature dependences of the thermal and electrical properties of the wire, the emissivity of the insulation, and the possibility that not only can temperature vary along the wire but, in addition, the ends of the wire can be thermally grounded at different temperatures. The resulting second-order differential equation for the steady-state temperature as a function of position along the wire is highly nonlinear. The wire is discretized along its length, and the equation is solved numerically by use of an iterative algorithm that utilizes a multidimensional version of the Newton-Raphson method.

Effect of viscous dissipation and radiation in an annular cone

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

Ahmed, N. J. Salman; Kamangar, Sarfaraz; Khan, T. M. Yunus, E-mail: yunus.tatagar@gmail.com

The viscous dissipation is an effect due to which heat is generated inside the medium. The presence of radiation further complicates the heat transfer behavior inside porous medium. The present paper discusses the combined effect of viscous dissipation and radiation inside a porous medium confined in an annular cone with inner radius r{sub i}. The viscous dissipation and radiation terms are included in the energy equation thereby solving the coupled momentum and energy equations with the help of finite element method. The results are presented in terms of isothermal and streamline indicating the thermal and fluid flow behavior of porousmore » medium. It is found that the combination of viscous dissipation and radiation parameter and the cone angle has significant effect on the heat transfer and fluid flow behavior inside the porous medium. The fluid velocity is found to increase with the increase in Raleigh number.« less

A Transport Model for Non-Local Heating of Electrons in ICP Reactors

NASA Technical Reports Server (NTRS)

Chang, C. H.; Bose, Deepak; Arnold, James O. (Technical Monitor)

1998-01-01

A new model has been developed for non-local heating of electrons in ICP reactors, based on a hydrodynamic approach. The model has been derived using the electron momentum conservation in azimuthal direction with electromagnetic and frictional forces respectively as driving force and damper of harmonic oscillatory motion of electrons. The resulting transport equations include the convection of azimuthal electron momentum in radial and axial directions, thereby accounting for the non-local effects. The azimuthal velocity of electrons and the resulting electrical current are coupled to the Maxwell's relations, thus forming a self-consistent model for non-local heating. This model is being implemented along with a set of Navier-Stokes equations for plasma dynamics and gas flow to simulate low-pressure (few mTorr's) ICP discharges. Characteristics of nitrogen plasma in a TCP 300mm etch reactor is being studied. The results will be compared against the available Langmuir probe measurements.

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.

Test of a new heat-flow equation for dense-fluid shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2010-09-21

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

Sensitivity Equation Derivation for Transient Heat Transfer Problems

NASA Technical Reports Server (NTRS)

Hou, Gene; Chien, Ta-Cheng; Sheen, Jeenson

2004-01-01

The focus of the paper is on the derivation of sensitivity equations for transient heat transfer problems modeled by different discretization processes. Two examples will be used in this study to facilitate the discussion. The first example is a coupled, transient heat transfer problem that simulates the press molding process in fabrication of composite laminates. These state equations are discretized into standard h-version finite elements and solved by a multiple step, predictor-corrector scheme. The sensitivity analysis results based upon the direct and adjoint variable approaches will be presented. The second example is a nonlinear transient heat transfer problem solved by a p-version time-discontinuous Galerkin's Method. The resulting matrix equation of the state equation is simply in the form of Ax = b, representing a single step, time marching scheme. A direct differentiation approach will be used to compute the thermal sensitivities of a sample 2D problem.

The study and development of the empirical correlations equation of natural convection heat transfer on vertical rectangular sub-channels

NASA Astrophysics Data System (ADS)

Kamajaya, Ketut; Umar, Efrizon; Sudjatmi, K. S.

2012-06-01

This study focused on natural convection heat transfer using a vertical rectangular sub-channel and water as the coolant fluid. To conduct this study has been made pipe heaters are equipped with thermocouples. Each heater is equipped with five thermocouples along the heating pipes. The diameter of each heater is 2.54 cm and 45 cm in length. The distance between the central heating and the pitch is 29.5 cm. Test equipment is equipped with a primary cooling system, a secondary cooling system and a heat exchanger. The purpose of this study is to obtain new empirical correlations equations of the vertical rectangular sub-channel, especially for the natural convection heat transfer within a bundle of vertical cylinders rectangular arrangement sub-channels. The empirical correlation equation can support the thermo-hydraulic analysis of research nuclear reactors that utilize cylindrical fuel rods, and also can be used in designing of baffle-free vertical shell and tube heat exchangers. The results of this study that the empirical correlation equations of natural convection heat transfer coefficients with rectangular arrangement is Nu = 6.3357 (Ra.Dh/x)0.0740.

Measuring the effects of heat wave episodes on the human body's thermal balance

NASA Astrophysics Data System (ADS)

Katavoutas, George; Theoharatos, George; Flocas, Helena A.; Asimakopoulos, Dimosthenis N.

2009-03-01

During the peak of an extensive heat wave episode on 23-25 July 2007, simultaneous thermophysiological measurements were made in two non-acclimated healthy adults of different sex in a suburban area of Greater Athens, Greece. Based on experimental measurements of mean skin temperature and metabolic heat production, heat fluxes to and from the human body were calculated, and the biometeorological index heat load (HL) produced was determined according to the heat balance equation. Comparing experimental values with those derived from theoretical estimates revealed a great heat stress for both individuals, especially the male, while theoretical values underestimated heat stress. The study also revealed that thermophysiological factors, such as mean skin temperature and metabolic heat production, play an important role in determining heat fluxes patterns in the heat balance equation. The theoretical values of mean skin temperature as derived from an empirical equation may not be appropriate to describe the changes that take place in a non-acclimated individual. Furthermore, the changes in metabolic heat production were significant even for standard activity.

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

PubMed

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

The equation of state of Song and Mason applied to fluorine

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

Eslami, H.; Boushehri, A.

1999-03-01

An analytical equation of state is applied to calculate the compressed and saturation thermodynamic properties of fluorine. The equation of state is that of Song and Mason. It is based on a statistical mechanical perturbation theory of hard convex bodies and is a fifth-order polynomial in the density. There exist three temperature-dependent parameters: the second virial coefficient, an effective molecular volume, and a scaling factor for the average contact pair distribution function of hard convex bodies. The temperature-dependent parameters can be calculated if the intermolecular pair potential is known. However, the equation is usable with much less input than themore » full intermolecular potential, since the scaling factor and effective volume are nearly universal functions when expressed in suitable reduced units. The equation of state has been applied to calculate thermodynamic parameters including the critical constants, the vapor pressure curve, the compressibility factor, the fugacity coefficient, the enthalpy, the entropy, the heat capacity at constant pressure, the ratio of heat capacities, the Joule-Thomson coefficient, the Joule-Thomson inversion curve, and the speed of sound for fluorine. The agreement with experiment is good.« less

Alfvén Wave Reflection and Turbulent Heating in the Solar Wind from 1 Solar Radius to 1 AU: An Analytical Treatment

NASA Astrophysics Data System (ADS)

Chandran, Benjamin D. G.; Hollweg, Joseph V.

2009-12-01

We study the propagation, reflection, and turbulent dissipation of Alfvén waves in coronal holes and the solar wind. We start with the Heinemann-Olbert equations, which describe non-compressive magnetohydrodynamic fluctuations in an inhomogeneous medium with a background flow parallel to the background magnetic field. Following the approach of Dmitruk et al., we model the nonlinear terms in these equations using a simple phenomenology for the cascade and dissipation of wave energy and assume that there is much more energy in waves propagating away from the Sun than waves propagating toward the Sun. We then solve the equations analytically for waves with periods of hours and longer to obtain expressions for the wave amplitudes and turbulent heating rate as a function of heliocentric distance. We also develop a second approximate model that includes waves with periods of roughly one minute to one hour, which undergo less reflection than the longer-period waves, and compare our models to observations. Our models generalize the phenomenological model of Dmitruk et al. by accounting for the solar wind velocity, so that the turbulent heating rate can be evaluated from the coronal base out past the Alfvén critical point—that is, throughout the region in which most of the heating and acceleration occurs. The simple analytical expressions that we obtain can be used to incorporate Alfvén-wave reflection and turbulent heating into fluid models of the solar wind.

Solar heating for an observatory--Lincoln, Nebraska

NASA Technical Reports Server (NTRS)

1981-01-01

Report describes solar-energy system for 50 seat observatory that provides 60 percent of space heating needs. System includes 9 flat-plate collectors, rock storage bin, blowers, controls, ducting, and auxiliary natural-gas furnace; it has five operation modes. Net energy savings were 11.31 million Btu for 12 months, or equivalent of 1.9 barrels of oil. Report appendixes list performance factor definitions, performance equations, and average area weather conditions.

Equation of State for Solid Phase I of Carbon Dioxide Valid for Temperatures up to 800 K and Pressures up to 12 GPa

NASA Astrophysics Data System (ADS)

Martin Trusler, J. P.

2011-12-01

The available thermodynamic-property data for solid phase I of carbon dioxide ("dry ice") are reviewed and used to determine the parameters of a new fundamental equation of state constructed in the form of a Helmholtz energy function with temperature and molar volume as the independent variables. The experimental data considered include the pressure, molar volume, and isobaric heat capacity along the sublimation curve, the melting-pressure curve, and molar volume in the compressed solid at temperatures from 295 to 764 K and pressures up to 12 GPa. The equation of state is based on the quasi-harmonic approximation, incorporating a Debye oscillator distribution for the vibrons, two discrete modes for the librons and a further three distinct modes for the internal vibrations of the CO2 molecule. A small anharmonic correction term is included, which is significant mainly in the region of the triple point. The estimated relative uncertainty of molar volume at specified temperature and pressure calculated from the equation of state is 0.02% on the sublimation curve and 1.5% in the compressed solid; for isobaric heat capacity on the sublimation curve, the uncertainty varies from 5.0% to 0.5% between 2 and 195 K. Auxiliary equations for the pressure and molar volume on the sublimation and melting curves are given. The equation of state is valid at temperatures from 0 to 800 K and at pressures from the solid-fluid phase boundary to 12 GPa.

Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source

NASA Astrophysics Data System (ADS)

Gururaja Rao, C.; Nagabhushana Rao, V.; Krishna Das, C.

2008-04-01

Prominent results of a simulation study on conjugate convection with surface radiation from an open cavity with a traversable flush mounted discrete heat source in the left wall are presented in this paper. The open cavity is considered to be of fixed height but with varying spacing between the legs. The position of the heat source is varied along the left leg of the cavity. The governing equations for temperature distribution along the cavity are obtained by making energy balance between heat generated, conducted, convected and radiated. Radiation terms are tackled using radiosity-irradiation formulation, while the view factors, therein, are evaluated using the crossed-string method of Hottel. The resulting non-linear partial differential equations are converted into algebraic form using finite difference formulation and are subsequently solved by Gauss Seidel iterative technique. An optimum grid system comprising 111 grids along the legs of the cavity, with 30 grids in the heat source and 31 grids across the cavity has been used. The effects of various parameters, such as surface emissivity, convection heat transfer coefficient, aspect ratio and thermal conductivity on the important results, including local temperature distribution along the cavity, peak temperature in the left and right legs of the cavity and relative contributions of convection and radiation to heat dissipation in the cavity, are studied in great detail.

Determination of Optimal Heat-Storage Thickness of Layer for “Smart Wall” by Methods of Nonlinear Heat Conduction Equations for Phase-transition Materials

NASA Astrophysics Data System (ADS)

Pospelova, I.

2017-11-01

The article suggests an original way of keeping heat load and its compensation for a microclimate system by proposing the “Smart Wall”. The construction consists of specially combined composite materials including phase-transition materials. The method for determination of the layer thickness is proposed for a certain accumulation time. Varying the thickness and composition of the layer it is possible to achieve a low amount of the thermal conductivity coefficient and to obtain various functional characteristics of fences.

Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

PubMed

Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

2014-12-01

A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

Theoretical Foundation for Weld Modeling

NASA Technical Reports Server (NTRS)

Traugott, S.

1986-01-01

Differential equations describe physics of tungsten/inert-gas and plasma-arc welding in aluminum. Report collects and describes necessary theoretical foundation upon which numerical welding model is constructed for tungsten/inert gas or plasma-arc welding in aluminum without keyhole. Governing partial differential equations for flow of heat, metal, and current given, together with boundary conditions relevant to welding process. Numerical estimates for relative importance of various phenomena and required properties of 2219 aluminum included

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)

Shivering heat production and body fat protect the core from cooling during body immersion, but not during head submersion: a structural equation model.

PubMed

Pretorius, Thea; Lix, Lisa; Giesbrecht, Gordon

2011-03-01

Previous studies showed that core cooling rates are similar when only the head or only the body is cooled. Structural equation modeling was used on data from two cold water studies involving body-only, or whole body (including head) cooling. Exposure of both the body and head increased core cooling, while only body cooling elicited shivering. Body fat attenuates shivering and core cooling. It is postulated that this protection occurs mainly during body cooling where fat acts as insulation against cold. This explains why head cooling increases surface heat loss with only 11% while increasing core cooling by 39%. Copyright © 2011 Elsevier Ltd. All rights reserved.

Forced Convection Heat Transfer in Circular Pipes

ERIC Educational Resources Information Center

Tosun, Ismail

2007-01-01

One of the pitfalls of engineering education is to lose the physical insight of the problem while tackling the mathematical part. Forced convection heat transfer (the Graetz-Nusselt problem) certainly falls into this category. The equation of energy together with the equation of motion leads to a partial differential equation subject to various…

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

PubMed

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Heat-flow equation motivated by the ideal-gas shock wave.

PubMed

Holian, Brad Lee; Mareschal, Michel

2010-08-01

We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

NASA Astrophysics Data System (ADS)

Nazari, Saman; Toghraie, Davood

2017-03-01

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.

Complete Mie-Gruneisen Equation of State

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

Menikoff, Ralph

2012-06-28

The Mie-Gruneisen equation of state (EOS) is frequently used in hydro simulations to model solids at high pressure (up to a few Mb). It is an incomplete EOS characterized by a Gruneisen coefficient, {Lambda} = -V({partial_derivative}{sub e}P){sub V}, that is a function of only V. Expressions are derived for isentropes and isotherms. This enables the extension to a complete EOS. Thermodynamic consistency requires that the specific heat is a function of a single scaled temperature. A complete extension is uniquely determined by the temperature dependence of the specific heat at a fixed reference density. In addition we show that ifmore » the domain of the EOS extends to T = 0 and the specific heat vanishes on the zero isotherm then {Lambda} a function of only V is equivalent to a specific heat with a single temperature scale. If the EOS domain does not include the zero isotherm, then a specific heat with a single temperature scale leads to a generalization of the Mie-Gruneisen EOS in which the pressure is linear in both the specific energy and the temperature. Such an EOS has previously been used to model liquid nitromethane.« less

Numerical analysis of heat and mass transfer for water recovery in an evaporative cooling tower

NASA Astrophysics Data System (ADS)

Lee, Hyunsub; Son, Gihun

2017-11-01

Numerical analysis is performed for water recovery in an evaporative cooling tower using a condensing heat exchanger, which consists of a humid air channel and an ambient dry air channel. The humid air including water vapor produced in an evaporative cooling tower is cooled by the ambient dry air so that the water vapor is condensed and recovered to the liquid water. The conservation equations of mass, momentum, energy and vapor concentration in each fluid region and the energy equation in a solid region are simultaneously solved with the heat and mass transfer boundary conditions coupled to the effect of condensation on the channel surface of humid air. The present computation demonstrates the condensed water film distribution on the humid air channel, which is caused by the vapor mass transfer between the humid air and the colder water film surface, which is coupled to the indirect heat exchange with the ambient air. Computations are carried out to predict water recovery rate in parallel, counter and cross-flow type heat exchangers. The effects of air flow rate and channel interval on the water recovery rate are quantified.

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!

Modelling the evaporation of a tear film over a contact lens.

PubMed

Talbott, Kevin; Xu, Amber; Anderson, Daniel M; Seshaiyer, Padmanabhan

2015-06-01

A contact lens (CL) separates the tear film into a pre-lens tear film (PrLTF), the fluid layer between the CL and the outside environment, and a post-lens tear film (PoLTF), the fluid layer between the CL and the cornea. We examine a model for evaporation of a PrLTF on a modern permeable CL allowing fluid transfer between the PrLTF and the PoLTF. Evaporation depletes the PrLTF, and continued evaporation causes depletion of the PoLTF via fluid loss through the CL. Governing equations include Navier-Stokes, heat and Darcy's equations for the fluid flow and heat transfer in the PrLTF and porous layer. The PoLTF is modelled by a fixed pressure condition on the posterior surface of the CL. The original model is simplified using lubrication theory for the PrLTF and CL applied to a sagittal plane through the eye. We obtain a partial differential equation (PDE) for the PrLTF thickness that is first-order in time and fourth-order in space. This model incorporates evaporation, conjoining pressure effects in the PrLTF, capillarity and heat transfer. For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically. This reduced model allows for interpretation of the various system parameters and captures most of the basic physics contained in the model. Comparisons of ODE and PDE models, including estimates for the loss of fluid through the lens due to evaporation, are given. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

GCKP84-general chemical kinetics code for gas-phase flow and batch processes including heat transfer effects

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1984-01-01

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

Investigation of obstacle effect to improve conjugate heat transfer in backward facing step channel using fast simulation of incompressible flow

NASA Astrophysics Data System (ADS)

Nouri-Borujerdi, Ali; Moazezi, Arash

2018-01-01

The current study investigates the conjugate heat transfer characteristics for laminar flow in backward facing step channel. All of the channel walls are insulated except the lower thick wall under a constant temperature. The upper wall includes a insulated obstacle perpendicular to flow direction. The effect of obstacle height and location on the fluid flow and heat transfer are numerically explored for the Reynolds number in the range of 10 ≤ Re ≤ 300. Incompressible Navier-Stokes and thermal energy equations are solved simultaneously in fluid region by the upwind compact finite difference scheme based on flux-difference splitting in conjunction with artificial compressibility method. In the thick wall, the energy equation is obtained by Laplace equation. A multi-block approach is used to perform parallel computing to reduce the CPU time. Each block is modeled separately by sharing boundary conditions with neighbors. The developed program for modeling was written in FORTRAN language with OpenMP API. The obtained results showed that using of the multi-block parallel computing method is a simple robust scheme with high performance and high-order accurate. Moreover, the obtained results demonstrated that the increment of Reynolds number and obstacle height as well as decrement of horizontal distance between the obstacle and the step improve the heat transfer.

Calibration of Heat Stress Monitor and its Measurement Uncertainty

NASA Astrophysics Data System (ADS)

Ekici, Can

2017-07-01

Wet-bulb globe temperature (WBGT) equation is a heat stress index that gives information for the workers in the industrial areas. WBGT equation is described in ISO Standard 7243 (ISO 7243 in Hot environments—estimation of the heat stress on working man, based on the WBGT index, ISO, Geneva, 1982). WBGT is the result of the combined quantitative effects of the natural wet-bulb temperature, dry-bulb temperature, and air temperature. WBGT is a calculated parameter. WBGT uses input estimates, and heat stress monitor measures these quantities. In this study, the calibration method of a heat stress monitor is described, and the model function for measurement uncertainty is given. Sensitivity coefficients were derived according to GUM. Two-pressure humidity generators were used to generate a controlled environment. Heat stress monitor was calibrated inside of the generator. Two-pressure humidity generator, which is located in Turkish Standard Institution, was used as the reference device. This device is traceable to national standards. Two-pressure humidity generator includes reference temperature Pt-100 sensors. The reference sensor was sheltered with a wet wick for the calibration of natural wet-bulb thermometer. The reference sensor was centred into a black globe that has got 150 mm diameter for the calibration of the black globe thermometer.

Correlational latent heat by nonlocal quantum kinetic theory

NASA Astrophysics Data System (ADS)

Morawetz, K.

2018-05-01

A kinetic equation of nonlocal and noninstantaneous character unifies the achievements of transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell motion appear, which are usually hidden in non-Markovian behaviors. The remaining corrections are expressed in terms of shifts in space and time that characterize the nonlocality of the scattering process. In this way, it is possible to recast quantum transport into a quasiclassical picture. In addition to the quasiparticle, the balance equations for density, momentum, energy, and entropy also include correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. For Maxwellian particles with time-dependent s -wave scattering, the correlated parts of the observables are calculated and a sign change of the latent heat is reported at a universal ratio of scattering length to the thermal de Broglie wavelength. This is interpreted as a change from correlational heating to cooling.

PKPD model of interleukin-21 effects on thermoregulation in monkeys--application and evaluation of stochastic differential equations.

PubMed

Overgaard, Rune Viig; Holford, Nick; Rytved, Klaus A; Madsen, Henrik

2007-02-01

To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling. A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM. The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function. The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

A fundamental equation of state for 1,1-difluoroethane (HFC-152a)

NASA Astrophysics Data System (ADS)

Tillner-Roth, R.

1995-01-01

A fundamental equation ofstale for HFC-152a ( 1,1-dilluorocthane) is presented covering temperatures between the triple-point temperature ( 154.56 K) and 435 K for pressures up to 311 M Pa. The equation is based on reliable ( p, g, T) data in the range mentioned above. These are generally represented within ±0.1 % of density. Furthermore. experimental values of the vapor pressure, the saturated liquid density, and some isobaric heat capacities in the liquid were included during the correlation process. The new equation of state is compared with experimental data and also with the equation of state developed by Tamatsu et al. Differences between the two equations of state generally result from using different experimental input data. It is shown that the new equation of state allows an accurate calculation of various thermodynamic properties for most technical applications.

A User Guide to PARET/ANL

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

Olson, A. P.; Dionne, B.; Marin-Lafleche, A.

2015-01-01

PARET was originally created in 1969 at what is now Idaho National Laboratory (INL), to analyze reactivity insertion events in research and test reactor cores cooled by light or heavy water, with fuel composed of either plates or pins. The use of PARET is also appropriate for fuel assemblies with curved fuel plates when their radii of curvatures are large with respect to the fuel plate thickness. The PARET/ANL version of the code has been developed at Argonne National Laboratory (ANL) under the sponsorship of the U.S. Department of Energy/NNSA, and has been used by the Reactor Conversion Program tomore » determine the expected transient behavior of a large number of reactors. PARET/ANL models the various fueled regions of a reactor core as channels. Each of these channels consists of a single flat fuel plate/pin (including cladding and, optionally, a gap) with water coolant on each side. In slab geometry the coolant channels for a given fuel plate are of identical dimensions (mirror symmetry), but they can be of different thickness in each channel. There can be many channels, but each channel is independent and coupled only through reactivity feedback effects to the whole core. The time-dependent differential equations that represent the system are replaced by an equivalent set of finite-difference equations in space and time, which are integrated numerically. PARET/ANL uses fundamentally the same numerical scheme as RELAP5 for the time-integration of the point-kinetics equations. The one-dimensional thermal-hydraulic model includes temperature-dependent thermal properties of the solid materials, such as heat capacity and thermal conductivity, as well as the transient heat production and heat transfer from the fuel meat to the coolant. Temperature- and pressure-dependent thermal properties of the coolant such as enthalpy, density, thermal conductivity, and viscosity are also used in determining parameters such as friction factors and heat transfer coefficients. The code first determines the steady-state solution for the initial state. Then the solution of the transient is obtained by integration in time and space. Multiple heat transfer, DNB and flow instability correlations are available. The code was originally developed to model reactors cooled by an open loop, which was adequate for rapid transients in pool-type cores. An external loop model appropriate for Miniature Neutron Source Reactors (MNSR’s) was also added to PARET/ANL to model natural circulation within the vessel, heat transfer from the vessel to pool and heat loss by evaporation from the pool. PARET/ANL also contains models for decay heat after shutdown, control rod reactivity versus time or position, time-dependent pump flow, and loss-of-flow event with flow reversal as well as logic for trips on period, power, and flow. Feedback reactivity effects from coolant density changes and temperature changes are represented by tables. Feedback reactivity from fuel heat-up (Doppler Effect) is represented by a four-term polynomial in powers of fuel temperature. Photo-neutrons produced in beryllium or in heavy water may be included in the point-kinetics equations by using additional delayed neutron groups.« less

Integrated multidisciplinary CAD/CAE environment for micro-electro-mechanical systems (MEMS)

NASA Astrophysics Data System (ADS)

Przekwas, Andrzej J.

1999-03-01

Computational design of MEMS involves several strongly coupled physical disciplines, including fluid mechanics, heat transfer, stress/deformation dynamics, electronics, electro/magneto statics, calorics, biochemistry and others. CFDRC is developing a new generation multi-disciplinary CAD systems for MEMS using high-fidelity field solvers on unstructured, solution-adaptive grids for a full range of disciplines. The software system, ACE + MEMS, includes all essential CAD tools; geometry/grid generation for multi- discipline, multi-equation solvers, GUI, tightly coupled configurable 3D field solvers for FVM, FEM and BEM and a 3D visualization/animation tool. The flow/heat transfer/calorics/chemistry equations are solved with unstructured adaptive FVM solver, stress/deformation are computed with a FEM STRESS solver and a FAST BEM solver is used to solve linear heat transfer, electro/magnetostatics and elastostatics equations on adaptive polygonal surface grids. Tight multidisciplinary coupling and automatic interoperability between the tools was achieved by designing a comprehensive database structure and APIs for complete model definition. The virtual model definition is implemented in data transfer facility, a publicly available tool described in this paper. The paper presents overall description of the software architecture and MEMS design flow in ACE + MEMS. It describes current status, ongoing effort and future plans for the software. The paper also discusses new concepts of mixed-level and mixed- dimensionality capability in which 1D microfluidic networks are simulated concurrently with 3D high-fidelity models of discrete components.

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

Ahmed, Jawad; Shahzad, Azeem; Khan, Masood

This article focuses on the exact solution regarding convective heat transfer of a magnetohydrodynamic (MHD) Jeffrey fluid over a stretching sheet. The effects of joule and viscous dissipation, internal heat source/sink and thermal radiation on the heat transfer characteristics are taken in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differentialmore » equations are developed in the form of confluent hypergeometric function. The influence of the pertinent parameters on the temperature profile is examined. In addition the results for the wall temperature gradient are also discussed in detail.« less

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.

Indriect Measurement Of Nitrogen In A Mult-Component Natural Gas By Heating The Gas

DOEpatents

Morrow, Thomas B.; Behring, II, Kendricks A.

2004-06-22

Methods of indirectly measuring the nitrogen concentration in a natural gas by heating the gas. In two embodiments, the heating energy is correlated to the speed of sound in the gas, the diluent concentrations in the gas, and constant values, resulting in a model equation. Regression analysis is used to calculate the constant values, which can then be substituted into the model equation. If the diluent concentrations other than nitrogen (typically carbon dioxide) are known, the model equation can be solved for the nitrogen concentration.

Application of Quasi-Heat-Pulse Solutions for Luikov’s Equations of Heat and Moisture Transfer for Calibrating and Utilizing Thermal Properties Apparatus

Treesearch

Mark A. Dietenberger; Charles R. Boardman

2014-01-01

Several years ago the Laplace transform solutions of Luikov’s differential equations were presented for one-dimensional heat and moisture transfer in porous hydroscopic orthotropic materials for the boundary condition of a gradual heat pulse applied to both surfaces of a flat slab. This paper presents calibration methods and data for the K-tester 637 (Lasercomp),...

Numerical Modeling of Coupled Water Flow and Heat Transport in Soil and Snow

NASA Astrophysics Data System (ADS)

Kelleners, T.

2015-12-01

A numerical model is developed to calculate coupled water flow and heat transport in seasonally frozen soil and snow. Both liquid water flow and water vapor flow are included. The effect of dissolved ions on soil water freezing point depression is included by combining an expression for osmotic head with the Clapeyron equation and the van Genuchten soil water retention function. The coupled water flow and heat transport equations are solved using the Thomas algorithm and Picard iteration. Ice pressure is always assumed zero and frost heave is neglected. The new model is tested using data from a high-elevation rangeland soil that is subject to significant soil freezing and a mountainous forest soil that is snow-covered for about 8 months of the year. Soil hydraulic parameters are mostly based on measurements and only vegetation parameters are fine-tuned to match measured and calculated soil water content, soil & snow temperature, and snow height. Modeling statistics for both systems show good performance for temperature, intermediate performance for snow height, and relatively low performance for soil water content, in accordance with earlier results with an older version of the model.

Investigation of pitchfork bifurcation phenomena effects on heat transfer of viscoelastic flow inside a symmetric sudden expansion

NASA Astrophysics Data System (ADS)

Shahbani-Zahiri, A.; Hassanzadeh, H.; Shahmardan, M. M.; Norouzi, M.

2017-11-01

In this paper, the inertial and non-isothermal flows of the viscoelastic fluid through a planar channel with symmetric sudden expansion are numerically simulated. Effects of pitchfork bifurcation phenomena on the heat transfer rate are examined for the thermally developing and fully developed flow of the viscoelastic fluid inside the expanded part of the planar channel with an expansion ratio of 1:3. The rheological model of exponential Phan Thien-Tanner is used to include both the effects of shear-thinning and elasticity in fluid viscosity. The properties of fluids are temperature-dependent, and the viscous dissipation and heat stored by fluid elasticity are considered in the heat transfer equation. For coupling the governing equations, the PISO algorithm (Pressure Implicit with Splitting of Operator) is applied and the system of equations is linearized using the finite volume method on the collocated grids. The main purpose of this study is to examine the pitchfork bifurcation phenomena and its influences on the temperature distribution, the local and mean Nusselt numbers, and the first and second normal stress differences at different Reynolds, elasticity, and Brinkman numbers. The results show that by increasing the Brinkman number for the heated flow of the viscoelastic fluid inside the expanded part of the channel, the value of the mean Nusselt number is almost linearly decreased. Also, the maximum values of the local Nusselt number for the thermally developing flow and the local Nusselt number of the thermally fully developed flow are decremented by enhancing the Brinkman number.

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.

CFD Analysis of Hypersonic Flowfields With Surface Thermochemistry and Ablation

NASA Technical Reports Server (NTRS)

Henline, W. D.

1997-01-01

In the past forty years much progress has been made in computational methods applied to the solution of problems in spacecraft hypervelocity flow and heat transfer. Although the basic thermochemical and physical modeling techniques have changed little in this time, several orders of magnitude increase in the speed of numerically solving the Navier-Stokes and associated energy equations have been achieved. The extent to which this computational power can be applied to the design of spacecraft heat shields is dependent on the proper coupling of the external flow equations to the boundary conditions and governing equations representing the thermal protection system in-depth conduction, pyrolysis and surface ablation phenomena. A discussion of the techniques used to do this in past problems as well as the current state-of-art is provided. Specific examples, including past missions such as Galileo, together with the more recent case studies of ESA/Rosetta Sample Comet Return, Mars Pathfinder and X-33 will be discussed. Modeling assumptions, design approach and computational methods and results are presented.

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.

Three-Dimensional Simulations of Marangoni-Benard Convection in Small Containers by the Least-Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Jiang, Bo-Nan; Wu, Jie; Duh, J. C.

1996-01-01

This paper reports a numerical study of the Marangoni-Benard (MB) convection in a planar fluid layer. The least-squares finite element method (LSFEM) is employed to solve the three-dimensional Stokes equations and the energy equation. First, the governing equations are reduced to be first-order by introducing variables such as vorticity and heat fluxes. The resultant first-order system is then cast into a div-curl-grad formulation, and its ellipticity and permissible boundary conditions are readily proved. This numerical approach provides an equal-order discretization for velocity, pressure, vorticity, temperature, and heat conduction fluxes, and therefore can provide high fidelity solutions for the complex flow physics of the MB convection. Numerical results reported include the critical Marangoni numbers (M(sub ac)) for the onset of the convection in containers with various aspect ratios, and the planforms of supercritical MB flows. The numerical solutions compared favorably with the experimental results reported by Koschmieder et al..

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

Numerical heat transfer study in a scattering, absorbing and emitting semi-transparent porous medium in a cylindrical enclosure

NASA Astrophysics Data System (ADS)

Timoumi, M.; Chérif, B.; Sifaoui, M. S.

2005-12-01

In this paper, heat transfer problem through a semi-transparent porous medium in a cylindrical enclosure is investigated. The governing equations for this problem and the boundary conditions are non-linear differential equations depending on the dimensionless radial coordinate, Planck number N, scattering albedo ω, walls emissivity and thermal conductivity ratio kr. The set of differential equations are solved by a numerical technique taken from the IMSL MATH/LIBRARY. Various results are obtained for the dimensionless temperature profiles in the solid and fluid phases and the radiative heat flux. The effects of some radiative properties of the medium on the heat transfer rate are examined.

Modeling the Performance of Water-Zeolite 13X Adsorption Heat Pump

NASA Astrophysics Data System (ADS)

Kowalska, Kinga; Ambrożek, Bogdan

2017-12-01

The dynamic performance of cylindrical double-tube adsorption heat pump is numerically analysed using a non-equilibrium model, which takes into account both heat and mass transfer processes. The model includes conservation equations for: heat transfer in heating/cooling fluids, heat transfer in the metal tube, and heat and mass transfer in the adsorbent. The mathematical model is numerically solved using the method of lines. Numerical simulations are performed for the system water-zeolite 13X, chosen as the working pair. The effect of the evaporator and condenser temperatures on the adsorption and desorption kinetics is examined. The results of the numerical investigation show that both of these parameters have a significant effect on the adsorption heat pump performance. Based on computer simulation results, the values of the coefficients of performance for heating and cooling are calculated. The results show that adsorption heat pumps have relatively low efficiency compared to other heat pumps. The value of the coefficient of performance for heating is higher than for cooling

Film Boiling Heat Transfer Properties of Liquid Hydrogen in Natural Convection

NASA Astrophysics Data System (ADS)

Horie, Y.; Shirai, Y.; Shiotsu, M.; Matsuzawa, T.; Yoneda, K.; Shigeta, H.; Tatsumoto, H.; Hata, K.; Naruo, Y.; Kobayashi, H.; Inatani, Y.

Film boiling heat transfer properties of LH2 for various pressures and subcooling conditions were measured by applying electric current to give an exponential heat input to a PtCo wire with a diameter of 1.2 mm submerged in LH2. The heated wire was set to be horizontal to the ground. The heat transfer coefficient in the film boiling region was higher for higher pressure and higher subcooling. The experimental results are compared with the equation of pool film boiling heat transfer. It is confirmed that the pool film boiling heat transfer coefficients in LH2 can be expressed by this equation.

Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

2017-11-01

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).

Transient thermohydraulic heat pipe modeling

NASA Astrophysics Data System (ADS)

Hall, Michael L.; Doster, Joseph M.

Many space based reactor designs employ heat pipes as a means of conveying heat. In these designs, thermal radiation is the principle means for rejecting waste heat from the reactor system, making it desirable to operate at high temperatures. Lithium is generally the working fluid of choice as it undergoes a liquid-vapor transformation at the preferred operating temperature. The nature of remote startup, restart, and reaction to threats necessitates an accurate, detailed transient model of the heat pipe operation. A model is outlined of the vapor core region of the heat pipe which is part of a large model of the entire heat pipe thermal response. The vapor core is modeled using the area averaged Navier-Stokes equations in one dimension, which take into account the effects of mass, energy and momentum transfer. The core model is single phase (gaseous), but contains two components: lithium gas and a noncondensible vapor. The vapor core model consists of the continuity equations for the mixture and noncondensible, as well as mixture equations for internal energy and momentum.

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

NASA Astrophysics Data System (ADS)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

Compressible Flow Toolbox

NASA Technical Reports Server (NTRS)

Melcher, Kevin J.

2006-01-01

The Compressible Flow Toolbox is primarily a MATLAB-language implementation of a set of algorithms that solve approximately 280 linear and nonlinear classical equations for compressible flow. The toolbox is useful for analysis of one-dimensional steady flow with either constant entropy, friction, heat transfer, or Mach number greater than 1. The toolbox also contains algorithms for comparing and validating the equation-solving algorithms against solutions previously published in open literature. The classical equations solved by the Compressible Flow Toolbox are as follows: The isentropic-flow equations, The Fanno flow equations (pertaining to flow of an ideal gas in a pipe with friction), The Rayleigh flow equations (pertaining to frictionless flow of an ideal gas, with heat transfer, in a pipe of constant cross section), The normal-shock equations, The oblique-shock equations, and The expansion equations.

A transport model for non-local heating of electrons in ICP reactors

NASA Astrophysics Data System (ADS)

Chang, C. H.; Bose, Deepak

1998-10-01

A new model has been developed for non-local heating of electrons in ICP reactors, based on a hydrodynamic approach. The model has been derived using the electron momentum conservation in azimuthal direction with electromagnetic and frictional forces respectively as driving force and damper of harmonic oscillatory motion of electrons. The resulting transport equations include the convection of azimuthal electron momentum in radial and axial directions, thereby accounting for the non-local effects. The azimuthal velocity of electrons and the resulting electrical current are coupled to the Maxwell's relations, thus forming a self-consistent model for non-local heating. This model is being implemented along with a set of Navier-Stokes equations for plasma dynamics and gas flow to simulate low-pressure (few mTorr's) ICP discharges. Characteristics of nitrogen plasma in a TCP 300mm etch reactor is being studied. The results will be compared against the available Langmuir probe measurements [Collison et al. JVST-A 16(1),1998].

One-dimensional analysis of supersonic two-stage HVOF process

NASA Astrophysics Data System (ADS)

Katanoda, Hiroshi; Hagi, Junichi; Fukuhara, Minoru

2009-12-01

The one-dimensional calculation of the gas/particle flows of a supersonic two-stage high-velocity oxy-fuel (HVOF) thermal spray process was performed. The internal gas flow was solved by numerically integrating the equations of the quasi-one-dimensional flow including the effects of pipe friction and heat transfer. As for the supersonic jet flow, semi-empirical equations were used to obtain the gas velocity and temperature along the center line. The velocity and temperature of the particle were obtained by an one-way coupling method. The material of the spray particle selected in this study is ultra high molecular weight polyethylene (UHMWPE). The temperature distributions in the spherical UHMWPE particles of 50 and 150µm accelerated and heated by the supersonic gas flow was clarified.

Effect of Cattaneo-Christov heat flux on buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts

NASA Astrophysics Data System (ADS)

Dogonchi, A. S.; Ganji, D. D.

2018-06-01

In this study, buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts, are studied. Cattaneo-Christov heat flux model instead of conventional Fourier's law of heat conduction is applied to investigate the heat transfer characteristics. A similarity transformation is used to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The obtained non-linear ordinary differential equations are solved numerically. The impacts of diverse active parameters such as the magnetic parameter, the radiation parameter, the buoyancy parameter, the heat source parameter, the volume fraction of nanofluid and the thermal relaxation parameter are examined on the velocity and temperature profiles. In addition, the value of the Nusselt number is calculated and presented through figures. The results demonstrate that the temperature profile is lower in the case of Cattaneo-Christov heat flux model as compared to Fourier's law. Moreover, the Nusselt number raises with the raising volume fraction of nanofluid and it abates with the ascending the radiation parameter.

A model of heat transfer in immersed man

NASA Technical Reports Server (NTRS)

Montgomery, L. D.

1974-01-01

An equation representing man's thermal balance under water is considered. The equation states that the body thermal loading from metabolic heat production and artificial heat input must be offset by respiratory and environmental heat exchange to maintain a constant body temperature. Critical body regions are affected by cold-water thermal stress. A model of the thermoregulatory system may be divided into the physical-controlled system and the dynamic controlling system. The thermal model is simulated by computer programs.

Continuum-atomistic simulation of picosecond laser heating of copper with electron heat capacity from ab initio calculation

NASA Astrophysics Data System (ADS)

Ji, Pengfei; Zhang, Yuwen

2016-03-01

On the basis of ab initio quantum mechanics (QM) calculation, the obtained electron heat capacity is implemented into energy equation of electron subsystem in two temperature model (TTM). Upon laser irradiation on the copper film, energy transfer from the electron subsystem to the lattice subsystem is modeled by including the electron-phonon coupling factor in molecular dynamics (MD) and TTM coupled simulation. The results show temperature and thermal melting difference between the QM-MD-TTM integrated simulation and pure MD-TTM coupled simulation. The successful construction of the QM-MD-TTM integrated simulation provides a general way that is accessible to other metals in laser heating.

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.

The turbulent mean-flow, Reynolds-stress, and heat flux equations in mass-averaged dependent variables

NASA Technical Reports Server (NTRS)

Rubesin, M. W.; Rose, W. C.

1973-01-01

The time-dependent, turbulent mean-flow, Reynolds stress, and heat flux equations in mass-averaged dependent variables are presented. These equations are given in conservative form for both generalized orthogonal and axisymmetric coordinates. For the case of small viscosity and thermal conductivity fluctuations, these equations are considerably simpler than the general Reynolds system of dependent variables for a compressible fluid and permit a more direct extension of low speed turbulence modeling to computer codes describing high speed turbulence fields.

Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating.

PubMed

Hussanan, Abid; Zuki Salleh, Mohd; Tahar, Razman Mat; Khan, Ilyas

2014-01-01

In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.

Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

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

Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.

1975-11-01

A mathematical model and a numerical solution scheme for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)

The present state and future direction of second order closure models for compressible flows

NASA Technical Reports Server (NTRS)

Gatski, Thomas B.; Sarkar, Sutanu; Speziale, Charles G.

1992-01-01

The topics are presented in viewgraph form and include: (1) Reynolds stress closure models; (2) Favre averages and governing equations; (3) the model for the deviatoric part of the pressure-strain rate correlation; (4) the SSG pressure-strain correlation model; (5) a compressible turbulent dissipation rate model; (6) variable viscosity effects; (7) near-wall stiffness problems; (8) models of the Reynolds mass and heat flux; and (9) a numerical solution of the compressible turbulent transport equation.

Cold Heat Storage Characteristics of O/W-type Latent Heat Emulsion Including Continuum Phase of Water Treated with a Freezing Point Depression

NASA Astrophysics Data System (ADS)

Inaba, Hideo; Morita, Shin-Ichi

This paper deals with flow and cold heat storage characteristics of the oil (tetradecane, C14H30, freezing point 278.9 K, Latent heat 229 kJ/kg)/water emulsion as a latent heat storage material having a low melting point. The test emulsion includes a water-urea solution as a continuum phase. The freezing point depression of the continuum phase permits enhancement of the heat transfer rate of the emulison, due to the large temperature difference between the latent heat storage material and water-urea solution. The velocity of emulsion flow and the inlet temperature of coolant in a coiled double tube heat exchanger are chosen as the experimental parameters. The pressure drop, the heat transfer coefficient of the emulsion in the coiled tube are measured in the temperture region over solid and liquid phase of the latent heat storage material. The finishing time of the cold heat storage is defined experimentally in the range of sensible and latent heat storage. It is clarified that the flow behavior of the emulsion as a non-Newtonian fluid has an important role in cold heat storage. The useful nondimentional correlation equations for the additional pressure loss coefficient, the heat transfer coefficient and the finishing time of the cold heat storage are derived in terms of Dean number and heat capacity ratio.

Experiences on p-Version Time-Discontinuous Galerkin's Method for Nonlinear Heat Transfer Analysis and Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Hou, Gene

2004-01-01

The focus of this research is on the development of analysis and sensitivity analysis equations for nonlinear, transient heat transfer problems modeled by p-version, time discontinuous finite element approximation. The resulting matrix equation of the state equation is simply in the form ofA(x)x = c, representing a single step, time marching scheme. The Newton-Raphson's method is used to solve the nonlinear equation. Examples are first provided to demonstrate the accuracy characteristics of the resultant finite element approximation. A direct differentiation approach is then used to compute the thermal sensitivities of a nonlinear heat transfer problem. The report shows that only minimal coding effort is required to enhance the analysis code with the sensitivity analysis capability.

Survey and evaluation of multilayer insulation heat transfer measurements

NASA Astrophysics Data System (ADS)

Doenecke, Jochen

About 40 papers treating multilayer insulations were studied and compared. Most of these papers present heat transfer measurements in addition to thermal analysis. Here the equations are given which are required for an evaluation of the measurements and in particular for comparisons. Equations are presented which are required to predict the influences of the packing density, temperatures, fraction of perforation area and interstitial pressure. The equation giving gas conductivity versus pressure is modified according to measurements. In space the interstitial pressure is usually below 0.01 Pa and the heat transfer can be expressed as the sum of a conductive and radiative term. The equation finally proposed for spacecraft permits to consider the influence of temperature, number of layers, blanket size and perforation area.

Lattice Boltzmann model for the compressible Navier-Stokes equations with flexible specific-heat ratio.

PubMed

Kataoka, Takeshi; Tsutahara, Michihisa

2004-03-01

We have developed a lattice Boltzmann model for the compressible Navier-Stokes equations with a flexible specific-heat ratio. Several numerical results are presented, and they agree well with the corresponding solutions of the Navier-Stokes equations. In addition, an explicit finite-difference scheme is proposed for the numerical calculation that can make a stable calculation with a large Courant number.

Heat of capillary condensation in nanopores: new insights from the equation of state.

PubMed

Tan, Sugata P; Piri, Mohammad

2017-02-15

Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) coupled with the Young-Laplace equation is a recently developed equation of state (EOS) that successfully presents not only the capillary condensation but also the pore critical phenomena. The development of this new EOS allows further investigation of the heats involved in condensation. Compared to the conventional approaches, the EOS calculations present the temperature-dependent behavior of the heat of capillary condensation as well as that of the contributing effects. The confinement effect was found to be the strongest at the pore critical point. Therefore, contrary to the bulk heat condensation that vanishes at the critical point, the heat of capillary condensation in small pores shows a minimum and then increases with temperature when approaching the pore critical temperature. Strong support for the existence of the pore critical point is also discussed as the volume expansivity of the condensed phase in confinement was found to increase dramatically near the pore critical temperature. At high reduced temperatures, the Clausius-Clapeyron equation was found to apply better for confined fluids than it does for bulk fluids.

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

NASA Technical Reports Server (NTRS)

Johnson, W. L.

2009-01-01

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

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.

A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems

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

Hansen, Glen, E-mail: Glen.Hansen@inl.gov

2011-07-20

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO{sub 2}) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. Themore » accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

A Jacobian-Free Newton Krylov Method for Mortar-Discretized Thermomechanical Contact Problems

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

Glen Hansen

2011-07-01

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear reactor fuel rod, which consists of cylindrical pellets of uranium dioxide (UO2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. Themore » accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.« less

Direct numerical simulations of fluid flow, heat transfer and phase changes

NASA Technical Reports Server (NTRS)

Juric, D.; Tryggvason, G.; Han, J.

1997-01-01

Direct numerical simulations of fluid flow, heat transfer, and phase changes are presented. The simulations are made possible by a recently developed finite difference/front tracking method based on the one-field formulation of the governing equations where a single set of conservation equations is written for all the phases involved. The conservation equations are solved on a fixed rectangular grid, but the phase boundaries are kept sharp by tracking them explicitly by a moving grid of lower dimension. The method is discussed and applications to boiling heat transfer and the solidification of drops colliding with a wall are shown.

Effect of quantum correction on nonlinear thermal wave of electrons driven by laser heating

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

Nafari, F.; Ghoranneviss, M., E-mail: ghoranneviss@gmail.com

2016-08-15

In thermal interaction of laser pulse with a deuterium-tritium (DT) plane, the thermal waves of electrons are generated instantly. Since the thermal conductivity of electron is a nonlinear function of temperature, a nonlinear heat conduction equation is used to investigate the propagation of waves in solid DT. This paper presents a self-similar analytic solution for the nonlinear heat conduction equation in a planar geometry. The thickness of the target material is finite in numerical computation, and it is assumed that the laser energy is deposited at a finite initial thickness at the initial time which results in a finite temperaturemore » for electrons at initial time. Since the required temperature range for solid DT ignition is higher than the critical temperature which equals 35.9 eV, the effects of quantum correction in thermal conductivity should be considered. This letter investigates the effects of quantum correction on characteristic features of nonlinear thermal wave, including temperature, penetration depth, velocity, heat flux, and heating and cooling domains. Although this effect increases electron temperature and thermal flux, penetration depth and propagation velocity are smaller. This effect is also applied to re-evaluate the side-on laser ignition of uncompressed DT.« less

Optimization of the transition path of the head hardening with using the genetic algorithms

NASA Astrophysics Data System (ADS)

Wróbel, Joanna; Kulawik, Adam

2016-06-01

An automated method of choice of the transition path of the head hardening in heat treatment process for the plane steel element is proposed in this communication. This method determines the points on the path of moving heat source using the genetic algorithms. The fitness function of the used algorithm is determined on the basis of effective stresses and yield point depending on the phase composition. The path of the hardening tool and also the area of the heat affected zone is determined on the basis of obtained points. A numerical model of thermal phenomena, phase transformations in the solid state and mechanical phenomena for the hardening process is implemented in order to verify the presented method. A finite element method (FEM) was used for solving the heat transfer equation and getting required temperature fields. The moving heat source is modeled with a Gaussian distribution and the water cooling is also included. The macroscopic model based on the analysis of the CCT and CHT diagrams of the medium-carbon steel is used to determine the phase transformations in the solid state. A finite element method is also used for solving the equilibrium equations giving us the stress field. The thermal and structural strains are taken into account in the constitutive relations.

Complete Mie-Gruneisen Equation of State (update)

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

Menikoff, Ralph

2016-03-14

The Mie-Gruneisen equation of state (EOS) is frequently used in hydro simulations to model solids at high pressure (up to a few Mb). It is an incomplete EOS characterized by a Gr¨uneisen coefficient, = -V (@eP)V , that is a function of only V . Expressions are derived for isentropes and isotherms. This enables the extension to a complete EOS. Thermodynamic consistency requires that the specific heat is a function of a single scaled-temperature. A complete extension is uniquely determined by the temperature dependence of the specific heat at a fixed reference density. In addition we show that if themore » domain of the EOS extends to T = 0 and the specific heat vanishes on the zero isotherm then a function of only V is equivalent to a specific heat with a single temperature scale. If the EOS domain does not include the zero isotherm, then a specific heat with a single temperature scale leads to a generalization of the Mie-Gr¨uneisen EOS in which the pressure is linear in both the specific energy and the temperature. This corresponds to the limiting case of two temperature scales with one of the scales in the high temperature limit. Such an EOS has previously been used to model liquid nitromethane.« less

Approximate convective heating equations for hypersonic flows

NASA Technical Reports Server (NTRS)

Zoby, E. V.; Moss, J. N.; Sutton, K.

1979-01-01

Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.

Plasma Heating and Ultrafast Semiconductor Laser Modulation Through a Terahertz Heating Field

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Ning, C. Z.

2000-01-01

Electron-hole plasma heating and ultrafast modulation in a semiconductor laser under a terahertz electrical field are investigated using a set of hydrodynamic equations derived from the semiconductor Bloch equations. The self-consistent treatment of lasing and heating processes leads to the prediction of a strong saturation and degradation of modulation depth even at moderate terahertz field intensity. This saturation places a severe limit to bandwidth achievable with such scheme in ultrafast modulation. Strategies for increasing modulation depth are discussed.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

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

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

EFFECT OF A RADIATION COOLING AND HEATING FUNCTION ON STANDING LONGITUDINAL OSCILLATIONS IN CORONAL LOOPS

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

Kumar, S.; Nakariakov, V. M.; Moon, Y.-J., E-mail: sanjaykumar@khu.ac.kr

2016-06-10

Standing long-period (with periods longer than several minutes) oscillations in large, hot (with a temperature higher than 3 MK) coronal loops have been observed as the quasi-periodic modulation of the EUV and microwave intensity emission and the Doppler shift of coronal emission lines, and they have been interpreted as standing slow magnetoacoustic (longitudinal) oscillations. Quasi-periodic pulsations of shorter periods, detected in thermal and non-thermal emissions in solar flares could be produced by a similar mechanism. We present theoretical modeling of the standing slow magnetoacoustic mode, showing that this mode of oscillation is highly sensitive to peculiarities of the radiative coolingmore » and heating function. We generalized the theoretical model of standing slow magnetoacoustic oscillations in a hot plasma, including the effects of the radiative losses and accounting for plasma heating. The heating mechanism is not specified and taken empirically to compensate the cooling by radiation and thermal conduction. It is shown that the evolution of the oscillations is described by a generalized Burgers equation. The numerical solution of an initial value problem for the evolutionary equation demonstrates that different dependences of the radiative cooling and plasma heating on the temperature lead to different regimes of the oscillations, including growing, quasi-stationary, and rapidly decaying. Our findings provide a theoretical foundation for probing the coronal heating function and may explain the observations of decayless long-period, quasi-periodic pulsations in flares. The hydrodynamic approach employed in this study should be considered with caution in the modeling of non-thermal emission associated with flares, because it misses potentially important non-hydrodynamic effects.« less

A two-equation model for heat transport in wall turbulent shear flows

NASA Astrophysics Data System (ADS)

Nagano, Y.; Kim, C.

1988-08-01

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and epsilon equations, so the eddy diffusivity for heat is given as functions of temperature variance, and the dissipation rate of temperature fluctuations, together with k and epsilon. Thus, the proposed model does not require any questionable assumptions for the 'turbulent Prandtl number'. Modeled forms of the equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.

Non-invasive photo acoustic approach for human bone diagnosis.

PubMed

Thella, Ashok Kumar; Rizkalla, James; Helmy, Ahdy; Suryadevara, Vinay Kumar; Salama, Paul; Rizkalla, Maher

2016-12-01

The existing modalities of bone diagnosis including X-ray and ultrasound may cite drawback in some cases related to health issues and penetration depth, while the ultrasound modality may lack image quality. Photo acoustic approach however, provides light energy to the acoustic wave, enabling it to activate and respond according to the propagating media (which is type of bones in this case). At the same time, a differential temperature change may result in the bio heat response, resulting from the heat absorbed across the multiple materials under study. In this work, we have demonstrated the features of using photo acoustic modality in order to non-invasively diagnose the type of human bones based on their electrical, thermal, and acoustic properties that differentiate the output response of each type. COMSOL software was utilized to combine both acoustic equations and bio heat equations, in order to study both the thermal and acoustic responses through which the differential diagnosis can be obtained. In this study, we solved both the acoustic equation and bio heat equations for four types of bones, bone (cancellous), bone (cortical), bone marrow (red), and bone marrow (yellow). 1 MHz acoustic source frequency was chosen and 10(5) W/m(2) power source was used in the simulation. The simulation tested the dynamic response of the wave over a distance of 5 cm from each side for the source. Near 2.4 cm was detected from simulation from each side of the source with a temperature change of within 0.5 K for various types of bones, citing a promising technique for a practical model to detect the type of bones via the differential temperature as well as the acoustic was response via the multiple materials associated with the human bones (skin and blood). The simulation results suggest that the PA technique may be applied to non-invasive diagnosis for the different types of bones, including cancerous bones. A practical model for detecting both the temperature change via IR sensors, and acoustic wave signals may be detected via sensitive pressure transducer, which is reserved for future realization.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.

2004-01-01

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

Effects of selective fusion on the thermal history of the Moon, Mars, and Venus

USGS Publications Warehouse

Lee, W.H.K.

1968-01-01

A comparative study on the thermal history of the Moon, Mars, and Venus was made by numerical solutions of the heat equation including and excluding selective fusion of silicates. Selective fusion was approximated by melting in a multicomponent system and redistribution of radioactive elements. Effects on selective fusion on the thermal models are (1) lowering (by several hundred degrees centigrade) and stabilizing the internal temperature distribution, and (2) increasing the surface heat-flow. ?? 1968.

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows.

PubMed

Abel, I G; Plunk, G G; Wang, E; Barnes, M; Cowley, S C; Dorland, W; Schekochihin, A A

2013-11-01

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

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.

Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique

NASA Astrophysics Data System (ADS)

Abdelkhalek, M. M.

2009-05-01

Numerical results are presented for heat and mass transfer effect on hydromagnetic flow of a moving permeable vertical surface. An analysis is performed to study the momentum, heat and mass transfer characteristics of MHD natural convection flow over a moving permeable surface. The surface is maintained at linear temperature and concentration variations. The non-linear coupled boundary layer equations were transformed and the resulting ordinary differential equations were solved by perturbation technique [Aziz A, Na TY. Perturbation methods in heat transfer. Berlin: Springer-Verlag; 1984. p. 1-184; Kennet Cramer R, Shih-I Pai. Magneto fluid dynamics for engineers and applied physicists 1973;166-7]. The solution is found to be dependent on several governing parameter, including the magnetic field strength parameter, Prandtl number, Schmidt number, buoyancy ratio and suction/blowing parameter, a parametric study of all the governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Numerical results for the dimensionless velocity profiles, the temperature profiles, the concentration profiles, the local friction coefficient and the local Nusselt number are presented for various combinations of parameters.

Cattaneo-Christov based study of {TiO}_2 -CuO/EG Casson hybrid nanofluid flow over a stretching surface with entropy generation

NASA Astrophysics Data System (ADS)

Jamshed, Wasim; Aziz, Asim

2018-06-01

In the present research, a simplified mathematical model is presented to study the heat transfer and entropy generation analysis of thermal system containing hybrid nanofluid. Nanofluid occupies the space over an infinite horizontal surface and the flow is induced by the non-linear stretching of surface. A uniform transverse magnetic field, Cattaneo-Christov heat flux model and thermal radiation effects are also included in the present study. The similarity technique is employed to reduce the governing non-linear partial differential equations to a set of ordinary differential equation. Keller Box numerical scheme is then used to approximate the solutions for the thermal analysis. Results are presented for conventional copper oxide-ethylene glycol (CuO-EG) and hybrid titanium-copper oxide/ethylene glycol ({TiO}_2 -CuO/EG) nanofluids. The spherical, hexahedron, tetrahedron, cylindrical, and lamina-shaped nanoparticles are considered in the present analysis. The significant findings of the study is the enhanced heat transfer capability of hybrid nanofluids over the conventional nanofluids, greatest heat transfer rate for the smallest value of the shape factor parameter and the increase in Reynolds number and Brinkman number increases the overall entropy of the system.

Convection Heat and Mass Transfer in a Power Law Fluid with Non Constant Relaxation Time Past a Vertical Porous Plate in the Presence of Thermo and Thermal Diffusion

NASA Astrophysics Data System (ADS)

Olajuwon, B. I.; Oyelakin, I. S.

2012-12-01

The paper investigates convection heat and mass transfer in power law fluid flow with non relaxation time past a vertical porous plate in presence of a chemical reaction, heat generation, thermo diffu- sion and thermal diffusion. The non - linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method. The resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration profiles for pseudo plastic fluids and for different values of parameters governing the prob- lem. The skin friction, heat transfer and mass transfer rates are presented numerically in tabular form. The results show that these parameters have significant effects on the flow, heat transfer and mass transfer.

Solutions of the equation of heat flow. [in and around sunspots

NASA Technical Reports Server (NTRS)

Margolis, S. H.; Knobloch, E.

1980-01-01

The geometry of sunspots has been used to suggest a problem in heat flow. The equation of heat transport is solved for the case of a cylinder with a given thermal conductivity imbedded in an otherwise uniform medium with different conductivity. The surface of this region radiates heat with flux proportional to temperature. At a lower surface, either in heat flux or temperature is held constant. The cylinder can have an anisotropic thermal conductivity. The variations in temperature along the radiating surface have been determined. A simple approximation is noted which has been found to give a general solution with acceptable accuracy. This method may be of some use in other situations requiring the solution of Laplace's equation with a free surface. The analysis is used to set limits on the ratio of diameter to depth for cases which preserve the sharp surface temperature transition across the cylinder.

Design criterion for the heat-transfer coefficient in opposing flow, mixed convention heat transfer in a vertical tube

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

Joye, D.D.

1996-07-01

Mixed convection heat transfer in a vertical tube with opposing flow (downflow heating) was studied experimentally for Reynolds numbers ranging from about 1,000 to 30,000 at constant Grashof numbers ranging about 1{1/2} orders of magnitude under constant wall temperature (CWT) conditions. Three correlations developed for opposing mixed convection flows in vertical conduits predicted the data reasonably well, except near and into the asymptote region for which these equations were not designed. A critical Reynolds number is developed here, above which these equations can be used for design purposes regardless of the boundary condition. Below Re{sub crit}, the correlations, the asymptotemore » equation should be used for the CWT boundary condition, which is more prevalent in process situations than the uniform heat flux (UHF) boundary condition.« less

Peristaltic Transport of Prandtl-Eyring Liquid in a Convectively Heated Curved Channel

PubMed Central

Hayat, Tasawar; Bibi, Shahida; Alsaadi, Fuad; Rafiq, Maimona

2016-01-01

Here peristaltic activity for flow of a Prandtl-Eyring material is modeled and analyzed for curved geometry. Heat transfer analysis is studied using more generalized convective conditions. The channel walls satisfy complaint walls properties. Viscous dissipation in the thermal equation accounted. Unlike the previous studies is for uniform magnetic field on this topic, the radial applied magnetic field has been utilized in the problems development. Solutions for stream function (ψ), velocity (u), and temperature (θ) for small parameter β have been derived. The salient features of heat transfer coefficient Z and trapping are also discussed for various parameters of interest including magnetic field, curvature, material parameters of fluid, Brinkman, Biot and compliant wall properties. Main observations of present communication have been included in the conclusion section. PMID:27304458

Numerical study on microbubble-enhanced heating for various parameters in EUS-FUS

NASA Astrophysics Data System (ADS)

Okita, Kohei; Maezawa, Miyuki; Takagi, Shu; Matsumoto, Yoichiro

2012-11-01

Endoscopic ultrasonography guided focused ultrasound surgery (EUS-FUS) have been developed as a less-invasive treatment for pancreatic cancer. In the present study, microbubble-enhanced heating for various parameters in EUS-FUS is investigated numerically. Mass and momentum equations for bubbly mixture are solved to reproduce the propagation of ultrasound of 4.8MHz through the gel containing microbubbles as Sonazoid®. The dynamics of bubble is governed by the equation which considers the elasticity of both shell and surrounding media. Additionally, the heat equation with the time averaged heat source is solved to obtain a temperature distribution. The basic equations are discretized by the 6th-order finite difference method and developed based on FDTD method. The mixture and bubbles are coupled by Euler-Lagrange method. As the results, the temperature around the target increased due to the microbubble oscillation with increasing the initial void fraction fG0 from 10-5 to 10-4%. However, at fG0=10-3%, ultrasounds were too attenuated to heat the target. The heating region moved from the target to the transducer side. By comparing the results with and without shell, the shell of bubble induced the heating around focus. This is because the decrease of the attenuation due to the elasticity of the shell and the increase of the viscous dissipation rate due to the viscosity of the shell.

Thermal constitutive matrix applied to asynchronous electrical machine using the cell method

NASA Astrophysics Data System (ADS)

Domínguez, Pablo Ignacio González; Monzón-Verona, José Miguel; Rodríguez, Leopoldo Simón; Sánchez, Adrián de Pablo

2018-03-01

This work demonstrates the equivalence of two constitutive equations. One is used in Fourier's law of the heat conduction equation, the other in electric conduction equation; both are based on the numerical Cell Method, using the Finite Formulation (FF-CM). A 3-D pure heat conduction model is proposed. The temperatures are in steady state and there are no internal heat sources. The obtained results are compared with an equivalent model developed using the Finite Elements Method (FEM). The particular case of 2-D was also studied. The errors produced are not significant at less than 0.2%. The number of nodes is the number of the unknowns and equations to resolve. There is no significant gain in precision with increasing density of the mesh.

Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains

NASA Astrophysics Data System (ADS)

Ji, Songsong; Yang, Yibo; Pang, Gang; Antoine, Xavier

2018-01-01

The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green's functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green's functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated.

Projection scheme for a reflected stochastic heat equation with additive noise

NASA Astrophysics Data System (ADS)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

Numberical Solution to Transient Heat Flow Problems

ERIC Educational Resources Information Center

Kobiske, Ronald A.; Hock, Jeffrey L.

1973-01-01

Discusses the reduction of the one- and three-dimensional diffusion equation to the difference equation and its stability, convergence, and heat-flow applications under different boundary conditions. Indicates the usefulness of this presentation for beginning students of physics and engineering as well as college teachers. (CC)

Electroosmotic flow and Joule heating in preparative continuous annular electrochromatography.

PubMed

Laskowski, René; Bart, Hans-Jörg

2015-09-01

An openFOAM "computational fluid dynamic" simulation model was developed for the description of local interaction of hydrodynamics and Joule heating in annular electrochromatography. A local decline of electrical conductivity of the background eluent is caused by an electrokinetic migration of ions resulting in higher Joule heat generation. The model equations consider the Navier-Stokes equation for incompressible fluids, the energy equation for stationary temperature fields, and the mass transfer equation for the electrokinetic flow. The simulations were embedded in commercial ANSYS Fluent software and in open-source environment openFOAM. The annular gap (1 mm width) contained an inorganic C8 reverse-phase monolith as stationary phase prepared by an in situ sol-gel process. The process temperature generated by Joule heating was determined by thermal camera system. The local hydrodynamics in the prototype was detected by a gravimetric contact-free measurement method and experimental and simulated values matched quite well. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The effects of inlet turbulence and rotor/stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. Part 4: Aerodynamic data tabulation

NASA Technical Reports Server (NTRS)

Dring, R. P.; Joslyn, H. D.; Blair, M. F.

1987-01-01

A combined experimental and analytical program was conducted to examine the effects of inlet turbulence and airfoil heat transfer. The experimental portion of the study was conducted in a large-scale (approx. 5X engine), ambient temperature, rotating turbine model configured in both single-stage and stage-and-a-half arrangements. Heat transfer measurements were obtained using low-conductivity airfoils with miniature thermocouples welded to a thin, electrically heated surface skin. Heat transfer data were acquired for various combinations of low or high inlet turbulence intensity, flow coefficient, first stator-rotor axial spacing, Reynolds number and relative circumferential position of the first and second stators. Aerodynamic measurements obtained include distributions of the mean and fluctuating velocities at the turbine inlet and, for each airfoil row, midspan airfoil surface pressures and circumferential distributions of the downstream steady state pressures and fluctuating velocities. Results include airfoil heat transfer predictions produced using existing 2-D boundary layer computation schemes and an examination of solutions of the unsteady boundary layer equations.

Calculation of heat transfer on shuttle type configurations including the effects of variable entropy at boundary layer edge

NASA Technical Reports Server (NTRS)

Dejarnette, F. R.

1972-01-01

A relatively simple method is presented for including the effect of variable entropy at the boundary-layer edge in a heat transfer method developed previously. For each inviscid surface streamline an approximate shockwave shape is calculated using a modified form of Maslen's method for inviscid axisymmetric flows. The entropy for the streamline at the edge of the boundary layer is determined by equating the mass flux through the shock wave to that inside the boundary layer. Approximations used in this technique allow the heating rates along each inviscid surface streamline to be calculated independent of the other streamlines. The shock standoff distances computed by the present method are found to compare well with those computed by Maslen's asymmetric method. Heating rates are presented for blunted circular and elliptical cones and a typical space shuttle orbiter at angles of attack. Variable entropy effects are found to increase heating rates downstream of the nose significantly higher than those computed using normal-shock entropy, and turbulent heating rates increased more than laminar rates. Effects of Reynolds number and angles of attack are also shown.

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

NASA Technical Reports Server (NTRS)

Chapman, Dean R.; Fiscko, Kurt A.

1988-01-01

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

Numerical marching techniques for fluid flows with heat transfer

NASA Technical Reports Server (NTRS)

Hornbeck, R. W.

1973-01-01

The finite difference formulation and method of solution is presented for a wide variety of fluid flow problems with associated heat transfer. Only a few direct results from these formulations are given as examples, since the book is intended primarily to serve a discussion of the techniques and as a starting point for further investigations; however, the formulations are sufficiently complete that a workable computer program may be written from them. In the appendixes a number of topics are discussed which are of interest with respect to the finite difference equations presented. These include a very rapid method for solving certain sets of linear algebraic equations, a discussion of numerical stability, the inherent error in flow rate for confined flow problems, and a method for obtaining high accuracy with a relatively small number of mesh points.

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.

Experimental investigation and numerical modelling of positive corona discharge: ozone generation

NASA Astrophysics Data System (ADS)

Yanallah, K; Pontiga, F; Fernández-Rueda, A; Castellanos, A

2009-03-01

The spatial distribution of the species generated in a wire-cylinder positive corona discharge in pure oxygen has been computed using a plasma chemistry model that includes the most significant reactions between electrons, ions, atoms and molecules. The plasma chemistry model is included in the continuity equations of each species, which are coupled with Poisson's equation for the electric field and the energy conservation equation for the gas temperature. The current-voltage characteristic measured in the experiments has been used as an input data to the numerical simulation. The numerical model is able to reproduce the basic structure of the positive corona discharge and highlights the importance of Joule heating on ozone generation. The average ozone density has been computed as a function of current intensity and compared with the experimental measurements of ozone concentration determined by UV absorption spectroscopy.

A lumped model of venting during thermal runaway in a cylindrical Lithium Cobalt Oxide lithium-ion cell

NASA Astrophysics Data System (ADS)

Coman, Paul T.; Rayman, Sean; White, Ralph E.

2016-03-01

This paper presents a mathematical model built for analyzing the intricate thermal behavior of a 18650 LCO (Lithium Cobalt Oxide) battery cell during thermal runaway when venting of the electrolyte and contents of the jelly roll (ejecta) is considered. The model consists of different ODEs (Ordinary Differential Equations) describing reaction rates and electrochemical reactions, as well as the isentropic flow equations for describing electrolyte venting. The results are validated against experimental findings from Golubkov et al. [1] [Andrey W. Golubkov, David Fuchs, Julian Wagner, Helmar Wiltsche, Christoph Stangl, Gisela Fauler, Gernot Voitice Alexander Thaler and Viktor Hacker, RSC Advances, 4:3633-3642, 2014] for two cases - with flow and without flow. The results show that if the isentropic flow equations are not included in the model, the thermal runaway is triggered prematurely at the point where venting should occur. This shows that the heat dissipation due to ejection of electrolyte and jelly roll contents has a significant contribution. When the flow equations are included, the model shows good agreement with the experiment and therefore proving the importance of including venting.

Physical models for the normal YORP and diurnal Yarkovsky effects

NASA Astrophysics Data System (ADS)

Golubov, O.; Kravets, Y.; Krugly, Yu. N.; Scheeres, D. J.

2016-06-01

We propose an analytic model for the normal Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) and diurnal Yarkovsky effects experienced by a convex asteroid. Both the YORP torque and the Yarkovsky force are expressed as integrals of a universal function over the surface of an asteroid. Although in general this function can only be calculated numerically from the solution of the heat conductivity equation, approximate solutions can be obtained in quadratures for important limiting cases. We consider three such simplified models: Rubincam's approximation (zero heat conductivity), low thermal inertia limit (including the next order correction and thus valid for small heat conductivity), and high thermal inertia limit (valid for large heat conductivity). All three simplified models are compared with the exact solution.

Influence of Dissipation on Heat Transfer During Flow of a Non-Newtonian Fluid in a Porous Channel

NASA Astrophysics Data System (ADS)

Baranov, A. V.; Yunitskii, S. A.

2017-07-01

A study is made of flow and heat transfer during the motion of a non-Newtonian (power-law) fluid in a plane channel filled with porous material. The Brinkman equation is used as the equation of state, and a one-temperature model, in representing the energy equation. Account us taken of dissipative heat releases. The problem is solved for temperature boundary conditions of the first kind. The authors show the influence of dissipation on the development of the temperature profile, and also on the distributions of the local Nusselt number and the mass-mean temperature along the channel.

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

NASA Astrophysics Data System (ADS)

Kassem, M.

2006-03-01

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.

Heat and mass transfer in vertical porous medium due to partial heating

NASA Astrophysics Data System (ADS)

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

2018-05-01

The investigation of heat and mass transfer adjacent to vertical plate subjected to partial heating of plate in multiple segments is carried out. A section of the plate is heated with isothermal temperature Th and the far away condition is maintained at ambient temperature T∞.. The vertical plate is maintained at constant concentration Ch as opposed to lowest concentration at far away condition. Finite element method is used and governing equations are converted into simple form of equations using Galerkin approach. The results are discussed in terms of contour plots. Study is carried out with respect to various physical parameters. The heat and mass transfer rate found to increase with increase in Rayleigh number.

Laser short-pulse heating of an aluminum thin film: Energy transfer in electron and lattice sub-systems

NASA Astrophysics Data System (ADS)

Bin Mansoor, Saad; Sami Yilbas, Bekir

2015-08-01

Laser short-pulse heating of an aluminum thin film is considered and energy transfer in the film is formulated using the Boltzmann equation. Since the heating duration is short and the film thickness is considerably small, thermal separation of electron and lattice sub-systems is incorporated in the analysis. The electron-phonon coupling is used to formulate thermal communication of both sub-systems during the heating period. Equivalent equilibrium temperature is introduced to account for the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. Temperature predictions of the Boltzmann equation are compared with those obtained from the two-equation model. It is found that temperature predictions from the Boltzmann equation differ slightly from the two-equation model results. Temporal variation of equivalent equilibrium temperature does not follow the laser pulse intensity in the electron sub-system. The time occurrence of the peak equivalent equilibrium temperature differs for electron and lattice sub-systems, which is attributed to phonon scattering in the irradiated field in the lattice sub-system. In this case, time shift is observed for occurrence of the peak temperature in the lattice sub-system.

Solution to the differential equation for combined radiative and convective cooling for a heated sphere

NASA Technical Reports Server (NTRS)

Wills, F. D.; Katz, L.

1976-01-01

A solution is presented for the differential equation relating the combined effects of radiative and forced convective cooling for a heated sphere. The equation has the form where T and t are the variables temperature and time, respectively, and K sub o, T sub o, and H are constants. The solution can be used as a guideline for the design and understanding of space processing phenomena.

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.

Stochastic effects in a thermochemical system with Newtonian heat exchange.

PubMed

Nowakowski, B; Lemarchand, A

2001-12-01

We develop a mesoscopic description of stochastic effects in the Newtonian heat exchange between a diluted gas system and a thermostat. We explicitly study the homogeneous Semenov model involving a thermochemical reaction and neglecting consumption of reactants. The master equation includes a transition rate for the thermal transfer process, which is derived on the basis of the statistics for inelastic collisions between gas particles and walls of the thermostat. The main assumption is that the perturbation of the Maxwellian particle velocity distribution can be neglected. The transition function for the thermal process admits a continuous spectrum of temperature changes, and consequently, the master equation has a complicated integro-differential form. We perform Monte Carlo simulations based on this equation to study the stochastic effects in the Semenov system in the explosive regime. The dispersion of ignition times is calculated as a function of system size. For sufficiently small systems, the probability distribution of temperature displays transient bimodality during the ignition period. The results of the stochastic description are successfully compared with those of direct simulations of microscopic particle dynamics.

Nonlinear magnetoacoustic wave propagation with chemical reactions

NASA Astrophysics Data System (ADS)

Margulies, Timothy Scott

2002-11-01

The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.

Simulation of Oxygen Disintegration and Mixing With Hydrogen or Helium at Supercritical Pressure

NASA Technical Reports Server (NTRS)

Bellan, Josette; Taskinoglu, Ezgi

2012-01-01

The simulation of high-pressure turbulent flows, where the pressure, p, is larger than the critical value, p(sub c), for the species under consideration, is relevant to a wide array of propulsion systems, e.g. gas turbine, diesel, and liquid rocket engines. Most turbulence models, however, have been developed for atmospheric-p turbulent flows. The difference between atmospheric-p and supercritical-p turbulence is that, in the former situation, the coupling between dynamics and thermodynamics is moderate to negligible, but for the latter it is very significant, and can dominate the flow characteristics. The reason for this stems from the mathematical form of the equation of state (EOS), which is the perfect-gas EOS in the former case, and the real-gas EOS in the latter case. For flows at supercritical pressure, p, the large eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas EOS. The equations use transport properties that depend on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid scale (SGS) fluxes, but also new SGS terms, each denoted as a correction. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations, and represent differences between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) that is the difference between the filtered divergence of the heat flux and the divergence of the heat flux computed as a function of the filtered flow field. In a previous study, there was only partial success in modeling the q-correction term, but in this innovation, success has been achieved by using a different modeling approach. This analysis, based on a temporal mixing layer Direct Numerical Simulation database, shows that the focus in modeling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES heat flux calculation. Further, results for a study conducted for temporal mixing layers initially containing oxygen in the lower stream, and hydrogen or helium in the upper stream, show that, for any LES, including SGS-flux models (constant-coefficient Gradient or Scale-Similarity models, dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/Gradient models), the inclusion of the q-correction in the LES leads to the theoretical maximum reduction of the SGS heat-flux difference. The remaining error in modeling this new subgrid term is thus irreducible.

Analysis of Heat Transfers inside Counterflow Plate Heat Exchanger Augmented by an Auxiliary Fluid Flow

PubMed Central

Khaled, A.-R. A.

2014-01-01

Enhancement of heat transfers in counterflow plate heat exchanger due to presence of an intermediate auxiliary fluid flow is investigated. The intermediate auxiliary channel is supported by transverse conducting pins. The momentum and energy equations for the primary fluids are solved numerically and validated against a derived approximate analytical solution. A parametric study including the effect of the various plate heat exchanger, and auxiliary channel dimensionless parameters is conducted. Different enhancement performance indicators are computed. The various trends of parameters that can better enhance heat transfer rates above those for the conventional plate heat exchanger are identified. Large enhancement factors are obtained under fully developed flow conditions. The maximum enhancement factors can be increased by above 8.0- and 5.0-fold for the step and exponential distributions of the pins, respectively. Finally, counterflow plate heat exchangers with auxiliary fluid flows are recommended over the typical ones if these flows can be provided with the least cost. PMID:24719572

Analysis of heat transfers inside counterflow plate heat exchanger augmented by an auxiliary fluid flow.

PubMed

Khaled, A-R A

2014-01-01

Enhancement of heat transfers in counterflow plate heat exchanger due to presence of an intermediate auxiliary fluid flow is investigated. The intermediate auxiliary channel is supported by transverse conducting pins. The momentum and energy equations for the primary fluids are solved numerically and validated against a derived approximate analytical solution. A parametric study including the effect of the various plate heat exchanger, and auxiliary channel dimensionless parameters is conducted. Different enhancement performance indicators are computed. The various trends of parameters that can better enhance heat transfer rates above those for the conventional plate heat exchanger are identified. Large enhancement factors are obtained under fully developed flow conditions. The maximum enhancement factors can be increased by above 8.0- and 5.0-fold for the step and exponential distributions of the pins, respectively. Finally, counterflow plate heat exchangers with auxiliary fluid flows are recommended over the typical ones if these flows can be provided with the least cost.

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

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.

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.

Compressible Navier-Stokes equations: A study of leading edge effects

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Karbhari, P. R.

1987-01-01

A computational method is developed that allows numerical calculations of the time dependent compressible Navier-Stokes equations.The current results concern a study of flow past a semi-infinite flat plate.Flow develops from given inflow conditions upstream and passes over the flat plate to leave the computational domain without reflecting at the downstream boundary. Leading edge effects are included in this paper. In addition, specification of a heated region which gets convected with the flow is considered. The time history of this convection is obtained, and it exhibits a wave phenomena.

Heat transfer in condensing and evaporating two-component, two-phase flow inside a horizontal tube

NASA Astrophysics Data System (ADS)

Duval, W. M. B.

The effect of adding a small amount of oil to condensing and evaporation refrigerant R-12 following inside a horizontal tube is investigated both experimentally and analytically. Analytically, the problem is addressed assuming annular flow inside the tube. The analysis is based on the momentum and energy equations with the heat transfer in the liquid film determined using the Reynolds analogy between turbulent heat and momentum transfer. Two separate methods are developed for extending this model to include the effects of the two-component nature of the flow. Experimentally, two-phase local heat transfer measurements and flow pattern visualization are made for both condensation and evaporation. From the measurements, correlations are developed to predict two-phase heat transfer for the range of 0%, 2% and 5% oil fraction by mass flow.

A finite element analysis of the freeze/thaw behavior of external artery heat pipes

NASA Technical Reports Server (NTRS)

Lu, X. J.; Peterson, G. P.

1993-01-01

A two-dimensional finite element model was used to determine the freeze/thaw characteristics of an external artery heat pipe. During startup, the working fluid, which was located in the liquid channel and the circumferential wall grooves, experienced a phase transformation from a solid to a liquid state. The transient heat conduction equations with moving interfacial conditions were solved using the appropriate initial boundary conditions. The modelling results include the cross-sectional temperature distribution and the interfacial or melt front position as a function of time. A fixed grid approach was adopted in the model for the phase-change process during thawing of frozen working fluid. The interfacial position between the liquid and solid regions was found by balancing the latent heat caused by interfacial movement with the heat addition or extraction at the related grid points.

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

PubMed

Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

2018-01-01

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Teaching Modeling with Partial Differential Equations: Several Successful Approaches

ERIC Educational Resources Information Center

Myers, Joseph; Trubatch, David; Winkel, Brian

2008-01-01

We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

Multiscale modeling of localized resistive heating in nanocrystalline metals subjected to electropulsing

NASA Astrophysics Data System (ADS)

Zhao, Jingyi; Wang, G.-X.; Dong, Yalin; Ye, Chang

2017-08-01

Many electrically assisted processes have been reported to induce changes in microstructure and metal plasticity. To understand the physics-based mechanisms behind these interesting phenomena, however, requires an understanding of the interaction between the electric current and heterogeneous microstructure. In this work, multiscale modeling of the electric current flow in a nanocrystalline material is reported. The cellular automata method was used to track the nanoscale grain boundaries in the matrix. Maxwell's electromagnetic equations were solved to obtain the electrical potential distribution at the macro scale. Kirchhoff's circuit equation was solved to obtain the electric current flow at the micro/nano scale. The electric current distribution at two representative locations was investigated. A significant electric current concentration was observed near the grain boundaries, particularly near the triple junctions. This higher localized electric current leads to localized resistive heating near the grain boundaries. The electric current distribution could be used to obtain critical information such as localized resistive heating rate and extra system free energy, which are critical for explaining many interesting phenomena, including microstructure evolution and plasticity enhancement in many electrically assisted processes.

Comparative Study of Shrinkage and Non-Shrinkage Model of Food Drying

NASA Astrophysics Data System (ADS)

Shahari, N.; Jamil, N.; Rasmani, KA.

2016-08-01

A single phase heat and mass model has always been used to represent the moisture and temperature distribution during the drying of food. Several effects of the drying process, such as physical and structural changes, have been considered in order to increase understanding of the movement of water and temperature. However, the comparison between the heat and mass equation with and without structural change (in terms of shrinkage), which can affect the accuracy of the prediction model, has been little investigated. In this paper, two mathematical models to describe the heat and mass transfer in food, with and without the assumption of structural change, were analysed. The equations were solved using the finite difference method. The converted coordinate system was introduced within the numerical computations for the shrinkage model. The result shows that the temperature with shrinkage predicts a higher temperature at a specific time compared to that of the non-shrinkage model. Furthermore, the predicted moisture content decreased faster at a specific time when the shrinkage effect was included in the model.

Simulation analysis of air flow and turbulence statistics in a rib grit roughened duct.

PubMed

Vogiatzis, I I; Denizopoulou, A C; Ntinas, G K; Fragos, V P

2014-01-01

The implementation of variable artificial roughness patterns on a surface is an effective technique to enhance the rate of heat transfer to fluid flow in the ducts of solar air heaters. Different geometries of roughness elements investigated have demonstrated the pivotal role that vortices and associated turbulence have on the heat transfer characteristics of solar air heater ducts by increasing the convective heat transfer coefficient. In this paper we investigate the two-dimensional, turbulent, unsteady flow around rectangular ribs of variable aspect ratios by directly solving the transient Navier-Stokes and continuity equations using the finite elements method. Flow characteristics and several aspects of turbulent flow are presented and discussed including velocity components and statistics of turbulence. The results reveal the impact that different rib lengths have on the computed mean quantities and turbulence statistics of the flow. The computed turbulence parameters show a clear tendency to diminish downstream with increasing rib length. Furthermore, the applied numerical method is capable of capturing small-scale flow structures resulting from the direct solution of Navier-Stokes and continuity equations.

Flow and heat transfer of nanofluid over a stretching sheet with non-linear velocity in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Madaki, A. G.; Roslan, R.; Kandasamy, R.; Chowdhury, M. S. H.

2017-04-01

In this paper, the effects of Brownian motion, thermophoresis, chemical reaction, heat generation, magnetohydrodynamic and thermal radiation has been included in the model of nanofluid flow and heat transfer over a moving surface with variable thickness. The similarity transformation is used to transform the governing boundary layer equations into ordinary differential equations (ODE). Both optimal homotopy asymptotic method (OHAM) and Runge-Kutta fourth order method with shooting technique are employed to solve the resulting ODEs. For different values of the pertinent parameters on the velocity, temperature and concentration profiles have been studied and details are given in tables and graphs respectively. A comparison with the previous study is made, where an excellent agreement is achieved. The results demonstrate that the radiation parameter N increases, with the increase in both the temperature and the thermal boundary layer thickness respectively. While the nanoparticles concentration profiles increase with the influence of generative chemical reaction γ < 0, while it decreases with destructive chemical reaction γ > 0.

Theory of noise equivalent power of a high-temperature superconductor far-infrared bolometer in a photo-thermoelectrical mode of operation

NASA Astrophysics Data System (ADS)

Kaila, M. M.; Russell, G. J.

2000-12-01

We present a theory of noise equivalent power (NEP) and related parameters for a high-temperature superconductor (HTSC) bolometer in which temperature and resistance are the noise sources for open circuit operation and phonon and resistance are the noise sources for voltage-biased operation of the bolometer. The bolometer is designed to use a photo-thermoelectrical mode of operation. A mathematical formulation for the open circuit operation is first presented followed by an analysis of the heterodyne case with a bias applied in constant voltage mode. For the first time electrothermal (ET) and thermoelectrical (TE) feedback are treated in the heat balance equation simultaneously. A parallel resistance geometry consisting of thermoelectric and HTSC material legs has been chosen for the device. Computations for the ET-TE feedback show that the response time improves by three orders of magnitude and the responsivity becomes double for the same TE feedback. In the heat balance equation we have included among the heat transfer processes the temperature dependence of the thermal conductance at the bolometer-substrate interface for the dynamic state.

The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet

NASA Astrophysics Data System (ADS)

Isa, Siti Suzilliana Putri Mohamed; Arifin, Norihan Md.; Nazar, Roslinda; Bachok, Norfifah; Ali, Fadzilah Md

2017-12-01

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

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

B.B. Rokhman

A two-dimensional stationary model of motion, heat and mass exchange, and chemical reaction of polydisperse coke and ash particles in ascending gas-suspension flow has been constructed with allowance for the turbulent and pseudo turbulent mechanisms of transfer in the dispersed phase. The system of equations that describes motion and heat transfer in the solid phase has been closed at the level of the equations for the second moments of velocity and temperature pulsations, whereas the momentum equations of the carrying medium have been closed using the equation for turbulent gas energy, which allows for the influence of the particles andmore » heterogeneous reactions.« less

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

Mathematical Modeling of Ultra-Superheated Steam Gasification

NASA Astrophysics Data System (ADS)

Xin, Fen

Pure steam gasification has been of interest in hydrogen production, but with the challenge of supplying heat for endothermic reactions. Traditional solutions included either combusting feedstocks at the price of decreasing carbon conversion ratio, or using costly heating apparatus. Therefore, a distributed gasifier with an Ultra-Superheated-Steam (USS) generator was invented, satisfying the heat requirement and avoiding carbon combustion in steam gasification. This project developed the first version of the Ultra-Superheated-Steam-Fluidization-Model (USSFM V1.0) for the USS gasifier. A stand-alone equilibrium combustion model was firstly developed to calculate the USS mixture, which was the input to the USSFM V1.0. Model development of the USSFM V1.0 included assumptions, governing equations, boundary conditions, supporting equations and iterative schemes of guessed values. There were three nested loops in the dense bed and one loop in the freeboard. The USSFM V1.0 included one main routine and twenty-four subroutines. The USSFM V1.0 was validated with experimental data from the Enercon USS gasifier. The calculated USS mixture had a trace of oxygen, validating the initial expectation of creating an oxygen-free environment in the gasifier. Simulations showed that the USS mixture could satisfy the gasification heat requirement without partial carbon combustion. The USSFM V1.0 had good predictions on the H2% in all tests, and on other variables at a level of the lower oxygen feed. Provided with higher oxygen feed, the USSFM V1.0 simulated hotter temperatures, higher CO% and lower CO2%. Errors were explained by assumptions of equilibrium combustion, adiabatic reactors, reaction kinetics, etc. By investigating specific modeling data, gas-particle convective heat transfers were found to be critical in energy balance equations of both emulsion gas and particles, while bubble size controlled both the mass and energy balance equations of bubble gas. Parametric study suggested a lower level of oxygen feed for higher content of hydrogen. However, too little oxygen would impede fluidization in the bed. The reasonability of iterative schemes and the stability of USSFM V1.0 were tested by the sensitivity analysis of two guessed values. Analytical Hierarchy Process analysis indicated that large-scale gasification is advantageous for hydrogen production but with impediments of high capital cost and CO2 emissions. This study manifested the USS gasifier offering the possibility of generating H2-rich and CO2-lean syngas in a much cheaper distributed way. Currently, the FORTRAN-based USSFM V1.0 had a good correlation with experimental data with a small oxygen feed. On the demand of wider applications, suggestions were proposed at last for the model improvement in future.

Application of integral equation theory to analyze stability of electric field in multimode microwave heating cavity

NASA Astrophysics Data System (ADS)

Tang, Zhengming; Hong, Tao; Chen, Fangyuan; Zhu, Huacheng; Huang, Kama

2017-10-01

Microwave heating uniformity is mainly dependent on and affected by electric field. However, little study has paid attention to its stability characteristics in multimode cavity. In this paper, this problem is studied by the theory of Freedholm integral equation. Firstly, Helmholtz equation and the electric dyadic Green's function are used to derive the electric field integral equation. Then, the stability of electric field is demonstrated as the characteristics of solutions to Freedholm integral equation. Finally, the stability characteristics are obtained and verified by finite element calculation. This study not only can provide a comprehensive interpretation of electric field in multimode cavity but also help us make better use of microwave energy.

Local Equation of State for Protons, and Implications for Proton Heating in the Solar Wind.

NASA Astrophysics Data System (ADS)

Zaslavsky, A.; Maksimovic, M.; Kasper, J. C.

2017-12-01

The solar wind protons temperature is observed to decrease with distance to the Sun at a slower rate than expected from an adiabatic expansion law: the protons are therefore said to be heated. This observation raises the question of the evaluation of the heating rate, and the question of the heat source.These questions have been investigated by previous authors by gathering proton data on various distances to the Sun, using spacecraft as Helios or Ulysses, and then computing the radial derivative of the proton temperature in order to obtain a heating rate from the internal energy equation. The problem of such an approach is the computation of the radial derivative of the temperature profile, for which uncertainties are very large, given the dispersion of the temperatures measured at a given distance.An alternative approach, that we develop in this paper, consists in looking for an equation of state that links locally the pressure (or temperature) to the mass density. If such a relation exists then one can evaluate the proton heating rate on a local basis, without having any space derivative to compute.Here we use several years of STEREO and WIND proton data to search for polytropic equation of state. We show that such relationships are indeed a good approximation in given solar wind's velocity intervals and deduce the associated protons heating rates as a function of solar wind's speed. The obtained heating rates are shown to scale from around 1 kW/kg in the slow wind to around 10 kW/kg in the fast wind, in remarkable agreement with the rate of energy observed by previous authors to cascade in solar wind's MHD turbulence at 1 AU. These results therefore support the idea of proton turbulent heating in the solar wind.

Radiative property data for Venusian entry: A compendium

NASA Technical Reports Server (NTRS)

Jones, J. J.; Boughner, R. E.; Haggard, K. V.; Nealy, J. E.; Schryer, D. R.; Zoby, E. V.

1974-01-01

A compilation of experimental and calculated data on the radiative properties of species important in Venusian entry is presented. Molecular band systems, atomic lines, free-bound continua, and free-free continua are considered for the principal radiating species of shock-heated carbon dioxide. Data pertinent to the species in the ablation layer are included. The Venus atmosphere so closely approximates pure carbon dioxide (CO2) that the inviscid layer radiation is due almost entirely to thermally excited CO2. Data are included on the violet band system of the cyanogen radical CN. Recommendations are made as to best property values for radiative heating calculations. A review of the basic equations and the relationships of the various emission-absorption gas properties is included.

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

Thermoelastic damping in thin microrings with two-dimensional heat conduction

NASA Astrophysics Data System (ADS)

Fang, Yuming; Li, Pu

2015-05-01

Accurate determination of thermoelastic damping (TED) is very challenging in the design of micro-resonators. Microrings are widely used in many micro-resonators. In the past, to model the TED effect on the microrings, some analytical models have been developed. However, in the previous works, the heat conduction within the microring is modeled by using the one-dimensional approach. The governing equation for heat conduction is solved only for the one-dimensional heat conduction along the radial thickness of the microring. This paper presents a simple analytical model for TED in microrings. The two-dimensional heat conduction over the thermoelastic temperature gradients along the radial thickness and the circumferential direction are considered in the present model. A two-dimensional heat conduction equation is developed. The solution of the equation is represented by the product of an assumed sine series along the radial thickness and an assumed trigonometric series along the circumferential direction. The analytical results obtained by the present 2-D model show a good agreement with the numerical (FEM) results. The limitations of the previous 1-D model are assessed.

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 Development of a Nonequilibrium Radiative Heat Transfer Computational Model for High Altitude Entry Vehicle Flowfield Methods

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1995-01-01

This final report will attempt to concisely summarize the activities and accomplishments associated with NASA Grant and to include pertinent documents in an appendix. The project initially had one primary and several secondary objectives. The original primary objective was to couple into the NASA Johnson Space Center (JSC) nonequilibrium chemistry Euler equation entry vehicle flowfield code, INEQ3D, the Texas A&M University (TAMU) local thermodynamic nonequilibrium (LTNE) radiation model. This model had previously been developed and verified under NASA Langley and NASA Johnson sponsorship as part of a viscous shock layer entry vehicle flowfield code. The secondary objectives were: (1) to investigate the necessity of including the radiative flux term in the vibrational-electron-electronic (VEE) energy equation as well as in the global energy equation, (2) to determine the importance of including the small net change in electronic energy between products and reactants which occurs during a chemical reaction, and (3) to study the effect of atom-atom impact ionization reactions on entry vehicle nonequilibrium flowfield chemistry and radiation. For each, of these objectives, it was assumed that the code would be applicable to lunar return entry conditions, i.e. altitude above 75 km, velocity greater, than 11 km/sec, where nonequilibrium chemistry and radiative heating phenomena would be significant. In addition, it was tacitly assumed that as part of the project the code would be applied to a variety of flight conditions and geometries.

Numerical analysis of fractional MHD Maxwell fluid with the effects of convection heat transfer condition and viscous dissipation

NASA Astrophysics Data System (ADS)

Bai, Yu; Jiang, Yuehua; Liu, Fawang; Zhang, Yan

2017-12-01

This paper investigates the incompressible fractional MHD Maxwell fluid due to a power function accelerating plate with the first order slip, and the numerical analysis on the flow and heat transfer of fractional Maxwell fluid has been done. Moreover the deformation motion of fluid micelle is simply analyzed. Nonlinear velocity equation are formulated with multi-term time fractional derivatives in the boundary layer governing equations, and convective heat transfer boundary condition and viscous dissipation are both taken into consideration. A newly finite difference scheme with L1-algorithm of governing equations are constructed, whose convergence is confirmed by the comparison with analytical solution. Numerical solutions for velocity and temperature show the effects of pertinent parameters on flow and heat transfer of fractional Maxwell fluid. It reveals that the fractional derivative weakens the effects of motion and heat conduction. The larger the Nusselt number is, the greater the heat transfer capacity of fluid becomes, and the temperature gradient at the wall becomes more significantly. The lower Reynolds number enhances the viscosity of the fluid because it is the ratio of the viscous force and the inertia force, which resists the flow and heat transfer.

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.

Ventilation equations for improved exothermic process control.

PubMed

McKernan, John L; Ellenbecker, Michael J

2007-04-01

Exothermic or heated processes create potentially unsafe work environments for an estimated 5-10 million American workers each year. Excessive heat and process contaminants have the potential to cause acute health effects such as heat stroke, and chronic effects such as manganism in welders. Although millions of workers are exposed to exothermic processes, insufficient attention has been given to continuously improving engineering technologies for these processes to provide effective and efficient control. Currently there is no specific occupational standard established by OSHA regarding exposure to heat from exothermic processes, therefore it is important to investigate techniques that can mitigate known and potential adverse occupational health effects. The current understanding of engineering controls for exothermic processes is primarily based on a book chapter written by W. C. L. Hemeon in 1955. Improvements in heat transfer and meteorological theory necessary to design improved process controls have occurred since this time. The research presented involved a review of the physical properties, heat transfer and meteorological theories governing buoyant air flow created by exothermic processes. These properties and theories were used to identify parameters and develop equations required for the determination of buoyant volumetric flow to assist in improving ventilation controls. Goals of this research were to develop and describe a new (i.e. proposed) flow equation, and compare it to currently accepted ones by Hemeon and the American Conference of Governmental Industrial Hygienists (ACGIH). Numerical assessments were conducted to compare solutions from the proposed equations for plume area, mean velocity and flow to those from the ACGIH and Hemeon. Parameters were varied for the dependent variables and solutions from the proposed, ACGIH, and Hemeon equations for plume area, mean velocity and flow were analyzed using a randomized complete block statistical design (ANOVA). Results indicate that the proposed plume mean velocity equation provides significantly greater means than either the ACGIH or Hemeon equations throughout the range of parameters investigated. The proposed equations for plume area and flow also provide significantly greater means than either the ACGIH or Hemeon equations at distances >1 m above exothermic processes. With an accurate solution for the total volumetric flow, ventilation engineers and practicing industrial hygienists are equipped with the necessary information to design and size hoods, as well as place them at an optimal distance from the source to provide adequate control of the rising plume. The equations developed will allow researchers and practitioners to determine the critical control parameters for exothermic processes, such as the exhaust flow necessary to improve efficacy and efficiency, while ensuring adequate worker protection.

Three-dimensional fully-coupled electrical and thermal transport model of dynamic switching in oxide memristors

DOE PAGES

Gao, Xujiao; Mamaluy, Denis; Mickel, Patrick R.; ...

2015-09-08

In this paper, we present a fully-coupled electrical and thermal transport model for oxide memristors that solves simultaneously the time-dependent continuity equations for all relevant carriers, together with the time-dependent heat equation including Joule heating sources. The model captures all the important processes that drive memristive switching and is applicable to simulate switching behavior in a wide range of oxide memristors. The model is applied to simulate the ON switching in a 3D filamentary TaOx memristor. Simulation results show that, for uniform vacancy density in the OFF state, vacancies fill in the conduction filament till saturation, and then fill outmore » a gap formed in the Ta electrode during ON switching; furthermore, ON-switching time strongly depends on applied voltage and the ON-to-OFF current ratio is sensitive to the filament vacancy density in the OFF state.« less

Boundary layers and scaling relations in natural thermal convection

NASA Astrophysics Data System (ADS)

Shishkina, Olga; Lohse, Detlef; Grossmann, Siegfried

2017-11-01

We analyse the boundary layer (BL) equations in natural thermal convection, which includes vertical convection (VC), where the fluid is confined between two differently heated vertical walls, horizontal convection (HC), where the fluid is heated at one part of the bottom plate and cooled at some other part, and Rayleigh-Benard convection (RBC). For BL dominated regimes we derive the scaling relations of the Nusselt and Reynolds numbers (Nu, Re) with the Rayleigh and Prandtl numbers (Ra, Pr). For VC the scaling relations are obtained directly from the BL equations, while for HC they are derived by applying the Grossmann-Lohse theory to the case of VC. In particular, for RBC with large Pr we derive Nu Pr0Ra1/3 and Re Pr-1Ra2/3. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh 405/4 - Heisenberg fellowship.

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.

Application of electron closures in extended MHD

NASA Astrophysics Data System (ADS)

Held, Eric; Adair, Brett; Taylor, Trevor

2017-10-01

Rigorous closure of the extended MHD equations in plasma fluid codes includes the effects of electron heat conduction along perturbed magnetic fields and contributions of the electron collisional friction and stress to the extended Ohms law. In this work we discuss application of a continuum numerical solution to the Chapman-Enskog-like electron drift kinetic equation using the NIMROD code. The implementation is a tightly-coupled fluid/kinetic system that carefully addresses time-centering in the advance of the fluid variables with their kinetically-computed closures. Comparisons of spatial accuracy, computational efficiency and required velocity space resolution are presented for applications involving growing magnetic islands in cylindrical and toroidal geometry. The reduction in parallel heat conduction due to particle trapping in toroidal geometry is emphasized. Work supported by DOE under Grant Nos. DE-FC02-08ER54973 and DE-FG02-04ER54746.

Another self-similar blast wave: Early time asymptote with shock heated electrons and high thermal conductivity

NASA Technical Reports Server (NTRS)

Cox, D. P.; Edgar, R. J.

1982-01-01

Accurate approximations are presented for the self-similar structures of nonradiating blast waves with adiabatic ions, isothermal electrons, and equation ion and electron temperatures at the shock. The cases considered evolve in cavities with power law ambient densities (including the uniform density case) and have negligible external pressure. The results provide the early time asymptote for systems with shock heating of electrons and strong thermal conduction. In addition, they provide analytical results against which two fluid numerical hydrodynamic codes can be checked.

Thermal-Interaction Matrix For Resistive Test Structure

NASA Technical Reports Server (NTRS)

Buehler, Martin G.; Dhiman, Jaipal K.; Zamani, Nasser

1990-01-01

Linear mathematical model predicts increase in temperature in each segment of 15-segment resistive structure used to test electromigration. Assumption of linearity based on fact: equations that govern flow of heat are linear and coefficients in equations (heat conductivities and capacities) depend only weakly on temperature and considered constant over limited range of temperature.

Semi-empirical estimation of organic compound fugacity ratios at environmentally relevant system temperatures.

PubMed

van Noort, Paul C M

2009-06-01

Fugacity ratios of organic compounds are used to calculate (subcooled) liquid properties, such as solubility or vapour pressure, from solid properties and vice versa. They can be calculated from the entropy of fusion, the melting temperature, and heat capacity data for the solid and the liquid. For many organic compounds, values for the fusion entropy are lacking. Heat capacity data are even scarcer. In the present study, semi-empirical compound class specific equations were derived to estimate fugacity ratios from molecular weight and melting temperature for polycyclic aromatic hydrocarbons and polychlorinated benzenes, biphenyls, dibenzo[p]dioxins and dibenzofurans. These equations estimate fugacity ratios with an average standard error of about 0.05 log units. In addition, for compounds with known fusion entropy values, a general semi-empirical correction equation based on molecular weight and melting temperature was derived for estimation of the contribution of heat capacity differences to the fugacity ratio. This equation estimates the heat capacity contribution correction factor with an average standard error of 0.02 log units for polycyclic aromatic hydrocarbons, polychlorinated benzenes, biphenyls, dibenzo[p]dioxins and dibenzofurans.

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.

Heat transfer in pipes

NASA Technical Reports Server (NTRS)

Burbach, T.

1985-01-01

The heat transfer from hot water to a cold copper pipe in laminar and turbulent flow condition is determined. The mean flow through velocity in the pipe, relative test length and initial temperature in the vessel were varied extensively during tests. Measurements confirm Nusselt's theory for large test lengths in laminar range. A new equation is derived for heat transfer for large starting lengths which agrees satisfactorily with measurements for large starting lengths. Test results are compared with the new Prandtl equation for heat transfer and correlated well. Test material for 200- and to 400-diameter test length is represented at four different vessel temperatures.

Numerical simulation of forced convection in a duct subjected to microwave heating

NASA Astrophysics Data System (ADS)

Zhu, J.; Kuznetsov, A. V.; Sandeep, K. P.

2007-01-01

In this paper, forced convection in a rectangular duct subjected to microwave heating is investigated. Three types of non-Newtonian liquids flowing through the duct are considered, specifically, apple sauce, skim milk, and tomato sauce. A finite difference time domain method is used to solve Maxwell’s equations simulating the electromagnetic field. The three-dimensional temperature field is determined by solving the coupled momentum, energy, and Maxwell’s equations. Numerical results show that the heating pattern strongly depends on the dielectric properties of the fluid in the duct and the geometry of the microwave heating system.

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

The effects of inlet turbulence and rotor/stator interactions on the aerodynamics and heat transfer of a large-scale rotating turbine model. Volume 2: Heat transfer data tabulation. 15 percent axial spacing

NASA Technical Reports Server (NTRS)

Dring, R. P.; Blair, M. F.; Joslyn, H. D.

1986-01-01

A combined experimental and analytical program was conducted to examine the effects of inlet turbulence on airfoil heat transfer. The experimental portion of the study was conducted in a large-scale (approx 5X engine), ambient temperature, rotating turbine model configured in both single stage and stage-and-a-half arrangements. Heat transfer measurements were obtained using low-conductivity airfoils with miniature thermcouples welded to a thin, electrically heated surface skin. Heat transfer data were acquired for various combinations of low or high inlet turbulence intensity, flow coefficient, first-stator/rotor axial spacing, Reynolds number and relative circumferential position of the first and second stators. Aerodynamic measurements obtained as part of the program include distributions of the mean and fluctuating velocities at the turbine inlet and, for each airfoil row, midspan airfoil surface pressures and circumferential distributions of the downstream steady state pressures and fluctuating velocities. Analytical results include airfoil heat transfer predictions produced using existing 2-D boundary layer computation schemes and an examination of solutions of the unsteady boundary layer equations. The results are reported in four separate volumes, of which this is Volume 2: Heat Transfer Data Tabulation; 15 Percent Axial Spacing.

An exact closed form solution for constant area compressible flow with friction and heat transfer

NASA Technical Reports Server (NTRS)

Sturas, J. I.

1971-01-01

The well-known differential equation for the one-dimensional flow of a compressible fluid with heat transfer and wall friction has no known solution in closed form for the general case. This report presents a closed form solution for the special case of constant heat flux per unit length and constant specific heat. The solution was obtained by choosing the square of a dimensionless flow parameter as one of the independent variables to describe the flow. From this exact solution, an approximate simplified form is derived that is applicable for predicting subsonic flow performance characteristics for many types of constant area passages in internal flow. The data included in this report are considered sufficiently accurate for use as a guide in analyzing and designing internal gas flow systems.

Reinterpretation of Mariner 9 IRIS data on the basis of a simulation of radiative-conductive convective transfer in the dust laden Martian atmosphere

NASA Technical Reports Server (NTRS)

Pallman, A. J.

1974-01-01

Time dependent vertical distributions of atmospheric temperature and static stability were determined by a radiative-convective-conductive heat transfer model attuned to Mariner 9 IRIS radiance data. Of particular interest were conditions of both the dust-laden and dust-free atmosphere in the middle latitudes on Mars during the late S.H. summer season. The numerical model simulates at high spatial and temporal resolution (52 atmospheric and 30 subsurface levels; with a time-step of 7.5 min.) the heat transports in the ground-atmosphere system. The algorithm is based on the solution of the appropriate heating rate equation which includes radiative, molecular-conductive and convective heat transfer terms. Ground and atmosphere are coupled by an internal thermal boundary condition.

Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps

NASA Astrophysics Data System (ADS)

Fang, En; Wu, Xiaojie; Yu, Yuesen; Xiu, Junrui

2017-03-01

In this paper, a numerical model is developed by combining thermodynamics with heat transfer theory. Taking inner and external multi-irreversibility into account, it is with a complementary equation for heat circulation in air gaps of a steady cooling system with commercial thermoelectric modules operating in refrigeration mode. With two modes concerned, the equation presents the heat flowing through air gaps which forms heat circulations between both sides of thermoelectric coolers (TECs). In numerical modelling, a TEC is separated as two temperature controlled constant heat flux reservoirs in a thermal resistance network. In order to obtain the parameter values, an experimental apparatus with a commercial thermoelectric cooler was built to characterize the performance of a TEC with heat source and sink assembly. At constant power dissipation, steady temperatures of heat source and both sides of the thermoelectric cooler were compared with those in a standard numerical model. The method displayed that the relationship between Φf and the ratio Φ_{c}'/Φ_{c} was linear as expected. Then, for verifying the accuracy of proposed numerical model, the data in another system were recorded. It is evident that the experimental results are in good agreement with simulation(proposed model) data at different heat transfer rates. The error is small and mainly results from the instabilities of thermal resistances with temperature change and heat flux, heat loss of the device vertical surfaces and measurements.

CHAP III- CHARRING ABLATOR PROGRAM FOR ADVANCED INVESTIGATION OF THERMAL PROTECTION SYSTEMS FOR ENTRY

NASA Technical Reports Server (NTRS)

Stroud, C. W.

1994-01-01

The transient response of a thermal protection material to heat applied to the surface can be calculated using the CHAP III computer program. CHAP III can be used to analyze pyrolysis gas chemical kinetics in detail and examine pyrolysis reactions-indepth. The analysis includes the deposition of solid products produced by chemical reactions in the gas phase. CHAP III uses a modelling technique which can approximate a wide range of ablation problems. The energy equation used in CHAP III incorporates pyrolysis (both solid and gas reactions), convection, conduction, storage, work, kinetic energy, and viscous dissipation. The chemically reacting components of the solid are allowed to vary as a function of position and time. CHAP III employs a finite difference method to approximate the energy equations. Input values include specific heat, thermal conductivity, thermocouple locations, enthalpy, heating rates, and a description of the chemical reactions expected. The output tabulates the temperature at locations throughout the ablator, gas flow within the solid, density of the solid, weight of pyrolysis gases, and rate of carbon deposition. A sample case is included, which analyzes an ablator material containing several pyrolysis reactions subjected to an environment typical of entry at lunar return velocity. CHAP III is written in FORTRAN IV for batch execution and has been implemented on a CDC CYBER 170 series computer operating under NOS with a central memory requirement of approximately 102K (octal) of 60 bit words. This program was developed in 1985.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

A new computational method for reacting hypersonic flows

NASA Astrophysics Data System (ADS)

Niculescu, M. L.; Cojocaru, M. G.; Pricop, M. V.; Fadgyas, M. C.; Pepelea, D.; Stoican, M. G.

2017-07-01

Hypersonic gas dynamics computations are challenging due to the difficulties to have reliable and robust chemistry models that are usually added to Navier-Stokes equations. From the numerical point of view, it is very difficult to integrate together Navier-Stokes equations and chemistry model equations because these partial differential equations have different specific time scales. For these reasons, almost all known finite volume methods fail shortly to solve this second order partial differential system. Unfortunately, the heating of Earth reentry vehicles such as space shuttles and capsules is very close linked to endothermic chemical reactions. A better prediction of wall heat flux leads to smaller safety coefficient for thermal shield of space reentry vehicle; therefore, the size of thermal shield decreases and the payload increases. For these reasons, the present paper proposes a new computational method based on chemical equilibrium, which gives accurate prediction of hypersonic heating in order to support the Earth reentry capsule design.

A practical nonlocal model for heat transport in magnetized laser plasmas

NASA Astrophysics Data System (ADS)

Nicolaï, Ph. D.; Feugeas, J.-L. A.; Schurtz, G. P.

2006-03-01

A model of nonlocal transport for multidimensional radiation magnetohydrodynamics codes is presented. In laser produced plasmas, it is now believed that the heat transport can be strongly modified by the nonlocal nature of the electron conduction. Other mechanisms, such as self-generated magnetic fields, may also affect the heat transport. The model described in this work, based on simplified Fokker-Planck equations aims at extending the model of G. Schurtz, Ph. Nicolaï, and M. Busquet [Phys. Plasmas 7, 4238 (2000)] to magnetized plasmas. A complete system of nonlocal equations is derived from kinetic equations with self-consistent electric and magnetic fields. These equations are analyzed and simplified in order to be implemented into large laser fusion codes and coupled to other relevant physics. The model is applied to two laser configurations that demonstrate the main features of the model and point out the nonlocal Righi-Leduc effect in a multidimensional case.

Navier-Stokes turbine heat transfer predictions using two-equation turbulence closures

NASA Technical Reports Server (NTRS)

Ameri, Ali A.; Arnone, Andrea

1992-01-01

Navier-Stokes calculations were carried out in order to predict the heat-transfer rates on turbine blades. The calculations were performed using TRAF2D which is a k-epsilon, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using Coakley's q-omega and Chien's k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a nonperiodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the SSME high-pressure fuel turbine. The comparison serves to highlight the weaknesses of the turbulence models for use in turbomachinery heat-transfer calculations.

A mathematical model for mixed convective flow of chemically reactive Oldroyd-B fluid between isothermal stretching disks

NASA Astrophysics Data System (ADS)

Hashmi, M. S.; Khan, N.; Ullah Khan, Sami; Rashidi, M. M.

In this study, we have constructed a mathematical model to investigate the heat source/sink effects in mixed convection axisymmetric flow of an incompressible, electrically conducting Oldroyd-B fluid between two infinite isothermal stretching disks. The effects of viscous dissipation and Joule heating are also considered in the heat equation. The governing partial differential equations are converted into ordinary differential equations by using appropriate similarity variables. The series solution of these dimensionless equations is constructed by using homotopy analysis method. The convergence of the obtained solution is carefully examined. The effects of various involved parameters on pressure, velocity and temperature profiles are comprehensively studied. A graphical analysis has been presented for various values of problem parameters. The numerical values of wall shear stress and Nusselt number are computed at both upper and lower disks. Moreover, a graphical and tabular explanation for critical values of Frank-Kamenetskii regarding other flow parameters.

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.

A Model for Hydrogen Thermal Conductivity and Viscosity Including the Critical Point

NASA Technical Reports Server (NTRS)

Wagner, Howard A.; Tunc, Gokturk; Bayazitoglu, Yildiz

2001-01-01

In order to conduct a thermal analysis of heat transfer to liquid hydrogen near the critical point, an accurate understanding of the thermal transport properties is required. A review of the available literature on hydrogen transport properties identified a lack of useful equations to predict the thermal conductivity and viscosity of liquid hydrogen. The tables published by the National Bureau of Standards were used to perform a series of curve fits to generate the needed correlation equations. These equations give the thermal conductivity and viscosity of hydrogen below 100 K. They agree with the published NBS tables, with less than a 1.5 percent error for temperatures below 100 K and pressures from the triple point to 1000 KPa. These equations also capture the divergence in the thermal conductivity at the critical point

Model of formation of droplets during electric arc surfacing of functional coatings

NASA Astrophysics Data System (ADS)

Sarychev, Vladimir D.; Granovskii, Alexei Yu; Nevskii, Sergey A.; Gromov, Victor E.

2016-01-01

The mathematical model was developed for the initial stage of formation of an electrode metal droplet in the process of arc welding. Its essence lies in the fact that the presence of a temperature gradient in the boundary layer of the molten metal causes thermo-capillary instability, which leads to the formation of electrode metal droplets. A system of equations including Navier-Stokes equations, heat conduction and Maxwell's equations was solved as well as the boundary conditions for the system electrodes-plasma. Dispersion equation for thermo-capillary waves in the linear approximation for the plane layer was received and analyzed. The values of critical wavelengths, at which thermo-capillary instability appears in the nanometer wavelength range, were found. The parameters at which the mode of a fine-droplet transfer of the material takes place were theoretically defined.

Computer program grade 2 for the design and analysis of heat-pipe wicks

NASA Technical Reports Server (NTRS)

Eninger, J. E.; Edwards, D. K.

1976-01-01

This user's manual describes the revised version of the computer program GRADE(1), which designs and analyzes heat pipes with graded porosity fibrous slab wicks. The revisions are: (1) automatic calculation of the minimum condenser-end stress that will not result in an excess-liquid puddle or a liquid slug in the vapor space; (2) numerical solution of the equations describing flow in the circumferential grooves to assess the burnout criterion; (3) calculation of the contribution of excess liquid in fillets and puddles to the heat-transport; (4) calculation of the effect of partial saturation on the wick performance; and (5) calculation of the effect of vapor flow, which includes viscousinertial interactions.

Temperature distribution of thick thermoset composites

NASA Astrophysics Data System (ADS)

Guo, Zhan-Sheng; Du, Shanyi; Zhang, Boming

2004-05-01

The development of temperature distribution of thick polymeric matrix laminates during an autoclave vacuum bag process was measured and compared with numerically calculated results. The finite element formulation of the transient heat transfer problem was carried out for polymeric matrix composite materials from the heat transfer differential equations including internal heat generation produced by exothermic chemical reactions. Software based on the general finite element software package was developed for numerical simulation of the entire composite process. From the experimental and numerical results, it was found that the measured temperature profiles were in good agreement with the numerical ones, and conventional cure cycles recommended by prepreg manufacturers for thin laminates should be modified to prevent temperature overshoot.

An advanced computational bioheat transfer model for a human body with an embedded systemic circulation.

PubMed

Coccarelli, Alberto; Boileau, Etienne; Parthimos, Dimitris; Nithiarasu, Perumal

2016-10-01

In the present work, an elaborate one-dimensional thermofluid model for a human body is presented. By contrast to the existing pure conduction-/perfusion-based models, the proposed methodology couples the arterial fluid dynamics of a human body with a multi-segmental bioheat model of surrounding solid tissues. In the present configuration, arterial flow is included through a network of elastic vessels. More than a dozen solid segments are employed to represent the heat conduction in the surrounding tissues, and each segment is constituted by a multilayered circular cylinder. Such multi-layers allow flexible delineation of the geometry and incorporation of properties of different tissue types. The coupling of solid tissue and fluid models requires subdivision of the arterial circulation into large and small arteries. The heat exchange between tissues and arterial wall occurs by convection in large vessels and by perfusion in small arteries. The core region, including the heart, provides the inlet conditions for the fluid equations. In the proposed model, shivering, sweating, and perfusion changes constitute the basis of the thermoregulatory system. The equations governing flow and heat transfer in the circulatory system are solved using a locally conservative Galerkin approach, and the heat conduction in the surrounding tissues is solved using a standard implicit backward Euler method. To investigate the effectiveness of the proposed model, temperature field evolutions are monitored at different points of the arterial tree and in the surrounding tissue layers. To study the differences due to flow-induced convection effects on thermal balance, the results of the current model are compared against those of the widely used modelling methodologies. The results show that the convection significantly influences the temperature distribution of the solid tissues in the vicinity of the arteries. Thus, the inner convection has a more predominant role in the human body heat balance than previously thought. To demonstrate its capabilities, the proposed new model is used to study different scenarios, including thermoregulation inactivity and variation in surrounding atmospheric conditions.

Effects of feather wear and temperature on prediction of food intake and residual food consumption.

PubMed

Herremans, M; Decuypere, E; Siau, O

1989-03-01

Heat production, which accounts for 0.6 of gross energy intake, is insufficiently represented in predictions of food intake. Especially when heat production is elevated (for example by lower temperature or poor feathering) the classical predictions based on body weight, body-weight change and egg mass are inadequate. Heat production was reliably estimated as [35.5-environmental temperature (degree C)] x [Defeathering (=%IBPW) + 21]. Including this term (PHP: predicted heat production) in equations predicting food intake significantly increased accuracy of prediction, especially under suboptimal conditions. Within the range of body weights tested (from 1.6 kg in brown layers to 2.8 kg in dwarf broiler breeders), body weight as an independent variable contributed little to the prediction of food intake; especially within strains its effect was better included in the intercept. Significantly reduced absolute values of residual food consumption were obtained over a wide range of conditions by using predictions of food intake based on body-weight change, egg mass, predicted heat production (PHP) and an intercept, instead of body weight, body-weight change, egg mass and an intercept.

DIY EOS: Experimentally Validated Equations of State for Planetary Fluids to GPa Pressures, Tools for Understanding Planetary Processes and Habitability

NASA Astrophysics Data System (ADS)

Vance, Steven; Brown, J. Michael; Bollengier, Olivier

2016-10-01

Sound speeds are fundamental to seismology, and provide a path allowing the accurate determination of thermodynamic potentials. Prior equations of state (EOS) for pure ammonia (Harr and Gallagher 1978, Tillner-Roth et al. 1993) are based primarily on measured densities and heat capacities. Sound speeds, not included in the fitting, are poorly predicted.We couple recent high pressure sound speed data with prior densities and heat capacities to generate a new equation of state. Our representation fits both the earlier lower pressure work as well as measured sound speeds to 4 GPa and 700 K and the Hugoniot to 70 GPa and 6000 K.In contrast to the damped polynomial representation previously used, our equation of state is based on local basis functions in the form of tensor b-splines. Regularization allows the thermodynamic surface to be continued into regimes poorly sampled by experiments. We discuss application of this framework for aqueous equations of state validated by experimental measurements. Preliminary equations of state have been prepared applying the local basis function methodology to aqueous NH3, Mg2SO4, NaCl, and Na2SO4. We describe its use for developing new equations of state, and provide some applications of the new thermodynamic data to the interior structures of gas giant planets and ocean worlds.References:L. Haar and J. S. Gallagher. Thermodynamic properties of ammonia. American Chemical Society and the American Institute of Physics for the National Bureau of Standards, 1978.R. Tillner-Roth, F. Harms-Watzenberg, and H. Baehr. Eine neue fundamentalgleichung fuer ammoniak. DKV TAGUNGSBERICHT, 20:67-67, 1993.

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.

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.

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.

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.

MHD Free Convective Boundary Layer Flow of a Nanofluid past a Flat Vertical Plate with Newtonian Heating Boundary Condition

PubMed Central

Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmed I.

2012-01-01

Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688

Study of velocity and temperature distributions in boundary layer flow of fourth grade fluid over an exponential stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Najeeb Alam; Saeed, Umair Bin; Sultan, Faqiha; Ullah, Saif; Rehman, Abdul

2018-02-01

This study deals with the investigation of boundary layer flow of a fourth grade fluid and heat transfer over an exponential stretching sheet. For analyzing two heating processes, namely, (i) prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF), the temperature distribution in a fluid has been considered. The suitable transformations associated with the velocity components and temperature, have been employed for reducing the nonlinear model equation to a system of ordinary differential equations. The flow and temperature fields are revealed by solving these reduced nonlinear equations through an effective analytical method. The important findings in this analysis are to observe the effects of viscoelastic, cross-viscous, third grade fluid, and fourth grade fluid parameters on the constructed analytical expression for velocity profile. Likewise, the heat transfer properties are studied for Prandtl and Eckert numbers.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

NASA Astrophysics Data System (ADS)

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

2017-09-01

Present exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

NASA Astrophysics Data System (ADS)

Bhadauria, B. S.; Singh, M. K.; Singh, A.; Singh, B. K.; Kiran, P.

2016-12-01

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

Thermal radiation heat transfer in participating media by finite volume discretization using collimated beam incidence

NASA Astrophysics Data System (ADS)

Harijishnu, R.; Jayakumar, J. S.

2017-09-01

The main objective of this paper is to study the heat transfer rate of thermal radiation in participating media. For that, a generated collimated beam has been passed through a two dimensional slab model of flint glass with a refractive index 2. Both Polar and azimuthal angle have been varied to generate such a beam. The Temperature of the slab and Snells law has been validated by Radiation Transfer Equation (RTE) in OpenFOAM (Open Field Operation and Manipulation), a CFD software which is the major computational tool used in Industry and research applications where the source code is modified in which radiation heat transfer equation is added to the case and different radiation heat transfer models are utilized. This work concentrates on the numerical strategies involving both transparent and participating media. Since Radiation Transfer Equation (RTE) is difficult to solve, the purpose of this paper is to use existing solver buoyantSimlpeFoam to solve radiation model in the participating media by compiling the source code to obtain the heat transfer rate inside the slab by varying the Intensity of radiation. The Finite Volume Method (FVM) is applied to solve the Radiation Transfer Equation (RTE) governing the above said physical phenomena.

A User-Friendly Software Package for HIFU Simulation

NASA Astrophysics Data System (ADS)

Soneson, Joshua E.

2009-04-01

A freely-distributed, MATLAB (The Mathworks, Inc., Natick, MA)-based software package for simulating axisymmetric high-intensity focused ultrasound (HIFU) beams and their heating effects is discussed. The package (HIFU_Simulator) consists of a propagation module which solves the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and a heating module which solves Pennes' bioheat transfer (BHT) equation. The pressure, intensity, heating rate, temperature, and thermal dose fields are computed, plotted, the output is released to the MATLAB workspace for further user analysis or postprocessing.

Two-fluid description of wave-particle interactions in strong Buneman turbulence

NASA Astrophysics Data System (ADS)

Che, H.

2014-06-01

To understand the nature of anomalous resistivity in magnetic reconnection, we investigate turbulence-induced momentum transport and energy dissipation while a plasma is unstable to the Buneman instability in force-free current sheets. Using 3D particle-in-cell simulations, we find that the macroscopic effects generated by wave-particle interactions in Buneman instability can be approximately described by a set of electron fluid equations. We show that both energy dissipation and momentum transport along electric current in the current layer are locally quasi-static, but globally dynamic and irreversible. Turbulent drag dissipates both the streaming energy of the current sheet and the associated magnetic energy. The net loss of streaming energy is converted into the electron component heat conduction parallel to the magnetic field and increases the electron Boltzmann entropy. The growth of self-sustained Buneman waves satisfies a Bernoulli-like equation that relates the turbulence-induced convective momentum transport and thermal momentum transport. Electron trapping and de-trapping drive local momentum transports, while phase mixing converts convective momentum into thermal momentum. The drag acts like a micro-macro link in the anomalous heating processes. The decrease of magnetic field maintains an inductive electric field that re-accelerates electrons, but most of the magnetic energy is dissipated and converted into the component heat of electrons perpendicular to the magnetic field. This heating process is decoupled from the heating of Buneman instability in the current sheets. Ion heating is weak but ions play an important role in assisting energy exchanges between waves and electrons. Cold ion fluid equations together with our electron fluid equations form a complete set of equations that describes the occurrence, growth, saturation and decay of the Buneman instability.

Comments on "Modified wind chill temperatures determined by a whole body thermoregulation model and human-based convective coefficients" by Ben Shabat, Shitzer and Fiala (2013) and "Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments" by Ben Shabat and Shitzer (2012)

NASA Astrophysics Data System (ADS)

Osczevski, Randall J.

2014-08-01

Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) present revised charts for wind chill equivalent temperatures (WCET) and facial skin temperatures (FST) that differ significantly from currently accepted charts. They credit these differences to their more sophisticated calculation model and to the human-based equation that it used for finding the convective heat transfer coefficient (Ben Shabat and Shitzer, Int J Biometeorol 56:639-651, 2012). Because a version of the simple model that was used to create the current charts accurately reproduces their results when it uses the human-based equation, the differences that they found must be entirely due to this equation. In deriving it, Ben Shabat and Shitzer assumed that all of the heat transfer from the surface of their cylindrical model was due to forced convection alone. Because several modes of heat transfer were occurring in the human experiments they were attempting to simulate, notably radiation, their coefficients are actually total external heat transfer coefficients, not purely convective ones, as the calculation models assume. Data from the one human experiment that used heat flux sensors supports this conclusion and exposes the hazard of using a numerical model with several adjustable parameters that cannot be measured. Because the human-based equation is faulty, the values in the proposed charts are not correct. The equation that Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) propose to calculate WCET should not be used.

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

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.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

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.

Hierarchical equations of motion method applied to nonequilibrium heat transport in model molecular junctions: Transient heat current and high-order moments of the current operator

NASA Astrophysics Data System (ADS)

Song, Linze; Shi, Qiang

2017-02-01

We present a theoretical approach to study nonequilibrium quantum heat transport in molecular junctions described by a spin-boson type model. Based on the Feynman-Vernon path integral influence functional formalism, expressions for the average value and high-order moments of the heat current operators are derived, which are further obtained directly from the auxiliary density operators (ADOs) in the hierarchical equations of motion (HEOM) method. Distribution of the heat current is then derived from the high-order moments. As the HEOM method is nonperturbative and capable of treating non-Markovian system-environment interactions, the method can be applied to various problems of nonequilibrium quantum heat transport beyond the weak coupling regime.

A Step Towards CO2-Neutral Aviation

NASA Technical Reports Server (NTRS)

Brankovic, Andreja; Ryder, Robert C.; Hendricks, Robert C.; Huber, Marcia L.

2008-01-01

An approximation method for evaluation of the caloric equations used in combustion chemistry simulations is described. The method is applied to generate the equations of specific heat, static enthalpy, and Gibb's free energy for fuel mixtures of interest to gas turbine engine manufacturers. Liquid-phase fuel properties are also derived. The fuels investigated include JP-8, synthetic fuel, and two blends of JP-8 and synthetic fuel. The complete set of fuel property equations for both phases are implemented into a computational fluid dynamics (CFD) flow solver database, and multiphase, reacting flow simulations of a well-tested liquid-fueled combustor are performed. The simulations are a first step in understanding combustion system performance and operational issues when using alternate fuels, at practical engine operating conditions.

HEAT TRANSFER MEANS

DOEpatents

Fraas, A.P.; Wislicenus, G.F.

1961-07-11

A heat exchanger is adapted to unifomly cool a spherical surface. Equations for the design of a spherical heat exchanger hav~g tubes with a uniform center-to-center spining are given. The heat exchanger is illustrated in connection with a liquid-fueled reactor.

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

NASA Technical Reports Server (NTRS)

Eckert, E.R.G.; Livingood, John N.B.

1951-01-01

An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Sensor fault detection and isolation system for a condensation process.

PubMed

Castro, M A López; Escobar, R F; Torres, L; Aguilar, J F Gómez; Hernández, J A; Olivares-Peregrino, V H

2016-11-01

This article presents the design of a sensor Fault Detection and Isolation (FDI) system for a condensation process based on a nonlinear model. The condenser is modeled by dynamic and thermodynamic equations. For this work, the dynamic equations are described by three pairs of differential equations which represent the energy balance between the fluids. The thermodynamic equations consist in algebraic heat transfer equations and empirical equations, that allow for the estimation of heat transfer coefficients. The FDI system consists of a bank of two nonlinear high-gain observers, in order to detect, estimate and to isolate the fault in any of both outlet temperature sensors. The main contributions of this work were the experimental validation of the condenser nonlinear model and the FDI system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

The impact of standard and hard-coded parameters on the hydrologic fluxes in the Noah-MP land surface model

NASA Astrophysics Data System (ADS)

Thober, S.; Cuntz, M.; Mai, J.; Samaniego, L. E.; Clark, M. P.; Branch, O.; Wulfmeyer, V.; Attinger, S.

2016-12-01

Land surface models incorporate a large number of processes, described by physical, chemical and empirical equations. The agility of the models to react to different meteorological conditions is artificially constrained by having hard-coded parameters in their equations. Here we searched for hard-coded parameters in the computer code of the land surface model Noah with multiple process options (Noah-MP) to assess the model's agility during parameter estimation. We found 139 hard-coded values in all Noah-MP process options in addition to the 71 standard parameters. We performed a Sobol' global sensitivity analysis to variations of the standard and hard-coded parameters. The sensitivities of the hydrologic output fluxes latent heat and total runoff, their component fluxes, as well as photosynthesis and sensible heat were evaluated at twelve catchments of the Eastern United States with very different hydro-meteorological regimes. Noah-MP's output fluxes are sensitive to two thirds of its standard parameters. The most sensitive parameter is, however, a hard-coded value in the formulation of soil surface resistance for evaporation, which proved to be oversensitive in other land surface models as well. Latent heat and total runoff show very similar sensitivities towards standard and hard-coded parameters. They are sensitive to both soil and plant parameters, which means that model calibrations of hydrologic or land surface models should take both soil and plant parameters into account. Sensible and latent heat exhibit almost the same sensitivities so that calibration or sensitivity analysis can be performed with either of the two. Photosynthesis has almost the same sensitivities as transpiration, which are different from the sensitivities of latent heat. Including photosynthesis and latent heat in model calibration might therefore be beneficial. Surface runoff is sensitive to almost all hard-coded snow parameters. These sensitivities get, however, diminished in total runoff. It is thus recommended to include the most sensitive hard-coded model parameters that were exposed in this study when calibrating Noah-MP.

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

NASA Technical Reports Server (NTRS)

Avissar, Roni; Chen, Fei

1993-01-01

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.

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.

ANL/RBC: A computer code for the analysis of Rankine bottoming cycles, including system cost evaluation and off-design performance

NASA Technical Reports Server (NTRS)

Mclennan, G. A.

1986-01-01

This report describes, and is a User's Manual for, a computer code (ANL/RBC) which calculates cycle performance for Rankine bottoming cycles extracting heat from a specified source gas stream. The code calculates cycle power and efficiency and the sizes for the heat exchangers, using tabular input of the properties of the cycle working fluid. An option is provided to calculate the costs of system components from user defined input cost functions. These cost functions may be defined in equation form or by numerical tabular data. A variety of functional forms have been included for these functions and they may be combined to create very general cost functions. An optional calculation mode can be used to determine the off-design performance of a system when operated away from the design-point, using the heat exchanger areas calculated for the design-point.

Investigation of two and three parameter equations of state for cryogenic fluids

NASA Technical Reports Server (NTRS)

Jenkins, Susan L.; Majumdar, Alok K.; Hendricks, Robert C.

1990-01-01

Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point.

Mathematical Model of the Processes of Heat and Mass Transfer and Diffusion of the Magnetic Field in an Induction Furnace

NASA Astrophysics Data System (ADS)

Perminov, A. V.; Nikulin, I. L.

2016-03-01

We propose a mathematical model describing the motion of a metal melt in a variable inhomogeneous magnetic field of a short solenoid. In formulating the problem, we made estimates and showed the possibility of splitting the complete magnetohydrodynamical problem into two subproblems: a magnetic field diffusion problem where the distributions of the external and induced magnetic fields and currents are determined, and a heat and mass transfer problem with known distributions of volume sources of heat and forces. The dimensionless form of the heat and mass transfer equation was obtained with the use of averaging and multiscale methods, which permitted writing and solving separately the equations for averaged flows and temperature fields and their oscillations. For the heat and mass transfer problem, the boundary conditions for a real technological facility are discussed. The dimensionless form of the magnetic field diffusion equation is presented, and the experimental computational procedure and results of the numerical simulation of the magnetic field structure in the melt for various magnetic Reynolds numbers are described. The extreme dependence of heat release on the magnetic Reynolds number has been interpreted.

Combustion-acoustic stability analysis for premixed gas turbine combustors

NASA Technical Reports Server (NTRS)

Darling, Douglas; Radhakrishnan, Krishnan; Oyediran, Ayo; Cowan, Lizabeth

1995-01-01

Lean, prevaporized, premixed combustors are susceptible to combustion-acoustic instabilities. A model was developed to predict eigenvalues of axial modes for combustion-acoustic interactions in a premixed combustor. This work extends previous work by including variable area and detailed chemical kinetics mechanisms, using the code LSENS. Thus the acoustic equations could be integrated through the flame zone. Linear perturbations were made of the continuity, momentum, energy, chemical species, and state equations. The qualitative accuracy of our approach was checked by examining its predictions for various unsteady heat release rate models. Perturbations in fuel flow rate are currently being added to the model.

Improved models of stellar core collapse and still no explosions: what is missing?

PubMed

Buras, R; Rampp, M; Janka, H-Th; Kifonidis, K

2003-06-20

Two-dimensional hydrodynamic simulations of stellar core collapse are presented which for the first time were performed by solving the Boltzmann equation for the neutrino transport including a state-of-the-art description of neutrino interactions. Stellar rotation is also taken into account. Although convection develops below the neutrinosphere and in the neutrino-heated region behind the supernova shock, the models do not explode. This suggests missing physics, possibly with respect to the nuclear equation of state and weak interactions in the subnuclear regime. However, it might also indicate a fundamental problem with the neutrino-driven explosion mechanism.

Differential invariants in nonclassical models of hydrodynamics

NASA Astrophysics Data System (ADS)

Bublik, Vasily V.

2017-10-01

In this paper, differential invariants are used to construct solutions for equations of the dynamics of a viscous heat-conducting gas and the dynamics of a viscous incompressible fluid modified by nanopowder inoculators. To describe the dynamics of a viscous heat-conducting gas, we use the complete system of Navier—Stokes equations with allowance for heat fluxes. Mathematical description of the dynamics of liquid metals under high-energy external influences (laser radiation or plasma flow) includes, in addition to the Navier—Stokes system of an incompressible viscous fluid, also heat fluxes and processes of nonequilibrium crystallization of a deformable fluid. Differentially invariant solutions are a generalization of partially invariant solutions, and their active study for various models of continuous medium mechanics is just beginning. Differentially invariant solutions can also be considered as solutions with differential constraints; therefore, when developing them, the approaches and methods developed by the science schools of academicians N. N. Yanenko and A. F. Sidorov will be actively used. In the construction of partially invariant and differentially invariant solutions, there are overdetermined systems of differential equations that require a compatibility analysis. The algorithms for reducing such systems to involution in a finite number of steps are described by Cartan, Finikov, Kuranishi, and other authors. However, the difficultly foreseeable volume of intermediate calculations complicates their practical application. Therefore, the methods of computer algebra are actively used here, which largely helps in solving this difficult problem. It is proposed to use the constructed exact solutions as tests for formulas, algorithms and their software implementations when developing and creating numerical methods and computational program complexes. This combination of effective numerical methods, capable of solving a wide class of problems, with analytical methods makes it possible to make the results of mathematical modeling more accurate and reliable.

Incorporating Density Properties of MgSO4 Brines Into Icy World Ocean Simulations

NASA Astrophysics Data System (ADS)

Goodman, J. C.; Vance, S.

2011-12-01

The structure and flow of the subsurface oceans in icy worlds depends on the sources of buoyancy within these oceans. Buoyancy is determined by the equation of state, in which density is a nonlinear function of temperature, salinity, and pressure. Equations of state for terrestrial seawater (with Na and Cl as the principal dissolved species) are well-developed, but icy world oceans may contain a different balance of species, including Na, Mg, SO4, and NH4 (Kargel et al, 2000). Recent work by Vance and Brown (2011, pers. comm.) has mapped out the density and thermodynamic properties of MgSO4 brines under icy world conditions. We have developed code to incorporate this equation of state data for MgSO4 brines into two different ocean simulation models. First, we investigate a single-column convection model, which is able to find the equilibrium structure and heat transport of an icy world ocean. We explore the heat transport through the ocean subject to a variety of assumptions about ocean salinity and seafloor heat and salt flux. We resolve the paradox posed by Vance and Brown (2004): warm salty MgSO4 brine emitted by a seafloor hydrothermal system may be positively buoyant at the seafloor, but become negatively buoyant (sinking) at lower pressure. How does heat escape the ocean, if it cannot be transported by convection? Second, we add MgSO4 dynamics to a full 3-D time-dependent general circulation model (the MIT GCM), which is able to simulate both the global-scale circulation of the world's ocean and investigate the highly turbulent dynamics of buoyant hydrothermal systems. We ask, "Are buoyancy-driven flows in a MgSO4 brine ocean significantly different than similarly-driven flows in terrestrial seawater?"

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.

Convective heat transfer from a pulsating radial jet reattachment (PRJR) nozzle

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

Pak, J.Y.; James, D.L.; Parameswaran, S.

1999-07-01

Impinging jets of fluid have been used to cool, heat or dry surfaces in many industries including high temperature gas turbines, paper and glass manufacturing, textile drying, and electronic components. Jets may be broadly classified as either inline or radial. Inline jets typically have some type of circular or planer opening through which the fluid exits. The circular opening may be converging, well rounded, or of the same diameter as the nozzle or tube through which the fluid is delivered. Here, a numerical investigation for air exiting a Pulsating Radial Jet Reattachment (PRJR) nozzle was performed with various flow andmore » geometric conditions. The transient ensemble averaged Navier-Stokes equation with the standard {kappa}-{epsilon} turbulence model and the standard transient turbulent energy equation were solved to predict the velocity, pressure, and temperature distributions as a function of the pulsation rate, nondimensionalized nozzle-to-plate spacing, amplitude ratio, exit angle and gap Reynolds number. Sinusoidal profile, square and triangular pulsation profiles were simulated to determine the effect on the convective heat transfer during pulsation of nozzle. Grid movement is coupled to the flow field in a manner by a grid convection. Calculated reattachment radii for various conditions correlated well with previously obtained experimental results. Calculated convective heat transfer coefficients and surface pressure profiles for various geometric and flow conditions were compared with experimental results. Convective heat transfer coefficient calculations matched the experimental values very well outside the reattachment regions and underpredicted the convective heat transfer data underneath the nozzle in the dead water region and on the reattachment radius.« less

Heat capacity and thermodynamic properties for coesite and jadeite, reexamination of the quartz-coesite equilibrium boundary

USGS Publications Warehouse

Hemingway, B.S.; Bohlen, S.R.; Hankins, W.B.; Westrum, E.F.; Kuskov, O.L.

1998-01-01

The heat capacities of synthetic coesite and jadeite were measured between about 15 and 850 K by adiabatic and differential scanning calorimetry. The experimental data were smoothed and estimates were made of heat capacities to 1800 K. The following equations represent our estimate of the heat capacities of coesite and jadeite between 298.15 and 1800 K: [see original article for formula]. Tables of thermodynamic values for coesite and jadeite to 1800 K are presented. The entropies of coesite and jadeite are 40.38 ?? 0.12 and 136.5 ?? 0.32 J/(mol.K), respectively, at 298.15 K. The entropy for coesite derived here confirms the value published earlier by Holm et al. (1967). We have derived an equation to describe the quartz-coesite boundary over the temperature range of 600 to 1500 K, P(GPa) = 1.76 + 0.001T(K). Our results are in agreement with the enthalpy of transition reported by Akaogi and Navrotsky (1984) and yield -907.6 ?? 1.4 kJ/mol for the enthalpy of formation of coesite from the elements at 298.15 K and 1 bar, in agreement with the value recommended by CODATA (Khodakovsky et al. 1995). Several sources of uncertainty remain unacceptably high, including: the heat capacities of coesite at temperatures above about 1000 K; the heat capacities and volumetric properties of ?? quartz at higher pressures and at temperatures above 844 K; the pressure corrections for the piston cylinder apparatus used to determine the quartz-coesite equilibrium boundary.

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules

1999-01-01

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Heat and Mass Transfer Analysis of MHD Nanofluid Flow with Radiative Heat Effects in the Presence of Spherical Au-Metallic Nanoparticles

NASA Astrophysics Data System (ADS)

Qureshi, M. Zubair Akbar; Rubbab, Qammar; Irshad, Saadia; Ahmad, Salman; Aqeel, M.

2016-10-01

Energy generation is currently a serious concern in the progress of human civilization. In this regard, solar energy is considered as a significant source of renewable energy. The purpose of the study is to establish a thermal energy model in the presence of spherical Au-metallic nanoparticles. It is numerical work which studies unsteady magnetohydrodynamic (MHD) nanofluid flow through porous disks with heat and mass transfer aspects. Shaped factor of nanoparticles is investigated using small values of the permeable Reynolds number. In order to scrutinize variation of thermal radiation effects, a dimensionless Brinkman number is introduced. The results point out that heat transfer significantly escalates with the increase of Brinkman number. Partial differential equations that govern this study are reduced into nonlinear ordinary differential equations by means of similarity transformations. Then using a shooting technique, a numerical solution of these equations is constructed. Radiative effects on temperature and mass concentration are quite opposite. Heat transfer increases in the presence of spherical Au-metallic nanoparticles.

Heat and Mass Transfer Analysis of MHD Nanofluid Flow with Radiative Heat Effects in the Presence of Spherical Au-Metallic Nanoparticles.

PubMed

Qureshi, M Zubair Akbar; Rubbab, Qammar; Irshad, Saadia; Ahmad, Salman; Aqeel, M

2016-12-01

Energy generation is currently a serious concern in the progress of human civilization. In this regard, solar energy is considered as a significant source of renewable energy. The purpose of the study is to establish a thermal energy model in the presence of spherical Au-metallic nanoparticles. It is numerical work which studies unsteady magnetohydrodynamic (MHD) nanofluid flow through porous disks with heat and mass transfer aspects. Shaped factor of nanoparticles is investigated using small values of the permeable Reynolds number. In order to scrutinize variation of thermal radiation effects, a dimensionless Brinkman number is introduced. The results point out that heat transfer significantly escalates with the increase of Brinkman number. Partial differential equations that govern this study are reduced into nonlinear ordinary differential equations by means of similarity transformations. Then using a shooting technique, a numerical solution of these equations is constructed. Radiative effects on temperature and mass concentration are quite opposite. Heat transfer increases in the presence of spherical Au-metallic nanoparticles.

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.

Effectiveness of a multi-channel volumetric air receiver for a solar power tower

NASA Astrophysics Data System (ADS)

Jung, Eui Guk; Boo, Joon Hong; Kang, Yong Heak; Kim, Nak Hoon

2013-08-01

In this study, the heat transfer performance of a multi-channel volumetric air receiver for a solar power tower was numerically analyzed. The governing equations, including the solar radiation heat flux, conduction, convection and radiation heat transfer for a single channel, were solved on the basis of valid related references and a methodology that can predict the temperature distribution of the receiver wall and the heat transfer fluid for specific dimensions and input conditions. Furthermore, a mathematical model of the effectiveness of the receiver was derived from an analysis of the temperature profiles of the wall and the heat transfer fluid. The receiver effectiveness as an appropriate criterion to assess economic feasibility regarding geometric size was investigated, as it would be applied to the design process of the receiver. The main parameters for the thermal performance simulations described in this paper are the air mass flow rate, receiver length and the influence of these parameters on the heat transfer performance from the viewpoint of receiver efficiency and effectiveness.

Application of nonlinear regression in the development of a wide range formulation for HCFC-22

NASA Astrophysics Data System (ADS)

Kamei, A.; Beyerlein, S. W.; Jacobsen, R. T.

1995-09-01

An equation of state has been developed for HCFC-22 for temperatures from the triple point (115.73 K) to 550 K, at pressures up to 60 MPa. Based on comparisons between experimental data and calculated properties, the accuracy of the wide-range equation of state is ±0.1% in density, ±0.3% in speed of sound, and ±1.0% in isobaric heat capacity, except in the critical region. Nonlinear fitting techniques were used to fit a liquid equation of state based on P-ρ-T, speed of sound, and isobaric heat capacity data. Properties calculated from the liquid equation of state were then used to expand the range of validity of the wide range equation of state for HCFC-22.

Maintenance of Austral Summertime Upper-Tropospheric Circulation over Tropical South America: The Bolivian High-Nordeste Low System.

NASA Astrophysics Data System (ADS)

Chen, Tsing-Chang; Weng, Shu-Ping; Schubert, Siegfried

1999-07-01

Using the NASA/GEOS reanalysis data for 1980-95, the austral-summer stationary eddies in the tropical-subtropical Southern Hemisphere are examined in two wave regimes: long and short wave (wave 1 and waves 2-6, respectively). The basic structure of the Bolivian high-Nordeste low (BH-NL) system is formed by a short-wave train across South America but modulated by the long-wave regime. The short-wave train exhibits a monsoonlike vertical phase reversal in the midtroposphere and a quarter-wave phase shift relative to the divergent circulation. As inferred from (a) the spatial relationship between the streamfunction and velocity potential and (b) the structure of the divergent circulation, the short-wave train forming the BH-NL system is maintained by South American local heating and remote African heating, while the long-wave regime is maintained by western tropical Pacific heating.The maintenance of the stationary waves in the two wave regimes is further illustrated by a simple diagnostic scheme that includes the velocity-potential maintenance equation (which links velocity potential and diabatic heating) and the streamfunction budget (which is the inverse Laplacian transform of the vorticity equation). Some simple relationships between streamfunction and velocity potential for both wave regimes are established to substantiate the links between diabatic heating and streamfunction; of particular interest is a Sverdrup balance in the short-wave regime. This simplified vorticity equation explains the vertical structure of the short-wave train associated with the BH-NL system and its spatial relationship with the divergent circulation.Based upon the diagnostic analysis of its maintenance a simple forced barotropic model is adopted to simulate the BH-NL system with idealized forcings, which imitates the real 200-mb divergence centers over South America, Africa, and the tropical Pacific. Numerical simulations demonstrate that the formation of the BH-NL system is affected not only by the African remote forcing, but also by the tropical Pacific forcing.

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

Optimal Design of a Thermoelectric Cooling/Heating System for Car Seat Climate Control (CSCC)

NASA Astrophysics Data System (ADS)

Elarusi, Abdulmunaem; Attar, Alaa; Lee, Hosung

2017-04-01

In the present work, the optimum design of thermoelectric car seat climate control (CSCC) is studied analytically in an attempt to achieve high system efficiency. Optimal design of a thermoelectric device (element length, cross-section area and number of thermocouples) is carried out using our newly developed optimization method based on the ideal thermoelectric equations and dimensional analysis to improve the performance of the thermoelectric device in terms of the heating/cooling power and the coefficient of performance (COP). Then, a new innovative system design is introduced which also includes the optimum input current for the initial (transient) startup warming and cooling before the car heating ventilation and air conditioner (HVAC) is active in the cabin. The air-to-air heat exchanger's configuration was taken into account to investigate the optimal design of the CSCC.

New developments in laser-heated diamond anvil cell with in situ synchrotron x-ray diffraction at High Pressure Collaborative Access Team

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

Meng, Yue; Hrubiak, Rostislav; Rod, Eric

An overview of the in situ laser heating system at the High Pressure Collaborative Access Team, with emphasis on newly developed capabilities, is presented. Since its establishment at the beamline 16-ID-B a decade ago, laser-heated diamond anvil cell coupled with in situ synchrotron x-ray diffraction has been widely used for studying the structural properties of materials under simultaneous high pressure and high temperature conditions. Recent developments in both continuous-wave and modulated heating techniques have been focusing on resolving technical issues of the most challenging research areas. Furthermore, the new capabilities have demonstrated clear benefits and provide new opportunities in researchmore » areas including high-pressure melting, pressure-temperature-volume equations of state, chemical reaction, and time resolved studies.« less

New developments in laser-heated diamond anvil cell with in situ synchrotron x-ray diffraction at High Pressure Collaborative Access Team

DOE PAGES

Meng, Yue; Hrubiak, Rostislav; Rod, Eric; ...

2015-07-17

An overview of the in situ laser heating system at the High Pressure Collaborative Access Team, with emphasis on newly developed capabilities, is presented. Since its establishment at the beamline 16-ID-B a decade ago, laser-heated diamond anvil cell coupled with in situ synchrotron x-ray diffraction has been widely used for studying the structural properties of materials under simultaneous high pressure and high temperature conditions. Recent developments in both continuous-wave and modulated heating techniques have been focusing on resolving technical issues of the most challenging research areas. Furthermore, the new capabilities have demonstrated clear benefits and provide new opportunities in researchmore » areas including high-pressure melting, pressure-temperature-volume equations of state, chemical reaction, and time resolved studies.« less

New developments in laser-heated diamond anvil cell with in situ synchrotron x-ray diffraction at High Pressure Collaborative Access Team

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

Meng, Yue; Hrubiak, Rostislav; Rod, Eric

An overview of the in situ laser heating system at the High Pressure Collaborative Access Team, with emphasis on newly developed capabilities, is presented. Since its establishment at the beamline 16-ID-B a decade ago, laser-heated diamond anvil cell coupled with in situ synchrotron x-ray diffraction has been widely used for studying the structural properties of materials under simultaneous high pressure and high temperature conditions. Recent developments in both continuous-wave and modulated heating techniques have been focusing on resolving technical issues of the most challenging research areas. The new capabilities have demonstrated clear benefits and provide new opportunities in research areasmore » including high-pressure melting, pressure-temperature-volume equations of state, chemical reaction, and time resolved studies.« less

Ergodicity of the Stochastic Nosé-Hoover Heat Bath

NASA Astrophysics Data System (ADS)

Wei Chung Lo,; Baowen Li,

2010-07-01

We numerically study the ergodicity of the stochastic Nosé-Hoover heat bath whose formalism is based on the Markovian approximation for the Nosé-Hoover equation [J. Phys. Soc. Jpn. 77 (2008) 103001]. The approximation leads to a Langevin-like equation driven by a fluctuating dissipative force and multiplicative Gaussian white noise. The steady state solution of the associated Fokker-Planck equation is the canonical distribution. We investigate the dynamics of this method for the case of (i) free particle, (ii) nonlinear oscillators and (iii) lattice chains. We derive the Fokker-Planck equation for the free particle and present approximate analytical solution for the stationary distribution in the context of the Markovian approximation. Numerical simulation results for nonlinear oscillators show that this method results in a Gaussian distribution for the particles velocity. We also employ the method as heat baths to study nonequilibrium heat flow in one-dimensional Fermi-Pasta-Ulam (FPU-β) and Frenkel-Kontorova (FK) lattices. The establishment of well-defined temperature profiles are observed only when the lattice size is large. Our results provide numerical justification for such Markovian approximation for classical single- and many-body systems.

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

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.

Modeling nuclear processes by Simulink

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

Rashid, Nahrul Khair Alang Md, E-mail: nahrul@iium.edu.my

2015-04-29

Modelling and simulation are essential parts in the study of dynamic systems behaviours. In nuclear engineering, modelling and simulation are important to assess the expected results of an experiment before the actual experiment is conducted or in the design of nuclear facilities. In education, modelling can give insight into the dynamic of systems and processes. Most nuclear processes can be described by ordinary or partial differential equations. Efforts expended to solve the equations using analytical or numerical solutions consume time and distract attention from the objectives of modelling itself. This paper presents the use of Simulink, a MATLAB toolbox softwaremore » that is widely used in control engineering, as a modelling platform for the study of nuclear processes including nuclear reactor behaviours. Starting from the describing equations, Simulink models for heat transfer, radionuclide decay process, delayed neutrons effect, reactor point kinetic equations with delayed neutron groups, and the effect of temperature feedback are used as examples.« less

The effect of atmospheric diabatic heating on low-frequency oscillations

NASA Astrophysics Data System (ADS)

Yen, Ming-Cheng

A diagnostic scheme is devised to illustrate a chain relationship between diabatic heating and planetary-scale divergent and rotational circulations. The scheme consists of the velocity-potential maintenance equation, which relates diabatic heating and velocity potential, and the streamfunction budget equation, which depicts the streamfunction tendency caused by the imbalance between streamfunction tendencies induced by vorticity advection and source. The proposed scheme is employed to examine the effect of tropical diabatic heating on the annual variation of subtropical jet streams. It was found that annual variations of both tropical diabatic heating and planetary-scale divergent circulation exhibit an annual in-phase seesaw oscillation between the winter and summer hemispheres. The annual variation of subtropical jet streams is caused by the adjustment of atmospheric rotational flow through planetary-scale divergent circulation in response to the annual cycle of tropical diabatic heating.

Effect of Cattaneo-Christov heat flux on Jeffrey fluid flow with variable thermal conductivity

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Javed, Mehwish; Imtiaz, Maria; Alsaedi, Ahmed

2018-03-01

This paper presents the study of Jeffrey fluid flow by a rotating disk with variable thickness. Energy equation is constructed by using Cattaneo-Christov heat flux model with variable thermal conductivity. A system of equations governing the model is obtained by applying boundary layer approximation. Resulting nonlinear partial differential system is transformed to ordinary differential system. Homotopy concept leads to the convergent solutions development. Graphical analysis for velocities and temperature is made to examine the influence of different involved parameters. Thermal relaxation time parameter signifies that temperature for Fourier's heat law is more than Cattaneo-Christov heat flux. A constitutional analysis is made for skin friction coefficient and heat transfer rate. Effects of Prandtl number on temperature distribution and heat transfer rate are scrutinized. It is observed that larger Reynolds number gives illustrious temperature distribution.

Effect of thermal radiation and suction on convective heat transfer of nanofluid along a wedge in the presence of heat generation/absorption

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

Kasmani, Ruhaila Md; Bhuvaneswari, M.; Sivasankaran, S.

2015-10-22

An analysis is presented to find the effects of thermal radiation and heat generation/absorption on convection heat transfer of nanofluid past a wedge in the presence of wall suction. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The resulting system is solved numerically using a fourth-order Runge–Kutta method with shooting technique. Numerical computations are carried out for different values of dimensionless parameters to predict the effects of wedge angle, thermophoresis, Brownian motion, heat generation/absorption, thermal radiation and suction. It is found that the temperature increases significantly when the value of themore » heat generation/absorption parameter increases. But the opposite observation is found for the effect of thermal radiation.« less

A Radiation Transfer Solver for Athena Using Short Characteristics

NASA Astrophysics Data System (ADS)

Davis, Shane W.; Stone, James M.; Jiang, Yan-Fei

2012-03-01

We describe the implementation of a module for the Athena magnetohydrodynamics (MHD) code that solves the time-independent, multi-frequency radiative transfer (RT) equation on multidimensional Cartesian simulation domains, including scattering and non-local thermodynamic equilibrium (LTE) effects. The module is based on well known and well tested algorithms developed for modeling stellar atmospheres, including the method of short characteristics to solve the RT equation, accelerated Lambda iteration to handle scattering and non-LTE effects, and parallelization via domain decomposition. The module serves several purposes: it can be used to generate spectra and images, to compute a variable Eddington tensor (VET) for full radiation MHD simulations, and to calculate the heating and cooling source terms in the MHD equations in flows where radiation pressure is small compared with gas pressure. For the latter case, the module is combined with the standard MHD integrators using operator splitting: we describe this approach in detail, including a new constraint on the time step for stability due to radiation diffusion modes. Implementation of the VET method for radiation pressure dominated flows is described in a companion paper. We present results from a suite of test problems for both the RT solver itself and for dynamical problems that include radiative heating and cooling. These tests demonstrate that the radiative transfer solution is accurate and confirm that the operator split method is stable, convergent, and efficient for problems of interest. We demonstrate there is no need to adopt ad hoc assumptions of questionable accuracy to solve RT problems in concert with MHD: the computational cost for our general-purpose module for simple (e.g., LTE gray) problems can be comparable to or less than a single time step of Athena's MHD integrators, and only few times more expensive than that for more general (non-LTE) problems.

Evaluation of 11 equations for determining evaporation for a small lake in the North Central United States

USGS Publications Warehouse

Winter, Thomas C.; Rosenberry, Donald O.; Sturrock, A.M.

1995-01-01

Eleven equations for calculating evaporation were compared with evaporation determined by the energy budget method for Williams Lake, Minnesota. Data were obtained from instruments on a raft, on land near the lake, and at a weather station 60 km south of the lake. The comparisons were based on monthly values for the open-water periods of 5 years, a total of 22 months. A modified DeBruin-Keijman, Priestley-Taylor, and a modified Penman equation resulted in monthly evaporation values that agreed most closely with energy budget values. To use these equations, net radiation, air temperature, wind speed, and relative humidity need to be measured near the lake. In addition, thermal surveys need to be made to determine change in heat stored in the lake. If data from distant climate stations are the only data available, and they include solar radiation, the Jensen-Haise and Makkink equations resulted in monthly evaporation values that agreed reasonably well with energy budget values.

Detailed Modeling and Irreversible Transfer Process Analysis of a Multi-Element Thermoelectric Generator System

NASA Astrophysics Data System (ADS)

Xiao, Heng; Gou, Xiaolong; Yang, Suwen

2011-05-01

Thermoelectric (TE) power generation technology, due to its several advantages, is becoming a noteworthy research direction. Many researchers conduct their performance analysis and optimization of TE devices and related applications based on the generalized thermoelectric energy balance equations. These generalized TE equations involve the internal irreversibility of Joule heating inside the thermoelectric device and heat leakage through the thermoelectric couple leg. However, it is assumed that the thermoelectric generator (TEG) is thermally isolated from the surroundings except for the heat flows at the cold and hot junctions. Since the thermoelectric generator is a multi-element device in practice, being composed of many fundamental TE couple legs, the effect of heat transfer between the TE couple leg and the ambient environment is not negligible. In this paper, based on basic theories of thermoelectric power generation and thermal science, detailed modeling of a thermoelectric generator taking account of the phenomenon of energy loss from the TE couple leg is reported. The revised generalized thermoelectric energy balance equations considering the effect of heat transfer between the TE couple leg and the ambient environment have been derived. Furthermore, characteristics of a multi-element thermoelectric generator with irreversibility have been investigated on the basis of the new derived TE equations. In the present investigation, second-law-based thermodynamic analysis (exergy analysis) has been applied to the irreversible heat transfer process in particular. It is found that the existence of the irreversible heat convection process causes a large loss of heat exergy in the TEG system, and using thermoelectric generators for low-grade waste heat recovery has promising potential. The results of irreversibility analysis, especially irreversible effects on generator system performance, based on the system model established in detail have guiding significance for the development and application of thermoelectric generators, particularly for the design and optimization of TE modules.

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Thermal boundary layer due to sudden heating of fluid

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

Kurkal, K.R.; Munukutla, S.

This paper proposes to solve computationally the heat-transfer problems (introduced by Munukutla and Venkataraman, 1988) related to a closed-cycle pulsed high-power laser flow loop. The continuity and the momentum equations as well as the unsteady energy equation are solved using the Keller-Box method. The solutions were compared with the steady-state solutions at large times, and the comparison was found to be excellent. Empirical formulas are proposed for calculating the time-dependent boundary-layer thickness and mass-heat transfer, that can be used by laser flow loop designers. 6 refs.

Thermal boundary layer due to sudden heating of fluid

NASA Astrophysics Data System (ADS)

Kurkal, K. R.; Munukutla, S.

1989-10-01

This paper proposes to solve computationally the heat-transfer problems (introduced by Munukutla and Venkataraman, 1988) related to a closed-cycle pulsed high-power laser flow loop. The continuity and the momentum equations as well as the unsteady energy equation are solved using the Keller-Box method. The solutions were compared with the steady-state solutions at large times, and the comparison was found to be excellent. Empirical formulas are proposed for calculating the time-dependent boundary-layer thickness and mass-heat transfer, that can be used by laser flow loop designers.

Computational simulation of laser heat processing of materials

NASA Astrophysics Data System (ADS)

Shankar, Vijaya; Gnanamuthu, Daniel

1987-04-01

A computational model simulating the laser heat treatment of AISI 4140 steel plates with a CW CO2 laser beam has been developed on the basis of the three-dimensional, time-dependent heat equation (subject to the appropriate boundary conditions). The solution method is based on Newton iteration applied to a triple-approximate factorized form of the equation. The method is implicit and time-accurate; the maintenance of time-accuracy in the numerical formulation is noted to be critical for the simulation of finite length workpieces with a finite laser beam dwell time.

FRAGMENTATION AND EVOLUTION OF MOLECULAR CLOUDS. II. THE EFFECT OF DUST HEATING

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

Urban, Andrea; Evans, Neal J.; Martel, Hugo

2010-02-20

We investigate the effect of heating by luminosity sources in a simulation of clustered star formation. Our heating method involves a simplified continuum radiative transfer method that calculates the dust temperature. The gas temperature is set by the dust temperature. We present the results of four simulations; two simulations assume an isothermal equation of state and the two other simulations include dust heating. We investigate two mass regimes, i.e., 84 M{sub sun} and 671 M{sub sun}, using these two different energetics algorithms. The mass functions for the isothermal simulations and simulations that include dust heating are drastically different. In themore » isothermal simulation, we do not form any objects with masses above 1 M{sub sun}. However, the simulation with dust heating, while missing some of the low-mass objects, forms high-mass objects ({approx}20 M{sub sun}) which have a distribution similar to the Salpeter initial mass function. The envelope density profiles around the stars formed in our simulation match observed values around isolated, low-mass star-forming cores. We find the accretion rates to be highly variable and, on average, increasing with final stellar mass. By including radiative feedback from stars in a cluster-scale simulation, we have determined that it is a very important effect which drastically affects the mass function and yields important insights into the formation of massive stars.« less

The effect of latent heat release on synoptic-to-planetary wave interactions and its implication for satellite observations: Theoretical modeling

NASA Technical Reports Server (NTRS)

Branscome, Lee E.; Bleck, Rainer; Obrien, Enda

1990-01-01

The project objectives are to develop process models to investigate the interaction of planetary and synoptic-scale waves including the effects of latent heat release (precipitation), nonlinear dynamics, physical and boundary-layer processes, and large-scale topography; to determine the importance of latent heat release for temporal variability and time-mean behavior of planetary and synoptic-scale waves; to compare the model results with available observations of planetary and synoptic wave variability; and to assess the implications of the results for monitoring precipitation in oceanic-storm tracks by satellite observing systems. Researchers have utilized two different models for this project: a two-level quasi-geostrophic model to study intraseasonal variability, anomalous circulations and the seasonal cycle, and a 10-level, multi-wave primitive equation model to validate the two-level Q-G model and examine effects of convection, surface processes, and spherical geometry. It explicitly resolves several planetary and synoptic waves and includes specific humidity (as a predicted variable), moist convection, and large-scale precipitation. In the past year researchers have concentrated on experiments with the multi-level primitive equation model. The dynamical part of that model is similar to the spectral model used by the National Meteorological Center for medium-range forecasts. The model includes parameterizations of large-scale condensation and moist convection. To test the validity of results regarding the influence of convective precipitation, researchers can use either one of two different convective schemes in the model, a Kuo convective scheme or a modified Arakawa-Schubert scheme which includes downdrafts. By choosing one or the other scheme, they can evaluate the impact of the convective parameterization on the circulation. In the past year researchers performed a variety of initial-value experiments with the primitive-equation model. Using initial conditions typical of climatological winter conditions, they examined the behavior of synoptic and planetary waves growing in moist and dry environments. Surface conditions were representative of a zonally averaged ocean. They found that moist convection associated with baroclinic wave development was confined to the subtropics.

Method and Apparatus for the Portable Identification Of Material Thickness And Defects Along Uneven Surfaces Using Spatially Controlled Heat Application

NASA Technical Reports Server (NTRS)

Reilly, Thomas L. (Inventor); Jacobstein, A. Ronald (Inventor); Cramer, K. Elliott (Inventor)

2006-01-01

A method and apparatus for testing a material such as the water-wall tubes in boilers includes the use of a portable thermal line heater having radiation shields to control the amount of thermal radiation that reaches a thermal imager. A procedure corrects for variations in the initial temperature of the material being inspected. A method of calibrating the testing device to determine an equation relating thickness of the material to temperatures created by the thermal line heater uses empirical data derived from tests performed on test specimens for each material type, geometry, density, specific heat, speed at which the line heater is moved across the material and heat intensity.

On the Development of Spray Submodels Based on Droplet Size Moments

NASA Astrophysics Data System (ADS)

Beck, J. C.; Watkins, A. P.

2002-11-01

Hitherto, all polydisperse spray models have been based on discretising the liquid flow field into groups of equally sized droplets. The authors have recently developed a spray model that captures the full polydisperse nature of the spray flow without using droplet size classes (Beck, 2000, Ph.D thesis, UMIST; Beck and Watkins, 2001, Proc. R. Soc. London A). The parameters used to describe the distribution of droplet sizes are the moments of the droplet size distribution function. Transport equations are written for the two moments which represent the liquid mass and surface area, and two more moments representing the sum of drop radii and droplet number are approximated via use of a presumed distribution function, which is allowed to vary in space and time. The velocities to be used in the two transport equations are obtained by defining moment-average quantities and constructing further transport equations for the relevant moment-average velocities. An equation for the energy of the liquid phase and standard gas phase equations, including a k-ɛ turbulence model, are also solved. All the equations are solved in an Eulerian framework using the finite-volume approach, and the phases are coupled through source terms. Effects such as interphase drag, droplet breakup, and droplet-droplet collisions are also captured through the use of source terms. The development of the submodels to describe these effects is the subject of this paper. All the source terms for the hydrodynamics of the spray are derived in this paper in terms of the four moments of the droplet size distribution in order to find the net effect on the whole spray flow field. The development of similar submodels to describe heat and mass transfer effects between the phases is the subject of a further paper (Beck and Watkins, 2001, J. Heat Fluid Flow). The model has been applied to a wide variety of different sprays, including high-pressure diesel sprays, wide-angle solid-cone water sprays, hollow-cone spray s, and evaporating sprays. The comparisons of the results with experimental data show that the model performs well. The interphase drag model, along with the model for the turbulent dispersion of the liquid, produces excellent agreement in the spray penetration results, and the moment-average velocity approach gives good radial distributions of droplet size, showing the capability of the model to predict polydisperse behaviour. Good submodel performance results in droplet breakup, collisions, and evaporation effects (see (Beck and Watkins, 2001, J. Heat Fluid Flow)) also being captured successfully.

Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-03-01

In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

Controlling Thermal Conduction by Graded Materials

NASA Astrophysics Data System (ADS)

Ji, Qin; Huang, Ji-Ping

2018-04-01

Manipulating thermal conductivities are fundamentally important for controlling the conduction of heat at will. Thermal cloaks and concentrators, which have been extensively studied recently, are actually graded materials designed according to coordinate transformation approaches, and their effective thermal conductivity is equal to that of the host medium outside the cloak or concentrator. Here we attempt to investigate a more general problem: what is the effective thermal conductivity of graded materials? In particular, we perform a first-principles approach to the analytic exact results of effective thermal conductivities of materials possessing either power-law or linear gradation profiles. On the other hand, by solving Laplace’s equation, we derive a differential equation for calculating the effective thermal conductivity of a material whose thermal conductivity varies along the radius with arbitrary gradation profiles. The two methods agree with each other for both external and internal heat sources, as confirmed by simulation and experiment. This work provides different methods for designing new thermal metamaterials (including thermal cloaks and concentrators), in order to control or manipulate the transfer of heat. Support by the National Natural Science Foundation of China under Grant No. 11725521, by the Science and Technology Commission of Shanghai Municipality under Grant No. 16ZR1445100

Quantitative Thermochronology

NASA Astrophysics Data System (ADS)

Braun, Jean; van der Beek, Peter; Batt, Geoffrey

2006-05-01

Thermochronology, the study of the thermal history of rocks, enables us to quantify the nature and timing of tectonic processes. Quantitative Thermochronology is a robust review of isotopic ages, and presents a range of numerical modeling techniques to allow the physical implications of isotopic age data to be explored. The authors provide analytical, semi-analytical, and numerical solutions to the heat transfer equation in a range of tectonic settings and under varying boundary conditions. They then illustrate their modeling approach built around a large number of case studies. The benefits of different thermochronological techniques are also described. Computer programs on an accompanying website at www.cambridge.org/9780521830577 are introduced through the text and provide a means of solving the heat transport equation in the deforming Earth to predict the ages of rocks and compare them directly to geological and geochronological data. Several short tutorials, with hints and solutions, are also included. Numerous case studies help geologists to interpret age data and relate it to Earth processes Essential background material to aid understanding and using thermochronological data Provides a thorough treatise on numerical modeling of heat transport in the Earth's crust Supported by a website hosting relevant computer programs and colour slides of figures from the book for use in teaching

Theoretcial studies of solar-pumped lasers

NASA Technical Reports Server (NTRS)

Harries, W. L.; Fong, Z. S.

1984-01-01

A method of pumping a COhZ laser by a hot cavity was demonstrated. The cavity, heated by solar radiation, should increase the efficiency of solar pumped lasers used for energy conversion. Kinetic modeling is used to examine the behavior of such a COhZ laser. The kinetic equations are solved numerically vs. time and, in addition, steady state solutions are obtained analytically. The effect of gas heating filling the lower laser level is included. The output power and laser efficiency are obtained as functions of black body temperature and gas ratios (COhZ-He-Ar) and pressures. The values are compared with experimental results.

Advances in modelling of biomimetic fluid flow at different scales

PubMed Central

2011-01-01

The biomimetic flow at different scales has been discussed at length. The need of looking into the biological surfaces and morphologies and both geometrical and physical similarities to imitate the technological products and processes has been emphasized. The complex fluid flow and heat transfer problems, the fluid-interface and the physics involved at multiscale and macro-, meso-, micro- and nano-scales have been discussed. The flow and heat transfer simulation is done by various CFD solvers including Navier-Stokes and energy equations, lattice Boltzmann method and molecular dynamics method. Combined continuum-molecular dynamics method is also reviewed. PMID:21711847

Collisionless solar wind protons: A comparison of kinetic and hydrodynamic descriptions

NASA Technical Reports Server (NTRS)

Leer, E.; Holzer, T. E.

1971-01-01

Kinetic and hydrodynamic descriptions of a collisionless solar wind proton gas are compared. Heat conduction and viscosity are neglected in the hydrodynamic formulation but automatically included in the kinetic formulation. The results of the two models are very nearly the same, indicating that heat conduction and viscosity are not important in the solar wind proton gas beyond about 0.1 AU. It is concluded that the hydrodynamic equations provide a valid description of the collisionless solar wind protons, and hence that future models of the quiet solar wind should be based on a hydrodynamic formulation.

Review and status of heat-transfer technology for internal passages of air-cooled turbine blades

NASA Technical Reports Server (NTRS)

Yeh, F. C.; Stepka, F. S.

1984-01-01

Selected literature on heat-transfer and pressure losses for airflow through passages for several cooling methods generally applicable to gas turbine blades is reviewed. Some useful correlating equations are highlighted. The status of turbine-blade internal air-cooling technology for both nonrotating and rotating blades is discussed and the areas where further research is needed are indicated. The cooling methods considered include convection cooling in passages, impingement cooling at the leading edge and at the midchord, and convection cooling in passages, augmented by pin fins and the use of roughened internal walls.

Large eddy simulation of rotating turbulent flows and heat transfer by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Liou, Tong-Miin; Wang, Chun-Sheng

2018-01-01

Due to its advantage in parallel efficiency and wall treatment over conventional Navier-Stokes equation-based methods, the lattice Boltzmann method (LBM) has emerged as an efficient tool in simulating turbulent heat and fluid flows. To properly simulate the rotating turbulent flow and heat transfer, which plays a pivotal role in tremendous engineering devices such as gas turbines, wind turbines, centrifugal compressors, and rotary machines, the lattice Boltzmann equations must be reformulated in a rotating coordinate. In this study, a single-rotating reference frame (SRF) formulation of the Boltzmann equations is newly proposed combined with a subgrid scale model for the large eddy simulation of rotating turbulent flows and heat transfer. The subgrid scale closure is modeled by a shear-improved Smagorinsky model. Since the strain rates are also locally determined by the non-equilibrium part of the distribution function, the calculation process is entirely local. The pressure-driven turbulent channel flow with spanwise rotation and heat transfer is used for validating the approach. The Reynolds number characterized by the friction velocity and channel half height is fixed at 194, whereas the rotation number in terms of the friction velocity and channel height ranges from 0 to 3.0. A working fluid of air is chosen, which corresponds to a Prandtl number of 0.71. Calculated results are demonstrated in terms of mean velocity, Reynolds stress, root mean square (RMS) velocity fluctuations, mean temperature, RMS temperature fluctuations, and turbulent heat flux. Good agreement is found between the present LBM predictions and previous direct numerical simulation data obtained by solving the conventional Navier-Stokes equations, which confirms the capability of the proposed SRF LBM and subgrid scale relaxation time formulation for the computation of rotating turbulent flows and heat transfer.

Formation of the Aerosol of Space Origin in Earth's Atmosphere

NASA Technical Reports Server (NTRS)

Kozak, P. M.; Kruchynenko, V. G.

2011-01-01

The problem of formation of the aerosol of space origin in Earth s atmosphere is examined. Meteoroids of the mass range of 10-18-10-8 g are considered as a source of its origin. The lower bound of the mass range is chosen according to the data presented in literature, the upper bound is determined in accordance with the theory of Whipple s micrometeorites. Basing on the classical equations of deceleration and heating for small meteor bodies we have determined the maximal temperatures of the particles, and altitudes at which they reach critically low velocities, which can be called as velocities of stopping . As a condition for the transformation of a space particle into an aerosol one we have used the condition of non-reaching melting temperature of the meteoroid. The simplified equation of deceleration without earth gravity and barometric formula for the atmosphere density are used. In the equation of heat balance the energy loss for heating is neglected. The analytical solution of the simplified equations is used for the analysis.

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

Fluid flow and heat transfer characteristics of an enclosure with fin as a top cover of a solar collector

NASA Astrophysics Data System (ADS)

Ambarita, H.; Ronowikarto, A. D.; Siregar, R. E. T.; Setyawan, E. Y.

2018-03-01

To reduce heat loses in a flat plate solar collector, double glasses cover is employed. Several studies show that the heat loss from the glass cover is still very significant in comparison with other losses. Here, double glasses cover with attached fins is proposed. In the present work, the fluid flow and heat transfer characteristics of the enclosure between the double glass cover are investigated numerically. The objective is to examine the effect of the fin to the heat transfer rate of the cover. Two-dimensional governing equations are developed. The governing equations and the boundary conditions are solved using commercial Computational Fluid Dynamics code. The fluid flow and heat transfer characteristics are plotted, and numerical results are compared with empirical correlation. The results show that the presence of the fin strongly affects the fluid flow and heat transfer characteristics. The fin can reduce the heat transfer rate up to 22.42% in comparison with double glasses cover without fins.

[Penetration of external thermal perturbations into homeothermic organisms, part I (author's transl)].

PubMed

Theves, B

1978-03-20

The general importance of the mean surface curvature for heat conduction problems is explained and a special symmetry with constant mean curvature on the isothermal surfaces is defined. The applicability for the body shapes of homeothermic organisms is demonstrated and the partial differential equation of heat conduction for this case is derived. The definition: heat release = real heat production + convective pseudoproduction eliminates the term of convective heat transfer through the blood stream and allows the reduction to a mere heat conduction problem. Formulas for the heat loss to the environment and for steady state temperature profiles are given. In case of sudden change of heat loss the partial differential equation is solved and a formula is derived, using dimensionless coordinates of time and distance. The mean surface curvature has strongest influence to the interior temperature field. The solution shows clearly the importance of thermal inertia of the homeothermic organism, for the external temperature wave penetrates into the body with a long phase displacement in time.

Theoretical and computational analyses of LNG evaporator

NASA Astrophysics Data System (ADS)

Chidambaram, Palani Kumar; Jo, Yang Myung; Kim, Heuy Dong

2017-04-01

Theoretical and numerical analysis on the fluid flow and heat transfer inside a LNG evaporator is conducted in this work. Methane is used instead of LNG as the operating fluid. This is because; methane constitutes over 80% of natural gas. The analytical calculations are performed using simple mass and energy balance equations. The analytical calculations are made to assess the pressure and temperature variations in the steam tube. Multiphase numerical simulations are performed by solving the governing equations (basic flow equations of continuity, momentum and energy equations) in a portion of the evaporator domain consisting of a single steam pipe. The flow equations are solved along with equations of species transport. Multiphase modeling is incorporated using VOF method. Liquid methane is the primary phase. It vaporizes into the secondary phase gaseous methane. Steam is another secondary phase which flows through the heating coils. Turbulence is modeled by a two equation turbulence model. Both the theoretical and numerical predictions are seen to match well with each other. Further parametric studies are planned based on the current research.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

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

Mishra, Subhash C.; Roy, Hillol K.

2007-04-10

The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The finite volume method (FVM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the FVM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 1-D planar and 2-D rectangular geometries were considered. In order to establish the suitability of the LBM, the energy equations of the two problems were also solved using the FVM of the computational fluid dynamics. The FVM used in the radiative heatmore » transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FVM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the FVM for the radiative information, results were analyzed for the effects of various parameters such as the scattering albedo, the conduction-radiation parameter and the boundary emissivity. The results of the LBM-FVM combination were found to be in excellent agreement with the FVM-FVM combination. The number of iterations and CPU times in both the combinations were found comparable.« less

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.

Microclimatic modeling of the desert in the United Arab Emirates

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

Khalil, A.K.; Abdrabboh, M.A.; Kamel, K.A.

1996-10-01

The present study is concerned with the prediction of the weather parameters in the microclimate layer (less than 2 m above the ground surface) in the desert and sparsely vegetated areas in the United Arab Emirates. A survey was made of the weather data in these regions including solar radiation, wind speed, screen temperatures and relative humidity. Additionally, wind speed data were obtained at heights below two meters and surface albedo was recorded for various soil and vegetation conditions. A survey was also carried out for the different plant species in various areas of the U.A.E. Data on soil andmore » surface temperature were then analyzed. An energy balance model was formulated including incident short- and long-wave length radiation between earth and sky, convective heat transfer to/from earth surface, surface reflection of solar radiation and soil/plant evapotranspiration. An explicit one dimensional finite difference scheme was adapted to solve the resulting algebraic finite difference equations. The equation for surface nodes included thermal radiation as well as convection effects. The heat transfer coefficient was evaluated on the basis of wind speed and surface roughness at the site where the energy balance was set. Theoretical predictions of air and soil temperatures were accordingly compared to experimental measurements in selected sites, where reasonable agreements were observed.« less

Regressed relations for forced convection heat transfer in a direct injection stratified charge rotary engine

NASA Technical Reports Server (NTRS)

Lee, Chi M.; Schock, Harold J.

1988-01-01

Currently, the heat transfer equation used in the rotary combustion engine (RCE) simulation model is taken from piston engine studies. These relations have been empirically developed by the experimental input coming from piston engines whose geometry differs considerably from that of the RCE. The objective of this work was to derive equations to estimate heat transfer coefficients in the combustion chamber of an RCE. This was accomplished by making detailed temperature and pressure measurements in a direct injection stratified charge (DISC) RCE under a range of conditions. For each specific measurement point, the local gas velocity was assumed equal to the local rotor tip speed. Local physical properties of the fluids were then calculated. Two types of correlation equations were derived and are described in this paper. The first correlation expresses the Nusselt number as a function of the Prandtl number, Reynolds number, and characteristic temperature ratio; the second correlation expresses the forced convection heat transfer coefficient as a function of fluid temperature, pressure and velocity.

Effect of nose shape on three-dimensional stagnation region streamlines and heating rates

NASA Technical Reports Server (NTRS)

Hassan, Basil; Dejarnette, Fred R.; Zoby, E. V.

1991-01-01

A new method for calculating the three-dimensional inviscid surface streamlines and streamline metrics using Cartesian coordinates and time as the independent variable of integration has been developed. The technique calculates the streamline from a specified point on the body to a point near the stagnation point by using a prescribed pressure distribution in the Euler equations. The differential equations, which are singular at the stagnation point, are of the two point boundary value problem type. Laminar heating rates are calculated using the axisymmetric analog concept for three-dimensional boundary layers and approximate solutions to the axisymmetric boundary layer equations. Results for elliptic conic forebody geometries show that location of the point of maximum heating depends on the type of conic in the plane of symmetry and the angle of attack, and that this location is in general different from the stagnation point. The new method was found to give smooth predictions of heat transfer in the nose region where previous methods gave oscillatory results.

Double diffusive conjugate heat transfer: Part II

NASA Astrophysics Data System (ADS)

Azeem, Soudagar, Manzoor Elahi M.

2018-05-01

Conjugate heat transfer in porous medium is an important study involved in many practical applications. The current study is aimed to investigate the double diffusive flow in a square porous cavity subjected to left vertical surface heating and right vertical surface cooling respectively along with left and right surfaces maintained at high and low concentration. The three governing equations are converted into algebraic form of equations by applying finite element method and solved in iterative manner. The study is focused to investigate the effect of presence of solid inside the cavity with respect to varying buoyancy ratio. It is found that the local heat and mass transfer rate decreases along the height of cavity.

A numerical study of three-dimensional flame propagation over thin solids in purely forced concurrent flow including gas-phase radiation

NASA Astrophysics Data System (ADS)

Feier, Ioan I., Jr.

The effect of flame radiation on concurrent-flow flame spread over a thin solid sample of finite width in a low-speed wind tunnel is modeled using three-dimensional full Navier-Stokes equations and three-dimensional flame radiation transfer equations. The formulation includes the conservation of mass, momentum, energy, and species: fuel vapor, oxygen, carbon dioxide and water vapor. The SN discrete ordinates method is used to solve the radiation transfer equation with a mean absorption coefficient kappa = Ckappa p, where kappap is the Planck mean absorption coefficient of the gas mixture. The varying parameter C has a value between 0 and 1; C represents the strength of flame radiation. In addition, the solid fuel absorptivity alpha is varied to ascertain the effect of flame radiation heat feedback to the solid. The flow tunnel modeled has a dimension of 10x10x30 cm, the solid fuel has a width of 6-cm with two 1-cm inert strips as edges. Incoming forced flow velocity (5 cm/s) of 21% oxygen is assumed. For comparison with the three-dimensional results, corresponding two-dimensional computations are also performed. Detailed spatial flame profiles, solid surface profiles, and heat fluxes are presented. Increasing the flame radiation strength decreases the flame length. Although flame radiation provides an additional heat transfer mechanism to preheat the solid, it is insufficient to offset the decreased convective heating due to the shorter flame; the net effect is a slower spread rate. The percentage of unreacted fuel vapor that escapes from the flame is under 2%. It is theorized that some of the pyrolyzed fuel vapor diffuses sideway and reacts at the flame edges. A radiative energy balance is analyzed also. Flame radiative feedback to the solid plays a more important role in two-dimensional flames. With high solid fuel absorptivity, a peak in the flame spread rate occurs at an intermediate value of flame radiation strength---due to the competition between two mechanisms: gas-radiation heat loss weakening the flame and the radiative feedback boosting the solid pyrolysis. Two-dimensional calculations suggest that a larger percentage of unreacted fuel vapor can escape from the flame when the flame radiation strength is high.

Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

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

Nataf, J.M.; Winkelmann, F.

We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less

Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

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

Nataf, J.M.; Winkelmann, F.

We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of thesemore » methods to solving the partial differential equations for two-dimensional heat flow is illustrated.« less

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

A Step Towards CO2-Neutral Aviation

NASA Technical Reports Server (NTRS)

Brankovic, Andreja; Ryder, Robert C.; Hendricks, Robert C.; Huber, Marcia L.

2007-01-01

An approximation method for evaluation of the caloric equations used in combustion chemistry simulations is described. The method is applied to generate the equations of specific heat, static enthalpy, and Gibb's free energy for fuel mixtures of interest to gas turbine engine manufacturers. Liquid-phase fuel properties are also derived. The fuels include JP-8, synthetic fuel, and two fuel blends consisting of a mixture of JP-8 and synthetic fuel. The complete set of fuel property equations for both phases are implemented into a computational fluid dynamics (CFD) flow solver database, and multi-phase, reacting flow simulations of a well-tested liquid-fueled combustor are performed. The simulations are a first step in understanding combustion system performance and operational issues when using alternate fuels, at practical engine operating conditions.

Wavelets solution of MHD 3-D fluid flow in the presence of slip and thermal radiation effects

NASA Astrophysics Data System (ADS)

Usman, M.; Zubair, T.; Hamid, M.; Haq, Rizwan Ul; Wang, Wei

2018-02-01

This article is devoted to analyze the magnetic field, slip, and thermal radiations effects on generalized three-dimensional flow, heat, and mass transfer in a channel of lower stretching wall. We supposed two various lateral direction rates for the lower stretching surface of the wall while the upper wall of the channel is subjected to constant injection. Moreover, influence of thermal slip on the temperature profile beside the viscous dissipation and Joule heating is also taken into account. The governing set of partial differential equations of the heat transfer and flow are transformed to nonlinear set of ordinary differential equations (ODEs) by using the compatible similarity transformations. The obtained nonlinear ODE set tackled by means of a new wavelet algorithm. The outcomes obtained via modified Chebyshev wavelet method are compared with Runge-Kutta (order-4). The worthy comparison, error, and convergence analysis shows an excellent agreement. Additionally, the graphical representation for various physical parameters including the skin friction coefficient, velocity, the temperature gradient, and the temperature profiles are plotted and discussed. It is observed that for a fixed value of velocity slip parameter a suitable selection of stretching ratio parameter can be helpful in hastening the heat transfer rate and in reducing the viscous drag over the stretching sheet. Finally, the convergence analysis is performed which endorsing that this proposed method is well efficient.

Computational evaluation of amplitude modulation for enhanced magnetic nanoparticle hyperthermia.

PubMed

Soetaert, Frederik; Dupré, Luc; Ivkov, Robert; Crevecoeur, Guillaume

2015-10-01

Magnetic nanoparticles (MNPs) can interact with alternating magnetic fields (AMFs) to deposit localized energy for hyperthermia treatment of cancer. Hyperthermia is useful in the context of multimodality treatments with radiation or chemotherapy to enhance disease control without increased toxicity. The unique attributes of heat deposition and transfer with MNPs have generated considerable attention and have been the focus of extensive investigations to elucidate mechanisms and optimize performance. Three-dimensional (3D) simulations are often conducted with the finite element method (FEM) using the Pennes' bioheat equation. In the current study, the Pennes' equation was modified to include a thermal damage-dependent perfusion profile to improve model predictions with respect to known physiological responses to tissue heating. A normal distribution of MNPs in a model liver tumor was combined with empirical nanoparticle heating data to calculate tumor temperature distributions and resulting survival fraction of cancer cells. In addition, calculated spatiotemporal temperature changes were compared among magnetic field amplitude modulations of a base 150-kHz sinusoidal waveform, specifically, no modulation, sinusoidal, rectangular, and triangular modulation. Complex relationships were observed between nanoparticle heating and cancer tissue damage when amplitude modulation and damage-related perfusion profiles were varied. These results are tantalizing and motivate further exploration of amplitude modulation as a means to enhance efficiency of and overcome technical challenges associated with magnetic nanoparticle hyperthermia (MNH).

Three-dimensional simulation of beam propagation and heat transfer in static gas Cs DPALs using wave optics and fluid dynamics models

NASA Astrophysics Data System (ADS)

Waichman, Karol; Barmashenko, Boris D.; Rosenwaks, Salman

2017-10-01

Analysis of beam propagation, kinetic and fluid dynamic processes in Cs diode pumped alkali lasers (DPALs), using wave optics model and gasdynamic code, is reported. The analysis is based on a three-dimensional, time-dependent computational fluid dynamics (3D CFD) model. The Navier-Stokes equations for momentum, heat and mass transfer are solved by a commercial Ansys FLUENT solver based on the finite volume discretization technique. The CFD code which solves the gas conservation equations includes effects of natural convection and temperature diffusion of the species in the DPAL mixture. The DPAL kinetic processes in the Cs/He/C2H6 gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 62S1/2, (2) 62P1/2 and (3) 62P3/2. The kinetic processes include absorption due to the 1->3 D2 transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2->1 D1 transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.

Technical geothermal potential of urban subsurface influenced by land surface effects

NASA Astrophysics Data System (ADS)

Rivera, Jaime A.; Blum, Philipp; Bayer, Peter

2016-04-01

Changes in land use are probably one of the most notorious anthropogenic perturbations in urban environments. They significantly change the coupled thermal regime at the ground surface leading in most cases to increased ground surface temperatures (GST). The associated elevated vertical heat fluxes act at different scales and can influence the thermal conditions in several tens of meters in the subsurface. Urban subsurface thus often stores a higher amount of heat than less affected rural surroundings. The stored heat is regarded as a potential source of low-enthalpy geothermal energy to supply the heating energy demands in urban areas. In this work, we explore the technical geothermal potential of urban subsurface via ground coupled heat pumps with borehole heat exchangers (BHE). This is tackled by semi-analytical line-source equations. The commonly used response factors or g-functions are modified to include transient land surface effects. By including this additional source of heat, the new formulation allows to analyse the effect of pre-existing urban warming as well as different exploitation schemes fulfilling standard renewable and sustainable criteria. In our generalized reference scenario, it is demonstrated that energy gains for a single BHE may be up to 40 % when compared to non-urbanized conditions. For a scenario including the interaction of multiple BHEs, results indicate that it would be possible to supply between 6 % and 27 % of the heating demands in Central European urban settlements in a renewable way. The methodology is also applied to a study case of the city of Zurich, Switzerland, where the detailed evolution of land use is available.

Control of ITBs in Fusion Self-Heated Plasmas

NASA Astrophysics Data System (ADS)

Panta, Soma; Newman, David; Terry, Paul; Sanchez, Raul

2015-11-01

Simple dynamical models have been able to capture a remarkable amount of the dynamics of the transport barriers found in many devices, including the often disconnected nature of the electron thermal transport channel sometimes observed in the presence of a standard (``ion channel'') barrier. By including in this rich though simple dynamic transport model an evolution equation for electron fluctuations we have previously investigated the interaction between the formation of the standard ion channel barrier and the somewhat less common electron channel barrier. The electron channel formation and evolution is even more sensitive to the alignment of the various gradients making up the sheared radial electric field then the ion barrier is. Because of this sensitivity and coupling of the barrier dynamics, the dynamic evolution of the fusion self-heating profile can have a significant impact on the barrier location and dynamics. To investigate this, self-heating has been added this model and the impact of the self-heating on the formation and controllability of the various barriers is explored. It has been found that the evolution of the heating profiles can suppress or collapse the electron channel barrier. NBI and RF schemes will be investigated for profile/barrier control.

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.

Non-Markovian Investigation of an Autonomous Quantum Heat Engine

NASA Astrophysics Data System (ADS)

Goyal, Ketan

A systematic study of a quantum heat engine is presented in this thesis. In particular, we study heat conduction through a two-two level composite system, which is then connected to a photon cavity to extract work, forming an autonomous quantum heat engine. The question as to what extent quantum effects such as quantum coherence and correlations impact thermodynamic properties of such a system is addressed. The investigated heat engine has been previously studied using the popular Born-Markovian quantum master equation under weak internal coupling approximation. However, we show that the used approach is quite limited in addressing such problems as it is incapable of correctly accounting for the quantum effects. By using a non-Markovian approach involving hierarchical equations of motion, we show that quantum coherence and correlations between system and environments play a significant role in energy transfer processes of heat conduction and work.

Intuitive Understanding of Solutions of Partially Differential Equations

ERIC Educational Resources Information Center

Kobayashi, Y.

2008-01-01

This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…

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.

Approximate analytical solution for induction heating of solid cylinders

DOE PAGES

Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

2015-10-20

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

Analytical assessment of some characteristic ratios for s-wave superconductors

NASA Astrophysics Data System (ADS)

Gonczarek, Ryszard; Krzyzosiak, Mateusz; Gonczarek, Adam; Jacak, Lucjan

2018-04-01

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ≲ T c are discussed using the method of successive approximations. The equation for the ratio R 1, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R 2, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low- T c superconductors. The prospect of application of the presented model in studies of high- T c superconductors and other superconducting systems of the new generation is also discussed.

Optimal temperature control of tissue embedded with gold nanoparticles for enhanced thermal therapy based on two-energy equation model.

PubMed

Wang, Shen-Ling; Qi, Hong; Ren, Ya-Tao; Chen, Qin; Ruan, Li-Ming

2018-05-01

Thermal therapy is a very promising method for cancer treatment, which can be combined with chemotherapy, radiotherapy and other programs for enhanced cancer treatment. In order to get a better effect of thermal therapy in clinical applications, optimal internal temperature distribution of the tissue embedded with gold nanoparticles (GNPs) for enhanced thermal therapy was investigated in present research. The Monte Carlo method was applied to calculate the heat generation of the tissue embedded with GNPs irradiated by continuous laser. To have a better insight into the physical problem of heat transfer in tissues, the two-energy equation was employed to calculate the temperature distribution of the tissue in the process of GNPs enhanced therapy. The Arrhenius equation was applied to evaluate the degree of permanent thermal damage. A parametric study was performed to investigate the influence factors on the tissue internal temperature distribution, such as incident light intensity, the GNPs volume fraction, the periodic heating and cooling time, and the incident light position. It was found that period heating and cooling strategy can effectively avoid overheating of skin surface and heat damage of healthy tissue. Lower GNPs volume fraction will be better for the heat source distribution. Furthermore, the ring heating strategy is superior to the central heating strategy in the treatment effect. All the analysis provides theoretical guidance for optimal temperature control of tissue embedded with GNP for enhanced thermal therapy. Copyright © 2018 Elsevier Ltd. All rights reserved.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

Heat Source/Sink in a Magneto-Hydrodynamic Non-Newtonian Fluid Flow in a Porous Medium: Dual Solutions.

PubMed

Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna

2016-01-01

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail.

Influence of stem temperature changes on heat pulse sap flux density measurements.

PubMed

Vandegehuchte, Maurits W; Burgess, Stephen S O; Downey, Alec; Steppe, Kathy

2015-04-01

While natural spatial temperature gradients between measurement needles have been thoroughly investigated for continuous heat-based sap flow methods, little attention has been given to how natural changes in stem temperature impact heat pulse-based methods through temporal rather than spatial effects. By modelling the theoretical equation for both an ideal instantaneous pulse and a step pulse and applying a finite element model which included actual needle dimensions and wound effects, the influence of a varying stem temperature on heat pulse-based methods was investigated. It was shown that the heat ratio (HR) method was influenced, while for the compensation heat pulse and Tmax methods changes in stem temperatures of up to 0.002 °C s(-1) did not lead to significantly different results. For the HR method, rising stem temperatures during measurements led to lower heat pulse velocity values, while decreasing stem temperatures led to both higher and lower heat pulse velocities, and to imaginary results for high flows. These errors of up to 40% can easily be prevented by including a temperature correction in the data analysis procedure, calculating the slope of the natural temperature change based on the measured temperatures before application of the heat pulse. Results of a greenhouse and outdoor experiment on Pinus pinea L. show the influence of this correction on low and average sap flux densities. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Using a Divided Bar Apparatus to Measure Thermal Conductivity of Samples of Odd Sizes and Shapes

NASA Astrophysics Data System (ADS)

Crowell, J. "; Gosnold, W. D.

2012-12-01

Standard procedure for measuring thermal conductivity using a divided bar apparatus requires a sample that has the same surface dimensions as the heat sink/source surface in the divided bar. Heat flow is assumed to be constant throughout the column and thermal conductivity (K) is determined by measuring temperatures (T) across the sample and across standard layers and using the basic relationship Ksample=(Kstandard*(ΔT1+ΔT2)/2)/(ΔTsample). Sometimes samples are not large enough or of correct proportions to match the surface of the heat sink/source, however using the equations presented here the thermal conductivity of these samples can still be measured with a divided bar. Measurements were done on the UND Geothermal Laboratories stationary divided bar apparatus (SDB). This SDB has been designed to mimic many in-situ conditions, with a temperature range of -20C to 150C and a pressure range of 0 to 10,000 psi for samples with parallel surfaces and 0 to 3000 psi for samples with non-parallel surfaces. The heat sink/source surfaces are copper disks and have a surface area of 1,772 mm2 (2.74 in2). Layers of polycarbonate 6 mm thick with the same surface area as the copper disks are located in the heat sink and in the heat source as standards. For this study, all samples were prepared from a single piece of 4 inch limestone core. Thermal conductivities were measured for each sample as it was cut successively smaller. The above equation was adjusted to include the thicknesses (Th) of the samples and the standards and the surface areas (A) of the heat sink/source and of the sample Ksample=(Kstandard*Astandard*Thsample*(ΔT1+ΔT3))/(ΔTsample*Asample*2*Thstandard). Measuring the thermal conductivity of samples of multiple sizes, shapes, and thicknesses gave consistent values for samples with surfaces as small as 50% of the heat sink/source surface, regardless of the shape of the sample. Measuring samples with surfaces smaller than 50% of the heat sink/source surface resulted in thermal conductivity values which were too high. The cause of the error with the smaller samples is being examined as is the relationship between the amount of error in the thermal conductivity and the difference in surface areas. As more measurements are made an equation to mathematically correct for the error is being developed on in case a way to physically correct the problem cannot be determined.

Determination of absorption coefficient based on laser beam thermal blooming in gas-filled tube.

PubMed

Hafizi, B; Peñano, J; Fischer, R; DiComo, G; Ting, A

2014-08-01

Thermal blooming of a laser beam propagating in a gas-filled tube is investigated both analytically and experimentally. A self-consistent formulation taking into account heating of the gas and the resultant laser beam spreading (including diffraction) is presented. The heat equation is used to determine the temperature variation while the paraxial wave equation is solved in the eikonal approximation to determine the temporal and spatial variation of the Gaussian laser spot radius, Gouy phase (longitudinal phase delay), and wavefront curvature. The analysis is benchmarked against a thermal blooming experiment in the literature using a CO₂ laser beam propagating in a tube filled with air and propane. New experimental results are presented in which a CW fiber laser (1 μm) propagates in a tube filled with nitrogen and water vapor. By matching laboratory and theoretical results, the absorption coefficient of water vapor is found to agree with calculations using MODTRAN (the MODerate-resolution atmospheric TRANsmission molecular absorption database) and HITRAN (the HIgh-resolution atmospheric TRANsmission molecular absorption database).

Wet cooling towers: rule-of-thumb design and simulation

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

Leeper, Stephen A.

1981-07-01

A survey of wet cooling tower literature was performed to develop a simplified method of cooling tower design and simulation for use in power plant cycle optimization. The theory of heat exchange in wet cooling towers is briefly summarized. The Merkel equation (the fundamental equation of heat transfer in wet cooling towers) is presented and discussed. The cooling tower fill constant (Ka) is defined and values derived. A rule-of-thumb method for the optimized design of cooling towers is presented. The rule-of-thumb design method provides information useful in power plant cycle optimization, including tower dimensions, water consumption rate, exit air temperature,more » power requirements and construction cost. In addition, a method for simulation of cooling tower performance at various operating conditions is presented. This information is also useful in power plant cycle evaluation. Using the information presented, it will be possible to incorporate wet cooling tower design and simulation into a procedure to evaluate and optimize power plant cycles.« less

Vibrational and thermodynamic properties of β-HMX: a first-principles investigation.

PubMed

Wu, Zhongqing; Kalia, Rajiv K; Nakano, Aiichiro; Vashishta, Priya

2011-05-28

Thermodynamic properties of β-HMX crystal are investigated using the quasi-harmonic approximation and density functional theory within the local density approximation (LDA), generalized gradient approximation (GGA), and GGA + empirical van der Waals (vdW) correction. It is found that GGA well describes the thermal expansion coefficient and heat capacity but fails to produce correct bulk modulus and equilibrium volume. The vdW correction improves the bulk modulus and volume, but worsens the thermal expansion coefficient and heat capacity. In contrast, LDA describes all thermodynamic properties with reasonable accuracy, and overall is a good exchange-correlation functional for β-HMX molecular crystal. The results also demonstrate significant contributions of phonons to the equation of state. The static calculation of equilibrium volume for β-HMX differs from the room-temperature value incorporating lattice vibrations by over 5%. Therefore, for molecular crystals, it is essential to include phonon contributions when calculated equation of state is compared with experimental data at ambient condition. © 2011 American Institute of Physics

A Model for coupled heat and moisture transfer in permafrost regions of three rivers source areas, Qinghai, China

NASA Astrophysics Data System (ADS)

Wu, X. L.; Xiang, X. H.; Wang, C. H.; Shao, Q. Q.

2012-04-01

Soil freezing occurs in winter in many parts of the world. The transfer of heat and moisture in freezing and thawing soil is interrelated, and this heat and moisture transport plays an important role in hydrological activity of seasonal frozen region especially for three rivers sources area of China. Soil freezing depth and ice content in frozen zone will significantly influence runoff and groundwater recharge. The purpose of this research is to develop a numerical model to simulate water and heat movement in the soil under freezing and thawing conditions. The basic elements of the model are the heat and water flow equations, which are heat conduction equation and unsaturated soil fluid mass conservation equation. A full-implicit finite volume scheme is used to solve the coupled equations in space. The model is calibrated and verified against the observed moisture and temperature of soil during freezing and thawing period from 2005 to 2007. Different characters of heat and moisture transfer are testified, such as frozen depth, temperature field of 40 cm depth and topsoil moisture content, et al. The model is calibrated and verified against observed value, which indicate that the new model can be used successfully to simulate numerically the coupled heat and mass transfer process in permafrost regions. By simulating the runoff generation process and the driven factors of seasonal changes, the agreement illustrates that the coupled model can be used to describe the local phonemes of hydrologic activities and provide a support to the local Ecosystem services. This research was supported by the National Natural Science Foundation of China (No. 51009045; 40930635; 41001011; 41101018; 51079038), the National Key Program for Developing Basic Science (No. 2009CB421105), the Fundamental Research Funds for the Central Universities (No. 2009B06614; 2010B00414), the National Non Profit Research Program of China (No. 200905013-8; 201101024; 20101224).

Heat simulation via Scilab programming

NASA Astrophysics Data System (ADS)

Hasan, Mohammad Khatim; Sulaiman, Jumat; Karim, Samsul Arifin Abdul

2014-07-01

This paper discussed the used of an open source sofware called Scilab to develop a heat simulator. In this paper, heat equation was used to simulate heat behavior in an object. The simulator was developed using finite difference method. Numerical experiment output show that Scilab can produce a good heat behavior simulation with marvellous visual output with only developing simple computer code.

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

Deschenes, Austin; Muneer, Sadid; Akbulut, Mustafa

Thermal assistance has been shown to significantly reduce the required operation power for spin torque transfer magnetic random access memory (STT-MRAM). Proposed heating methods include modified material stack compositions that result in increased self-heating or external heat sources. Here, we analyze the self-heating process of a standard perpendicular magnetic anisotropy STT-MRAM device through numerical simulations in order to understand the relative contributions of Joule, thermoelectric Peltier and Thomson, and tunneling junction heating. A 2D rotationally symmetric numerical model is used to solve the coupled electro-thermal equations including thermoelectric effects and heat absorbed or released at the tunneling junction. We comparemore » self-heating for different common passivation materials, positive and negative electrical current polarity, and different device thermal anchoring and boundaries resistance configurations. The variations considered are found to result in significant differences in maximum temperatures reached. Average increases of 3 K, 10 K, and 100 K for different passivation materials, positive and negative polarity, and different thermal anchoring configurations, respectively, are observed. Furthermore, the highest temperatures, up to 424 K, are obtained for silicon dioxide as the passivation material, positive polarity, and low thermal anchoring with thermal boundary resistance configurations. Interestingly it is also found that due to the tunneling heat, Peltier effect, device geometry, and numerous interfacial layers around the magnetic tunnel junction (MTJ), most of the heat is dissipated on the lower potential side of the magnetic junction. We have observed this asymmetry in heating and is important as thermally assisted switching requires heating of the free layer specifically and this will be significantly different for the two polarity operations, set and reset.« less

Heat Transfer Analysis for Stationary Boundary Layer Slip Flow of a Power-Law Fluid in a Darcy Porous Medium with Plate Suction/Injection

PubMed Central

Aziz, Asim; Ali, Yasir; Aziz, Taha; Siddique, J. I.

2015-01-01

In this paper, we investigate the slip effects on the boundary layer flow and heat transfer characteristics of a power-law fluid past a porous flat plate embedded in the Darcy type porous medium. The nonlinear coupled system of partial differential equations governing the flow and heat transfer of a power-law fluid is transformed into a system of nonlinear coupled ordinary differential equations by applying a suitable similarity transformation. The resulting system of ordinary differential equations is solved numerically using Matlab bvp4c solver. Numerical results are presented in the form of graphs and the effects of the power-law index, velocity and thermal slip parameters, permeability parameter, suction/injection parameter on the velocity and temperature profiles are examined. PMID:26407162

Magnetohydrodynamics Carreau nanofluid flow over an inclined convective heated stretching cylinder with Joule heating

NASA Astrophysics Data System (ADS)

Khan, Imad; Shafquatullah; Malik, M. Y.; Hussain, Arif; Khan, Mair

Current work highlights the computational aspects of MHD Carreau nanofluid flow over an inclined stretching cylinder with convective boundary conditions and Joule heating. The mathematical modeling of physical problem yields nonlinear set of partial differential equations. A suitable scaling group of variables is employed on modeled equations to convert them into non-dimensional form. The integration scheme Runge-Kutta-Fehlberg on the behalf of shooting technique is utilized to solve attained set of equations. The interesting aspects of physical problem (linear momentum, energy and nanoparticles concentration) are elaborated under the different parametric conditions through graphical and tabular manners. Additionally, the quantities (local skin friction coefficient, local Nusselt number and local Sherwood number) which are responsible to dig out the physical phenomena in the vicinity of stretched surface are computed and delineated by varying controlling flow parameters.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Technical Reports Server (NTRS)

Glass, Christopher E.

1990-01-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Computer program to solve two-dimensional shock-wave interference problems with an equilibrium chemically reacting air model

NASA Astrophysics Data System (ADS)

Glass, Christopher E.

1990-08-01

The computer program EASI, an acronym for Equilibrium Air Shock Interference, was developed to calculate the inviscid flowfield, the maximum surface pressure, and the maximum heat flux produced by six shock wave interference patterns on a 2-D, cylindrical configuration. Thermodynamic properties of the inviscid flowfield are determined using either an 11-specie, 7-reaction equilibrium chemically reacting air model or a calorically perfect air model. The inviscid flowfield is solved using the integral form of the conservation equations. Surface heating calculations at the impingement point for the equilibrium chemically reacting air model use variable transport properties and specific heat. However, for the calorically perfect air model, heating rate calculations use a constant Prandtl number. Sample calculations of the six shock wave interference patterns, a listing of the computer program, and flowcharts of the programming logic are included.

Temperature Controller System for Gas Gun Targets

NASA Astrophysics Data System (ADS)

Bucholtz, S. M.; Gehr, R. J.; Rupp, T. D.; Sheffield, S. A.; Robbins, D. L.

2006-07-01

A temperature controller system capable of heating and cooling gas gun targets over the range -75°C to +120°C was designed and tested. The system uses cold nitrogen gas from a liquid nitrogen Dewar for cooling and compressed air for heating. Two gas flow heaters control the gas temperature for both heating and cooling. One heater controls the temperature of the target mounting plate and the other the temperature of a copper tubing coil surrounding the target. Each heater is separately adjustable, so the target material will achieve a uniform temperature throughout its volume. A magnetic gauge membrane with integrated thermocouples was developed to measure the internal temperature of the target. Using this system, multiple magnetic gauge shock experiments, including equation-of-state measurements and shock initiation of high explosives, can be performed over a range of initial temperatures. Successful heating and cooling tests were completed on Teflon samples.

Numerical Modeling of Ablation Heat Transfer

NASA Technical Reports Server (NTRS)

Ewing, Mark E.; Laker, Travis S.; Walker, David T.

2013-01-01

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Assessment of different radiative transfer equation solvers for combined natural convection and radiation heat transfer problems

NASA Astrophysics Data System (ADS)

Sun, Yujia; Zhang, Xiaobing; Howell, John R.

2017-06-01

This work investigates the performance of the DOM, FVM, P1, SP3 and P3 methods for 2D combined natural convection and radiation heat transfer for an absorbing, emitting medium. The Monte Carlo method is used to solve the RTE coupled with the energy equation, and its results are used as benchmark solutions. Effects of the Rayleigh number, Planck number and optical thickness are considered, all covering several orders of magnitude. Temperature distributions, heat transfer rate and computational performance in terms of accuracy and computing time are presented and analyzed.

Black hole thermodynamics under the microscope

NASA Astrophysics Data System (ADS)

Falls, Kevin; Litim, Daniel F.

2014-04-01

A coarse-grained version of the effective action is used to study the thermodynamics of black holes, interpolating from largest to smallest masses. The physical parameters of the black hole are linked to the running couplings by thermodynamics, and the corresponding equation of state includes quantum corrections for temperature, specific heat, and entropy. If quantum gravity becomes asymptotically safe, the state function predicts conformal scaling in the limit of small horizon area and bounds on black hole mass and temperature. A metric-based derivation for the equation of state and quantum corrections to the thermodynamical, statistical, and phenomenological definition of entropy are also given. Further implications and limitations of our study are discussed.

Finite element procedures for coupled linear analysis of heat transfer, fluid and solid mechanics

NASA Technical Reports Server (NTRS)

Sutjahjo, Edhi; Chamis, Christos C.

1993-01-01

Coupled finite element formulations for fluid mechanics, heat transfer, and solid mechanics are derived from the conservation laws for energy, mass, and momentum. To model the physics of interactions among the participating disciplines, the linearized equations are coupled by combining domain and boundary coupling procedures. Iterative numerical solution strategy is presented to solve the equations, with the partitioning of temporal discretization implemented.

Solution of the equation of heat conduction with time dependent sources: Programmed application to planetary thermal history

NASA Technical Reports Server (NTRS)

Conel, J. E.

1975-01-01

A computer program (Program SPHERE) solving the inhomogeneous equation of heat conduction with radiation boundary condition on a thermally homogeneous sphere is described. The source terms are taken to be exponential functions of the time. Thermal properties are independent of temperature. The solutions are appropriate to studying certain classes of planetary thermal history. Special application to the moon is discussed.

Influence of Lorentz force, Cattaneo-Christov heat flux and viscous dissipation on the flow of micropolar fluid past a nonlinear convective stretching vertical surface

NASA Astrophysics Data System (ADS)

Gnaneswara Reddy, Machireddy

2017-12-01

The problem of micropolar fluid flow over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation is investigated. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model effect is properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton's methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically for two cases (linear and nonlinear) and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are reported with the aid of plots for the sundry flow parameters. The temperature and the related boundary enhances enhances with the boosting values of M. It is found that fluid temperature declines for larger thermal relaxation parameter. Also, it is revealed that the Nusselt number declines for the hike values of Bi.

Unsteady Magnetized Flow and Heat Transfer of a Viscoelastic fluid over a Stretching Surface

NASA Astrophysics Data System (ADS)

Ghosh, Sushil Kumar

2017-12-01

This paper is to study the flow of heated ferro-fluid over a stretching sheet under the influence of magnetic field. The fluid considered in the present investigation is a mixture of blood as well as fluid-dispersed magnetic nano particles and under this context blood is found to be the appropriate choice of viscoelastic, Walter's B fluid. The objective of the present work is to study the effect of various parameters found in the mathematical analysis. Taking into account the blood has zero electrical conductivity, magnetization effect has been considered in the governing equation of the present study with the use of ferro-fluid dynamics principle. By introducing appropriate non-dimensional variables into the governing equations of unsteady two-dimensional flow of viscoelastic fluid with heat transfer are converted to a set of ordinary differential equations with appropriate boundary conditions. Newton's linearization technique has been employed for the solution of non-linear ordinary differential equations. Important results found in the present investigation are the substantial influence of ferro-magnetic parameter, Prandlt number and the parameter associated with the thermal conductivity on the flow and heat transfer. It is observed that the presence of magnetic dipole essentially reduces the flow velocity in the vertical direction and that helps to damage the cancer cells in the tumor region.

Empirical equations for viscosity and specific heat capacity determination of paraffin PCM and fatty acid PCM

NASA Astrophysics Data System (ADS)

Barreneche, C.; Ferrer, G.; Palacios, A.; Solé, A.; Inés Fernández, A.; Cabeza, L. F.

2017-10-01

Phase change materials (PCM) used in thermal energy storage (TES) systems have been presented, over recent years, as one of the most effective options in energy storage. Paraffin and fatty acids are some of the most used PCM in TES systems, as they have high phase change enthalpy and in addition they do not present subcooling nor hysteresis and have proper cycling stability. The simulations and design of TES systems require the knowledge of the thermophysical properties of PCM. Thermal conductivity, viscosity, specific heat capacity (Cp) can be experimentally determined, but these are material and time consuming tasks. To avoid or to reduce them, and to have reliable data without the need of experimentation, thermal properties can be calculated by empirical equations. In this study, five different equations are given to calculate the viscosity and specific heat capacity of fatty acid PCM and paraffin PCM. Two of these equations concern, respectively, the empirical calculation of the viscosity and liquid Cp of the whole paraffin PCM family, while the other three equations presented are for the corresponding calculation of viscosity, solid Cp, liquid Cp of the whole fatty acid family of PCM. Therefore, this study summarize the work performed to obtain the main empirical equations to measure the above mentioned properties for whole fatty acid PCM family and whole paraffin PCM family. Moreover, empirical equations have been obtained to calculate these properties for other materials of these PCM groups and these empirical equations can be extrapolated for PCM with higher or lower phase change temperatures within a lower relative error 4%.

Three-phase flow? Consider helical-coil heat exchangers

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

Haraburda, S.S.

1995-07-01

In recent years, chemical process plants are increasingly encountering processes that require heat exchange in three-phase fluids. A typical application, for example, is heating liquids containing solid catalyst particles and non-condensable gases. Heat exchangers designed for three-phase flow generally have tubes with large diameters (typically greater than two inches), because solids can build-up inside the tube and lead to plugging. At the same time, in order to keep heat-transfer coefficients high, the velocity of the process fluid within the tube should also be high. As a result, heat exchangers for three-phase flow may require less than five tubes -- eachmore » having a required linear length that could exceed several hundred feet. Given these limitations, it is obvious that a basic shell-and-tube heat exchanger is not the most practical solution for this purpose. An alternative for three-phase flow is a helical-coil heat exchanger. The helical-coil units offer a number of advantages, including perpendicular, counter-current flow and flexible overall dimensions for the exchanger itself. The paper presents equations for: calculating the tube-side heat-transfer coefficient; calculating the shell-side heat-transfer coefficient; calculating the heat-exchanger size; calculating the tube-side pressure drop; and calculating shell-side pressure-drop.« less

Solar Water Heating System for Biodiesel Production

NASA Astrophysics Data System (ADS)

Syaifurrahman; Usman, A. Gani; Rinjani, Rakasiwi

2018-02-01

Nowadays, electricity become very expensive thing in some remote areas. Energy from solar panels give the solution as renewable energy that is environment friendly. West Borneo is located on the equator where the sun shines for almost 10-15 hours/day. Solar water heating system which is includes storage tank and solar collections becomes a cost-effective way to generate the energy. Solar panel heat water is delivered to water in storage tank. Hot water is used as hot fluid in biodiesel jacked reactor. The purposes of this research are to design Solar Water Heating System for Biodiesel Production and measure the rate of heat-transfer water in storage tank. This test has done for 6 days, every day from 8.30 am until 2.30 pm. Storage tank and collection are made from stainless steel and polystyrene a well-insulated. The results show that the heater can be reach at 50ºC for ±2.5 hours and the maximum temperature is 62ºC where the average of light intensity is 1280 lux.

Turbulent heat flux measurements in a transitional boundary layer

NASA Technical Reports Server (NTRS)

Sohn, K. H.; Zaman, K. B. M. Q.; Reshotko, E.

1992-01-01

During an experimental investigation of the transitional boundary layer over a heated flat plate, an unexpected result was encountered for the turbulent heat flux (bar-v't'). This quantity, representing the correlation between the fluctuating normal velocity and the temperature, was measured to be negative near the wall under certain conditions. The result was unexpected as it implied a counter-gradient heat transfer by the turbulent fluctuations. Possible reasons for this anomalous result were further investigated. The possible causes considered for this negative bar-v't' were: (1) plausible measurement error and peculiarity of the flow facility, (2) large probe size effect, (3) 'streaky structure' in the near wall boundary layer, and (4) contributions from other terms usually assumed negligible in the energy equation including the Reynolds heat flux in the streamwise direction (bar-u't'). Even though the energy balance has remained inconclusive, none of the items (1) to (3) appear to be contributing directly to the anomaly.

Dynamos driven by weak thermal convection and heterogeneous outer boundary heat flux

NASA Astrophysics Data System (ADS)

Sahoo, Swarandeep; Sreenivasan, Binod; Amit, Hagay

2016-01-01

We use numerical dynamo models with heterogeneous core-mantle boundary (CMB) heat flux to show that lower mantle lateral thermal variability may help support a dynamo under weak thermal convection. In our reference models with homogeneous CMB heat flux, convection is either marginally supercritical or absent, always below the threshold for dynamo onset. We find that lateral CMB heat flux variations organize the flow in the core into patterns that favour the growth of an early magnetic field. Heat flux patterns symmetric about the equator produce non-reversing magnetic fields, whereas anti-symmetric patterns produce polarity reversals. Our results may explain the existence of the geodynamo prior to inner core nucleation under a tight energy budget. Furthermore, in order to sustain a strong geomagnetic field, the lower mantle thermal distribution was likely dominantly symmetric about the equator.

One-dimensional analysis of unsteady flows due to supercritical heat addition in high speed condensing steam

NASA Astrophysics Data System (ADS)

Malek, N. A.; Hasini, H.; Yusoff, M. Z.

2013-06-01

Unsteadiness in supersonic flow in nozzles can be generated by the release of heat due to spontaneous condensation. The heat released is termed "supercritical" and may be responsible for turbine blades failure in turbine cascade as it causes a supersonic flow to decelerate. When the Mach number is reduced to unity, the flow can no longer sustain the additional heat and becomes unstable. This paper aims to numerically investigate the unsteadiness caused by supercritical heat addition in one-dimensional condensing flows. The governing equations for mass, momentum and energy, coupled with the equations describing the wetness fraction and droplet growth are integrated and solved iteratively to reveal the final solution. Comparison is made with well-established experimental and numerical solution done by previous researchers that shows similar phenomena.

Numerical reconstruction of unknown Robin inclusions inside a heat conductor by a non-iterative method

NASA Astrophysics Data System (ADS)

Nakamura, Gen; Wang, Haibing

2017-05-01

Consider the problem of reconstructing unknown Robin inclusions inside a heat conductor from boundary measurements. This problem arises from active thermography and is formulated as an inverse boundary value problem for the heat equation. In our previous works, we proposed a sampling-type method for reconstructing the boundary of the Robin inclusion and gave its rigorous mathematical justification. This method is non-iterative and based on the characterization of the solution to the so-called Neumann- to-Dirichlet map gap equation. In this paper, we give a further investigation of the reconstruction method from both the theoretical and numerical points of view. First, we clarify the solvability of the Neumann-to-Dirichlet map gap equation and establish a relation of its solution to the Green function associated with an initial-boundary value problem for the heat equation inside the Robin inclusion. This naturally provides a way of computing this Green function from the Neumann-to-Dirichlet map and explains what is the input for the linear sampling method. Assuming that the Neumann-to-Dirichlet map gap equation has a unique solution, we also show the convergence of our method for noisy measurements. Second, we give the numerical implementation of the reconstruction method for two-dimensional spatial domains. The measurements for our inverse problem are simulated by solving the forward problem via the boundary integral equation method. Numerical results are presented to illustrate the efficiency and stability of the proposed method. By using a finite sequence of transient input over a time interval, we propose a new sampling method over the time interval by single measurement which is most likely to be practical.

On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

ERIC Educational Resources Information Center

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…

Numerical simulation of two-dimensional heat transfer in composite bodies with application to de-icing of aircraft components. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Chao, D. F. K.

1983-01-01

Transient, numerical simulations of the de-icing of composite aircraft components by electrothermal heating were performed for a two dimensional rectangular geometry. The implicit Crank-Nicolson formulation was used to insure stability of the finite-difference heat conduction equations and the phase change in the ice layer was simulated using the Enthalpy method. The Gauss-Seidel point iterative method was used to solve the system of difference equations. Numerical solutions illustrating de-icer performance for various composite aircraft structures and environmental conditions are presented. Comparisons are made with previous studies. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Exact solution of conductive heat transfer in cylindrical composite laminate

NASA Astrophysics Data System (ADS)

Kayhani, M. H.; Shariati, M.; Nourozi, M.; Karimi Demneh, M.

2009-11-01

This paper presents an exact solution for steady-state conduction heat transfer in cylindrical composite laminates. This laminate is cylindrical shape and in each lamina, fibers have been wound around the cylinder. In this article heat transfer in composite laminates is being investigated, by using separation of variables method and an analytical relation for temperature distribution in these laminates has been obtained under specific boundary conditions. Also Fourier coefficients in each layer obtain by solving set of equations that related to thermal boundary layer conditions at inside and outside of the cylinder also thermal continuity and heat flux continuity between each layer is considered. In this research LU factorization method has been used to solve the set of equations.

A Computer Program for the Computation of Running Gear Temperatures Using Green's Function

NASA Technical Reports Server (NTRS)

Koshigoe, S.; Murdock, J. W.; Akin, L. S.; Townsend, D. P.

1996-01-01

A new technique has been developed to study two dimensional heat transfer problems in gears. This technique consists of transforming the heat equation into a line integral equation with the use of Green's theorem. The equation is then expressed in terms of eigenfunctions that satisfy the Helmholtz equation, and their corresponding eigenvalues for an arbitrarily shaped region of interest. The eigenfunction are obtalned by solving an intergral equation. Once the eigenfunctions are found, the temperature is expanded in terms of the eigenfunctions with unknown time dependent coefficients that can be solved by using Runge Kutta methods. The time integration is extremely efficient. Therefore, any changes in the time dependent coefficients or source terms in the boundary conditions do not impose a great computational burden on the user. The method is demonstrated by applying it to a sample gear tooth. Temperature histories at representative surface locatons are given.

Trajectory And Heating Of A Hypervelocity Projectile

NASA Technical Reports Server (NTRS)

Tauber, Michael E.

1992-01-01

Technical paper presents derivation of approximate, closed-form equation for relationship between velocity of projectile and density of atmosphere. Results of calculations based on approximate equation agree well with results from numerical integrations of exact equations of motion. Comparisons of results presented in series of graphs.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

Heat pipes and their use in technology

NASA Technical Reports Server (NTRS)

Vasilyev, L.

1977-01-01

Heat pipes may be employed as temperature regulators, heat diodes, transformers, storage batteries, or utilized for transforming thermal energy into mechanical, electric, or other forms of energy. General concepts were established for the analysis of the transfer process in heat pipes. A system of equations was developed to describe the thermodynamics of steam passage through a cross section of a heat pipe.

Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

NASA Astrophysics Data System (ADS)

Khan, Zeeshan; Khan, Ilyas; Ullah, Murad; Tlili, I.

2018-06-01

In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

Development of reliable predictive heat transfer correlations for low-rank coal-fired fluid bed combustors. Final report

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

Grewal, N.S.

(1) The proposed correlation of Equation (5) is recommended to predict the maximum value of heat transfer coefficient between a horzontal tube and a gas-solid fluidized bed of small particles under the conditions given. For high temperature applications (T/sub B/ > 600/sup 0/C), the radiative component is important and was estimated following Baskakov et al. (2) The proposed correlation of Equation (8) was found reliable to predict the existing data on the maximum value of heat transfer coefficient between a horizontal tube bundle and a gas-solid fluidized bed of small particles under the conditions given. At high temperatures, the radiativemore » component was estimated from the experimental data of Baskakov et al. (3) The correlation of Equation (8) predicted the GFETC data taken during the combustion of low-rank coal very well, when the contribution due to radiation was estimated following Baskakov et al. (4) The correlations proposed by Grewal and Bansal et al. were found to predict the data taken during low-rank coal combustion within +-25%, when the contribution due to radiation was included and estimated following Baskakov et al. (5) Finally, the correlations for large particles (anti d/sub p/ > 1mm) as proposed by Glicksman and Decker, Catipovic et al., Xavier and Davidson, and Zabrodsky et al. also predicted the data for low-rank coal fluidized bed combustor quite well, when the radiative component was estimated from the data of Baskakov et al. 64 references, 19 figures, 10 tables.« less

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

Bass, Jay D.

This project is aimed at experimental characterization of the sound velocities, equations of state (EOS), and derived physical and chemical properties of aqueous solutions and carbon dioxide at extreme pressure and temperature conditions relevant to processes occurring in the interior of the Earth. Chemical transport, phase changes (including melting), fluid-solid reactions, and formation of magmatic liquids at convergent plat boundaries are a key motivation for this project. Research in this area has long been limited by the extreme experimental challenges and lack of data under the appropriate pressure-temperature (P-T) conditions. The vast majority of studies of aqueous geochemistry relevant tomore » terrestrial problems of fluid-rock interactions have been conducted at 0.3 GPa or less, and the widely used Helgeson-Kirkham-Flowers equation of state for aqueous species is applicable only at ~ < 0.5 GPa. These limits are unfortunate because fluid flow and reactions plays a central role in many deeper environments. Recent efforts including our own, have resulted in new experimental techniques that now make it possible to investigate properties of homogeneous and heterogeneous equilibria involving aqueous species and minerals over a much broader range of pressure and temperature appropriate for deep crustal and upper mantle processes involving water-rich fluids. We carried out 1) Brillouin scattering measurements of the equations of state and molar volume of water and carbon dioxide to over 10 GPa and 870K using precise resistance heating of samples under pressure in the diamond anvil cell, and 2) the phase diagrams of the water and CO2, and 3) Exploring new experimental approaches, including CO2 laser heating of samples in a diamond cell, to measurements of sound velocities, EOS, and phase relations by Brillouin scattering to far greater pressures and temperatures.« less

Investigation of Conjugate Heat Transfer in Turbine Blades and Vanes

NASA Technical Reports Server (NTRS)

Kassab, A. J.; Kapat, J. S.

2001-01-01

We report on work carried out to develop a 3-D coupled Finite Volume/BEM-based temperature forward/flux back (TFFB) coupling algorithm to solve the conjugate heat transfer (CHT) which arises naturally in analysis of systems exposed to a convective environment. Here, heat conduction within a structure is coupled to heat transfer to the external fluid which is convecting heat into or out of the solid structure. There are two basic approaches to solving coupled fluid structural systems. The first is a direct coupling where the solution of the different fields is solved simultaneously in one large set of equations. The second approach is a loose coupling strategy where each set of field equations is solved to provide boundary conditions for the other. The equations are solved in turn until an iterated convergence criterion is met at the fluid-solid interface. The loose coupling strategy is particularly attractive when coupling auxiliary field equations to computational fluid dynamics codes. We adopt the latter method in which the BEM is used to solve heat conduction inside a structure which is exposed to a convective field which in turn is resolved by solving the NASA Glenn compressible Navier-Stokes finite volume code Glenn-HT. The BEM code features constant and bi-linear discontinuous elements and an ILU-preconditioned GMRES iterative solver for the resulting non-symmetric algebraic set arising in the conduction solution. Interface of flux and temperature is enforced at the solid/fluid interface, and a radial-basis function scheme is used to interpolated information between the CFD and BEM surface grids. Additionally, relaxation is implemented in passing the fluxes from the conduction solution to the fluid solution. Results from a simple test example are reported.

Iterative Methods to Solve Linear RF Fields in Hot Plasma

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2014-10-01

Most magnetic plasma confinement devices use radio frequency (RF) waves for current drive and/or heating. Numerical modeling of RF fields is an important part of performance analysis of such devices and a predictive tool aiding design and development of future devices. Prior attempts at this modeling have mostly used direct solvers to solve the formulated linear equations. Full wave modeling of RF fields in hot plasma with 3D nonuniformities is mostly prohibited, with memory demands of a direct solver placing a significant limitation on spatial resolution. Iterative methods can significantly increase spatial resolution. We explore the feasibility of using iterative methods in 3D full wave modeling. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating along test particle orbits. The wave equation is discretized using a finite difference approach. The initial guess is important in iterative methods, and we examine different initial guesses including the solution to the cold plasma wave equation. Work is supported by the U.S. DOE SBIR program.

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.

A Modified Benedict-Webb-Rubin Equation of State for the Thermodynamic Properties of R152a (1,1-difluoroethane)

NASA Astrophysics Data System (ADS)

Outcalt, Stephanie L.; McLinden, Mark O.

1996-03-01

A modified Benedict-Webb-Rubin (MBWR) equation of state has been developed for R152a (1,1-difluoroethane). The correlation is based on a selection of available experimental thermodynamic property data. Single-phase pressure-volume-temperature (PVT), heat capacity, and sound speed data, as well as second virial coefficient, vapor pressure, and saturated liquid and saturated vapor density data, were used with multi-property linear least-squares fitting to determine the 32 adjustable coefficients of the MBWR equation. Ancillary equations representing the vapor pressure, saturated liquid and saturated vapor densities, and the ideal gas heat capacity were determined. Coefficients for the equation of state and the ancillary equations are given. Experimental data used in this work covered temperatures from 162 K to 453 K and pressures to 35 MPa. The MBWR equation established in this work may be used to predict thermodynamic properties of R152a from the triple-point temperature of 154.56 K to 500 K and for pressures up to 60 MPa except in the immediate vicinity of the critical point.

Identification of unmeasured variables in the set of model constraints of the data reconciliation in a power unit

NASA Astrophysics Data System (ADS)

Szega, Marcin; Nowak, Grzegorz Tadeusz

2013-12-01

In generalized method of data reconciliation as equations of conditions beside substance and energy balances can be used equations which don't have precisely the status of conservation lows. Empirical coefficients in these equations are traded as unknowns' values. To this kind of equations, in application of the generalized method of data reconciliation in supercritical power unit, can be classified: steam flow capacity of a turbine for a group of stages, adiabatic internal efficiency of group of stages, equations for pressure drop in pipelines and equations for heat transfer in regeneration heat exchangers. Mathematical model of a power unit was developed in the code Thermoflex. Using this model the off-design calculation has been made in several points of loads for the power unit. Using these calculations identification of unknown values and empirical coefficients for generalized method of data reconciliation used in power unit has been made. Additional equations of conditions will be used in the generalized method of data reconciliation which will be used in optimization of measurement placement in redundant measurement system in power unit for new control systems

Recommended radiative property data for Venusian entry calculations

NASA Technical Reports Server (NTRS)

Jones, J. J.; Boughner, R. E.; Haggard, K. V.; Nealy, J. E.; Schryer, D. R.; Zoby, E. V.

1974-01-01

A compilation of experimental and calculated data on the radiative properties species important in Venusian entry is presented. Molecular band systems, atomic lines, free-bound, and free-free continua are considered for the principal radiating species of shock heated carbon dioxide. A limited amount of data pertinent to the species in the ablation layer is also included. The assumption is made that the Venus atmosphere so closely approximates pure CO2 that the inviscid layer radiation is due almost entirely to thermally excited CO2. The only exception is the inclusion of data on the Violet band system of CN. Recommendations are made as to best property values for radiative heating calculations. A review of the basic equations and the relationships of the various emission-absorption gas porperties is also included.

Analysis of self-heating of thermally assisted spin-transfer torque magnetic random access memory

DOE PAGES

Deschenes, Austin; Muneer, Sadid; Akbulut, Mustafa; ...

2016-11-11

Thermal assistance has been shown to significantly reduce the required operation power for spin torque transfer magnetic random access memory (STT-MRAM). Proposed heating methods include modified material stack compositions that result in increased self-heating or external heat sources. Here, we analyze the self-heating process of a standard perpendicular magnetic anisotropy STT-MRAM device through numerical simulations in order to understand the relative contributions of Joule, thermoelectric Peltier and Thomson, and tunneling junction heating. A 2D rotationally symmetric numerical model is used to solve the coupled electro-thermal equations including thermoelectric effects and heat absorbed or released at the tunneling junction. We comparemore » self-heating for different common passivation materials, positive and negative electrical current polarity, and different device thermal anchoring and boundaries resistance configurations. The variations considered are found to result in significant differences in maximum temperatures reached. Average increases of 3 K, 10 K, and 100 K for different passivation materials, positive and negative polarity, and different thermal anchoring configurations, respectively, are observed. Furthermore, the highest temperatures, up to 424 K, are obtained for silicon dioxide as the passivation material, positive polarity, and low thermal anchoring with thermal boundary resistance configurations. Interestingly it is also found that due to the tunneling heat, Peltier effect, device geometry, and numerous interfacial layers around the magnetic tunnel junction (MTJ), most of the heat is dissipated on the lower potential side of the magnetic junction. We have observed this asymmetry in heating and is important as thermally assisted switching requires heating of the free layer specifically and this will be significantly different for the two polarity operations, set and reset.« less

Can Disks Produce Companions by Gravitational Fragmentation?

NASA Astrophysics Data System (ADS)

Durisen, Richard H.

The nonlinear outcome of gravitational instabilities in disks depends critically on the thermal physics of the gas. Under conditions where thermal energy is lost efficiently, disks disrupt into dense arms, arclets, and clumps. However, the evidence about whether clumps can ever become permanent bound objects is currently inconclusive. Under conditions where cooling is less efficient or where a balance between heating and cooling is achieved, the amplitudes reached by gravitational instabilities are relatively modest. The result is disk heating and transport of mass and angular momentum rather than condensation of bound companions. Future numerical simulations need to resolve the disk vertical structure and include more realistic equations of state and energy transport.

Workshop Physics Activity Guide, Module 3: Heat Temperature and Nuclear Radiation, Thermodynamics, Kinetic Theory, Heat Engines, Nuclear Decay, and Random Monitoring (Units 16 - 18 & 28)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research.

A Numerical Analysis of the Transient Response of an Ablation System Including Effects of Thermal Nonequilibrium, Mass Transfer and Chemical Kinetics. Ph.D Thesis - Virginia Polytechnic Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Clark, R. K.

1972-01-01

The differential equations governing the transient response of a one-dimensional ablative thermal protection system undergoing stagnation ablation are derived. These equations are for thermal nonequilibrium effects between the pyrolysis gases and the char layer and kinetically controlled chemical reactions and mass transfer between the pyrolysis gases and the char layer. The boundary conditions are written for the particular case of stagnation heating with surface removal by oxidation or sublimation and pyrolysis of the uncharred layer occurring in a plane. The governing equations and boundary conditions are solved numerically using the modified implicit method (Crank-Nicolson method). Numerical results are compared with exact solutions for a number of simplified cases. The comparison is favorable in each instance.

Mixed convection and heat generation/absorption aspects in MHD flow of tangent-hyperbolic nanoliquid with Newtonian heat/mass transfer

NASA Astrophysics Data System (ADS)

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

2018-03-01

This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.

Effects of heat and mass transfer on unsteady boundary layer flow of a chemical reacting Casson fluid

NASA Astrophysics Data System (ADS)

Khan, Kashif Ali; Butt, Asma Rashid; Raza, Nauman

2018-03-01

In this study, an endeavor is to observe the unsteady two-dimensional boundary layer flow with heat and mass transfer behavior of Casson fluid past a stretching sheet in presence of wall mass transfer by ignoring the effects of viscous dissipation. Chemical reaction of linear order is also invoked here. Similarity transformation have been applied to reduce the governing equations of momentum, energy and mass into non-linear ordinary differential equations; then Homotopy analysis method (HAM) is applied to solve these equations. Numerical work is done carefully with a well-known software MATHEMATICA for the examination of non-dimensional velocity, temperature, and concentration profiles, and then results are presented graphically. The skin friction (viscous drag), local Nusselt number (rate of heat transfer) and Sherwood number (rate of mass transfer) are discussed and presented in tabular form for several factors which are monitoring the flow model.

Modeling thermionic emission from laser-heated nanoparticles

DOE PAGES

Mitrani, J. M.; Shneider, M. N.; Stratton, B. C.; ...

2016-02-01

An adjusted form of thermionic emission is applied to calculate emitted current from laser-heated nanoparticles and to interpret time-resolved laser-induced incandescence (TR-LII) signals. This adjusted form of thermionic emission predicts significantly lower values of emitted current compared to the commonly used Richardson-Dushman equation, since the buildup of positive charge in a laser-heated nanoparticle increases the energy barrier for further emission of electrons. Thermionic emission influences the particle's energy balance equation, which can influence TR-LII signals. Additionally, reports suggest that thermionic emission can induce disintegration of nanoparticle aggregates when the electrostatic Coulomb repulsion energy between two positively charged primary particles ismore » greater than the van der Waals bond energy. Furthermore, since the presence and size of aggregates strongly influences the particle's energy balance equation, using an appropriate form of thermionic emission to calculate emitted current may improve interpretation of TR-LII signals.« less

Viscous dissipation effects on MHD slip flow and heat transfer in porous micro duct with LTNE assumptions using modified lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Rabhi, R.; Amami, B.; Dhahri, H.; Mhimid, A.

2017-11-01

This paper deals with heat transfer and fluid flow in a porous micro duct under local thermal non equilibrium conditions subjected to an external oriented magnetic field. The considered sample is a micro duct filled with porous media assumed to be homogenous, isotropic and saturated. The slip velocity and the temperature jump were uniformly imposed to the wall. In modeling the flow, the Brinkmann-Forchheimer extended Darcy model was incorporated into the momentum equations. In the energy equation, the local thermal non equilibrium between the two phases was adopted. A modified axisymmetric lattice Boltzmann method was used to solve the obtained governing equation system. Attention was focused on the influence of the emerging parameters such as Knudsen number, Kn, Hartmann number, Ha, Eckert number, Ec, Biot number, Bi and the magnetic field inclination γ on flow and heat transfer throughout this paper.

Modeling of heat conduction via fractional derivatives

NASA Astrophysics Data System (ADS)

Fabrizio, Mauro; Giorgi, Claudio; Morro, Angelo

2017-09-01

The modeling of heat conduction is considered by letting the time derivative, in the Cattaneo-Maxwell equation, be replaced by a derivative of fractional order. The purpose of this new approach is to overcome some drawbacks of the Cattaneo-Maxwell equation, for instance possible fluctuations which violate the non-negativity of the absolute temperature. Consistency with thermodynamics is shown to hold for a suitable free energy potential, that is in fact a functional of the summed history of the heat flux, subject to a suitable restriction on the set of admissible histories. Compatibility with wave propagation at a finite speed is investigated in connection with temperature-rate waves. It follows that though, as expected, this is the case for the Cattaneo-Maxwell equation, the model involving the fractional derivative does not allow the propagation at a finite speed. Nevertheless, this new model provides a good description of wave-like profiles in thermal propagation phenomena, whereas Fourier's law does not.

Magnetohydrodynamics effect on convective boundary layer flow and heat transfer of viscoelastic micropolar fluid past a sphere

NASA Astrophysics Data System (ADS)

Amera Aziz, Laila; Kasim, Abdul Rahman Mohd; Zuki Salleh, Mohd; Syahidah Yusoff, Nur; Shafie, Sharidan

2017-09-01

The main interest of this study is to investigate the effect of MHD on the boundary layer flow and heat transfer of viscoelastic micropolar fluid. Governing equations are transformed into dimensionless form in order to reduce their complexity. Then, the stream function is applied to the dimensionless equations to produce partial differential equations which are then solved numerically using the Keller-box method in Fortran programming. The numerical results are compared to published study to ensure the reliability of present results. The effects of selected physical parameters such as the viscoelastic parameter, K, micropolar parameter, K1 and magnetic parameter, M on the flow and heat transfer are discussed and presented in tabular and graphical form. The findings from this study will be of critical importance in the fields of medicine, chemical as well as industrial processes where magnetic field is involved.

The effect of velocity slip and multiple convective boundary conditions in a Darcian porous media with microorganism past a vertical stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Latiff, Nur Amalina Abdul; Yahya, Elisa; Ismail, Ahmad Izani Md.; Amirsom, Ardiana; Basir, Faisal

2017-08-01

An analysis is carried out to study the steady mixed convective boundary layer flow of a nanofluid in a Darcian porous media with microorganisms past a vertical stretching/shrinking sheet. Heat generation/absorption and chemical reaction effects are incorporated in the model. The partial differential equations are transformed into a system of ordinary differential equations by using similarity transformations generated by scaling group transformations. The transformed equations with boundary conditions are solved numerically. The effects of controlling parameters such as velocity slip, Darcy number, heat generation/absorption and chemical reaction on the skin friction factor, heat transfer, mass transfer and microorganism transfer are shown and discuss through graphs. Comparison of numerical solutions in the present study with the previous existing results in literature are made and comparison results are in very good agreement.

STELLTRANS: A Transport Analysis Suite for Stellarators

NASA Astrophysics Data System (ADS)

Mittelstaedt, Joseph; Lazerson, Samuel; Pablant, Novimir; Weir, Gavin; W7-X Team

2016-10-01

The stellarator transport code STELLTRANS allows us to better analyze the power balance in W7-X. Although profiles of temperature and density are measured experimentally, geometrical factors are needed in conjunction with these measurements to properly analyze heat flux densities in stellarators. The STELLTRANS code interfaces with VMEC to find an equilibrium flux surface configuration and with TRAVIS to determine the RF heating and current drive in the plasma. Stationary transport equations are then considered which are solved using a boundary value differential equation solver. The equations and quantities considered are averaged over flux surfaces to reduce the system to an essentially one dimensional problem. We have applied this code to data from W-7X and were able to calculate the heat flux coefficients. We will also present extensions of the code to a predictive capacity which would utilize DKES to find neoclassical transport coefficients to update the temperature and density profiles.

A computational study of entropy generation in magnetohydrodynamic flow and heat transfer over an unsteady stretching permeable sheet

NASA Astrophysics Data System (ADS)

Saeed Butt, Adnan; Ali, Asif

2014-01-01

The present article aims to investigate the entropy effects in magnetohydrodynamic flow and heat transfer over an unsteady permeable stretching surface. The time-dependent partial differential equations are converted into non-linear ordinary differential equations by suitable similarity transformations. The solutions of these equations are computed analytically by the Homotopy Analysis Method (HAM) then solved numerically by the MATLAB built-in routine. Comparison of the obtained results is made with the existing literature under limiting cases to validate our study. The effects of unsteadiness parameter, magnetic field parameter, suction/injection parameter, Prandtl number, group parameter and Reynolds number on flow and heat transfer characteristics are checked and analysed with the aid of graphs and tables. Moreover, the effects of these parameters on entropy generation number and Bejan number are also shown graphically. It is examined that the unsteadiness and presence of magnetic field augments the entropy production.

Thermally induced vibrations of smart solar panel in a low-orbit satellite

NASA Astrophysics Data System (ADS)

Azadi, E.; Fazelzadeh, S. Ahmad; Azadi, M.

2017-03-01

In this paper, a smart flexible satellite moving in a circular orbit with two flexible panels are studied. The panels have been modeled as clamped-free-free-free rectangular plates with attached piezoelectric actuators. It is assumed that the satellite has a pitch angle rotation maneuver. Rapid temperature changes at day-night transitions in orbit generate time dependent bending moments. Satellite maneuver and temperature varying induce vibrations in the appendages. So, to simulate the system, heat radiation effects on the appendages have been considered. The nonlinear equations of motion and the heat transfer equations are coupled and solved simultaneously. So, the governing equations of motion are nonlinear and very complicated ones. Finally, the whole system is simulated and the effects of the heat radiation, radius of the orbit, piezoelectric voltages, and piezoelectric locations on the response of the system are studied.

Linearly exact parallel closures for slab geometry

NASA Astrophysics Data System (ADS)

Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun

2013-08-01

Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).

Heat-transfer processes in air-cooled engine cylinders

NASA Technical Reports Server (NTRS)

Pinkel, Benjamin

1938-01-01

From a consideration of heat-transfer theory, semi-empirical expressions are set up for the transfer of heat from the combustion gases to the cylinder of an air-cooled engine and from the cylinder to the cooling air. Simple equations for the average head and barrel temperatures as functions of the important engine and cooling variables are obtained from these expressions. The expressions involve a few empirical constants, which may be readily determined from engine tests. Numerical values for these constants were obtained from single-cylinder engine tests for cylinders of the Pratt & Whitney 1535 and 1340-h engines. The equations provide a means of calculating the effect of the various engine and cooling variables on the cylinder temperatures and also of correlating the results of engine cooling tests. An example is given of the application of the equations to the correlation of cooling-test data obtained in flight.

Antiparticle cloud temperatures for antihydrogen experiments

NASA Astrophysics Data System (ADS)

Bianconi, A.; Charlton, M.; Lodi Rizzini, E.; Mascagna, V.; Venturelli, L.

2017-07-01

A simple rate-equation description of the heating and cooling of antiparticle clouds under conditions typical of those found in antihydrogen formation experiments is developed and analyzed. We include single-particle collisional, radiative, and cloud expansion effects and, from the modeling calculations, identify typical cooling phenomena and trends and relate these to the underlying physics. Some general rules of thumb of use to experimenters are derived.

Optimal control penalty finite elements - Applications to integrodifferential equations

NASA Astrophysics Data System (ADS)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

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.

Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems

NASA Technical Reports Server (NTRS)

Padovan, Joe; Krishna, Lala

1986-01-01

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

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.

Unsteady boundary layer rotating flow and heat transfer in a copper-water nanofluid over a shrinking sheet

NASA Astrophysics Data System (ADS)

Dzulkifli, Nor Fadhilah; Bachok, Norfifah; Yacob, Nor Azizah; Arifin, Norihan Md; Rosali, Haliza

2017-04-01

The study of unsteady three-dimensional boundary layer rotating flow with heat transfer in Copper-water nanofluid over a shrinking sheet is discussed. The governing equations in terms of partial differential equations are transformed to ordinary differential equations by introducing the appropriate similarity variables which are then solved numerically by a shooting method with Maple software. The numerical results of velocity gradient in x and y directions, skin friction coefficient and local Nusselt number as well as dual velocity and temperature profiles are shown graphically. The study revealed that dual solutions exist in certain range of s > 0.

Dual solutions of three-dimensional flow and heat transfer over a non-linearly stretching/shrinking sheet

NASA Astrophysics Data System (ADS)

Naganthran, Kohilavani; Nazar, Roslinda; Pop, Ioan

2018-05-01

This study investigated the influence of the non-linearly stretching/shrinking sheet on the boundary layer flow and heat transfer. A proper similarity transformation simplified the system of partial differential equations into a system of ordinary differential equations. This system of similarity equations is then solved numerically by using the bvp4c function in the MATLAB software. The generated numerical results presented graphically and discussed in the relevance of the governing parameters. Dual solutions found as the sheet stretched and shrunk in the horizontal direction. Stability analysis showed that the first solution is physically realizable whereas the second solution is not practicable.

Effective Methods for Solving Band SLEs after Parabolic Nonlinear PDEs

NASA Astrophysics Data System (ADS)

Veneva, Milena; Ayriyan, Alexander

2018-04-01

A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer. Homogeneous Neumann boundary conditions and ideal contact ones are applied. A finite difference scheme on a special uneven mesh with a second-order approximation in the case of a piecewise constant spatial step is built. This discretization leads to a pentadiagonal system of linear equations (SLEs) with a matrix which is neither diagonally dominant, nor positive definite. Two different methods for solving such a SLE are developed - diagonal dominantization and symbolic algorithms.

Heat Source/Sink in a Magneto-Hydrodynamic Non-Newtonian Fluid Flow in a Porous Medium: Dual Solutions

PubMed Central

Hayat, Tasawar; Awais, Muhammad; Imtiaz, Amna

2016-01-01

This communication deals with the properties of heat source/sink in a magneto-hydrodynamic flow of a non-Newtonian fluid immersed in a porous medium. Shrinking phenomenon along with the permeability of the wall is considered. Mathematical modelling is performed to convert the considered physical process into set of coupled nonlinear mathematical equations. Suitable transformations are invoked to convert the set of partial differential equations into nonlinear ordinary differential equations which are tackled numerically for the solution computations. It is noted that dual solutions for various physical parameters exist which are analyzed in detail. PMID:27598314

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.

One-dimensional model and solutions for creeping gas flows in the approximation of uniform pressure

NASA Astrophysics Data System (ADS)

Vedernikov, A.; Balapanov, D.

2016-11-01

A model, along with analytical and numerical solutions, is presented to describe a wide variety of one-dimensional slow flows of compressible heat-conductive fluids. The model is based on the approximation of uniform pressure valid for the flows, in which the sound propagation time is much shorter than the duration of any meaningful density variation in the system. The energy balance is described by the heat equation that is solved independently. This approach enables the explicit solution for the fluid velocity to be obtained. Interfacial and volumetric heat and mass sources as well as boundary motion are considered as possible sources of density variation in the fluid. A set of particular tasks is analyzed for different motion sources in planar, axial, and central symmetries in the quasistationary limit of heat conduction (i.e., for large Fourier number). The analytical solutions are in excellent agreement with corresponding numerical solutions of the whole system of the Navier-Stokes equations. This work deals with the ideal gas. The approach is also valid for other equations of state.

Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

NASA Astrophysics Data System (ADS)

M. Salem, A.; Galal, Ismail; Rania, Fathy

2014-04-01

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

Improved momentum-transfer theory for ion mobility. 1. Derivation of the fundamental equation.

PubMed

Siems, William F; Viehland, Larry A; Hill, Herbert H

2012-11-20

For the first time the fundamental ion mobility equation is derived by a bottom-up procedure, with N real atomic ion-atomic neutral collisions replaced by N repetitions of an average collision. Ion drift velocity is identified as the average of all pre- and postcollision velocities in the field direction. To facilitate velocity averaging, collisions are sorted into classes that "cool" and "heat" the ion. Averaging over scattering angles establishes mass-dependent relationships between pre- and postcollision velocities for the cooling and heating classes, and a combined expression for drift velocity is obtained by weighted addition according to relative frequencies of the cooling and heating encounters. At zero field this expression becomes identical to the fundamental low-field ion mobility equation. The bottom-up derivation identifies the low-field drift velocity as 3/4 of the average precollision ion velocity in the field direction and associates the passage from low-field to high-field conditions with the increasing dominance of "cooling" collisions over "heating" collisions. Most significantly, the analysis provides a direct path for generalization to fields of arbitrary strength.

Large-Eddy Simulation of Flow and Pollutant Transport in Urban Street Canyons with Ground Heating

NASA Astrophysics Data System (ADS)

Li, Xian-Xiang; Britter, Rex E.; Koh, Tieh Yong; Norford, Leslie K.; Liu, Chun-Ho; Entekhabi, Dara; Leung, Dennis Y. C.

2010-11-01

Our study employed large-eddy simulation (LES) based on a one-equation subgrid-scale model to investigate the flow field and pollutant dispersion characteristics inside urban street canyons. Unstable thermal stratification was produced by heating the ground of the street canyon. Using the Boussinesq approximation, thermal buoyancy forces were taken into account in both the Navier-Stokes equations and the transport equation for subgrid-scale turbulent kinetic energy (TKE). The LESs were validated against experimental data obtained in wind-tunnel studies before the model was applied to study the detailed turbulence, temperature, and pollutant dispersion characteristics in the street canyon of aspect ratio 1. The effects of different Richardson numbers ( Ri) were investigated. The ground heating significantly enhanced mean flow, turbulence, and pollutant flux inside the street canyon, but weakened the shear at the roof level. The mean flow was observed to be no longer isolated from the free stream and fresh air could be entrained into the street canyon at the roof-level leeward corner. Weighed against higher temperature, the ground heating facilitated pollutant removal from the street canyon.

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.

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

The influence of meridional ice transport on Europa's ocean stratification and heat content

NASA Astrophysics Data System (ADS)

Zhu, Peiyun; Manucharyan, Georgy E.; Thompson, Andrew F.; Goodman, Jason C.; Vance, Steven D.

2017-06-01

Jupiter's moon Europa likely hosts a saltwater ocean beneath its icy surface. Geothermal heating and rotating convection in the ocean may drive a global overturning circulation that redistributes heat vertically and meridionally, preferentially warming the ice shell at the equator. Here we assess the previously unconstrained influence of ocean-ice coupling on Europa's ocean stratification and heat transport. We demonstrate that a relatively fresh layer can form at the ice-ocean interface due to a meridional ice transport forced by the differential ice shell heating between the equator and the poles. We provide analytical and numerical solutions for the layer's characteristics, highlighting their sensitivity to critical ocean parameters. For a weakly turbulent and highly saline ocean, a strong buoyancy gradient at the base of the freshwater layer can suppress vertical tracer exchange with the deeper ocean. As a result, the freshwater layer permits relatively warm deep ocean temperatures.

The influence of meridional ice transport on Europa's ocean stratification and heat content

NASA Astrophysics Data System (ADS)

Zhu, P.; Manucharyan, G.; Thompson, A. F.; Goodman, J. C.; Vance, S.

2017-12-01

Jupiter's moon Europa likely hosts a saltwater ocean beneath its icy surface. Geothermal heating and rotating convection in the ocean may drive a global overturning circulation that redistributes heat vertically and meridionally, preferentially warming the ice shell at the equator. Here we assess thepreviously unconstrained influence of ocean-ice coupling on Europa's ocean stratification and heat transport. We demonstrate that a relatively fresh layer can form at the ice-ocean interface due to a meridional ice transport forced by the differential ice shell heating between the equator and the poles. We provide analytical and numerical solutions for the layer's characteristics, highlighting their sensitivity to critical ocean parameters. For a weakly turbulent and highly saline ocean, a strong buoyancy gradient at the base of the freshwater layer can suppress vertical tracer exchange with the deeper ocean. As a result, the freshwater layer permits relatively warm deep ocean temperatures.

Investigation of the Conjugate Heat and Mass Transfer at Ignition and Subsequent Nonstationary Erosion Combustion of Powders Under Conditions Close to Those of Firing a Shot

NASA Astrophysics Data System (ADS)

Rusyak, I. G.; Lipanov, A. M.

2016-11-01

The laws of combustion of powders under conditions close to those of firing an artillery shot have been investigated. A solid-state local heat ignition model was used, and the process of powder combustion was simulated on the basis of the notions of the Belyaev-Zel'dovich thermal combustion theory. The complete formulation of the combustion problem includes the nonstationary processes of heat propagation and chemical transformation in the k-phase, as well as the quasi-stationary processes in the chemically reacting two-stage turbulent boundary layer near the combustion surface related to the characteristics of the averaged nonstationary flow by the boundary conditions at the outer boundary of the boundary layer. The features of the joint solution of the equations of the thermal combustion theory and the equations of internal ballistics have been analyzed. The questions on the convergence of the conjugate problem have been considered. The influence of various factors on the rate of combustion of powder has been investigated. The investigations conducted enabled us to formulate an approximate method for calculating the nonstationary and erosion rates of combustion of artillery powders at a shot on the basis of the Lenouard-Robillard-Karakozov approach.