Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

NASA Astrophysics Data System (ADS)

Issokolo, Remi J. Noumana; Dikandé, Alain M.

2018-05-01

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

A New Homotopy Perturbation Scheme for Solving Singular Boundary Value Problems Arising in Various Physical Models

NASA Astrophysics Data System (ADS)

Roul, Pradip; Warbhe, Ujwal

2017-08-01

The classical homotopy perturbation method proposed by J. H. He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999) is useful for obtaining the approximate solutions for a wide class of nonlinear problems in terms of series with easily calculable components. However, in some cases, it has been found that this method results in slowly convergent series. To overcome the shortcoming, we present a new reliable algorithm called the domain decomposition homotopy perturbation method (DDHPM) to solve a class of singular two-point boundary value problems with Neumann and Robin-type boundary conditions arising in various physical models. Five numerical examples are presented to demonstrate the accuracy and applicability of our method, including thermal explosion, oxygen-diffusion in a spherical cell and heat conduction through a solid with heat generation. A comparison is made between the proposed technique and other existing seminumerical or numerical techniques. Numerical results reveal that only two or three iterations lead to high accuracy of the solution and this newly improved technique introduces a powerful improvement for solving nonlinear singular boundary value problems (SBVPs).

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.

Numerical study for heat generation/absorption in flow of nanofluid by a rotating disk

NASA Astrophysics Data System (ADS)

Aziz, Arsalan; Alsaedi, Ahmed; Muhammad, Taseer; Hayat, Tasawar

2018-03-01

Here MHD three-dimensional flow of viscous nanoliquid by a rotating disk with heat generation/absorption and slip effects is addressed. Thermophoresis and random motion features are also incorporated. Velocity, temperature and concentration slip conditions are imposed at boundary. Applied magnetic field is utilized. Low magnetic Reynolds number and boundary layer approximations have been employed in the problem formulation. Suitable transformations lead to strong nonlinear ordinary differential system. The obtained nonlinear system is solved numerically through NDSolve technique. Graphs have been sketched in order to analyze that how the velocity, temperature and concentration fields are affected by various pertinent variables. Moreover the numerical values for rates of heat and mass transfer have been tabulated and discussed.

Method for solving the problem of nonlinear heating a cylindrical body with unknown initial temperature

NASA Astrophysics Data System (ADS)

Yaparova, N.

2017-10-01

We consider the problem of heating a cylindrical body with an internal thermal source when the main characteristics of the material such as specific heat, thermal conductivity and material density depend on the temperature at each point of the body. We can control the surface temperature and the heat flow from the surface inside the cylinder, but it is impossible to measure the temperature on axis and the initial temperature in the entire body. This problem is associated with the temperature measurement challenge and appears in non-destructive testing, in thermal monitoring of heat treatment and technical diagnostics of operating equipment. The mathematical model of heating is represented as nonlinear parabolic PDE with the unknown initial condition. In this problem, both the Dirichlet and Neumann boundary conditions are given and it is required to calculate the temperature values at the internal points of the body. To solve this problem, we propose the numerical method based on using of finite-difference equations and a regularization technique. The computational scheme involves solving the problem at each spatial step. As a result, we obtain the temperature function at each internal point of the cylinder beginning from the surface down to the axis. The application of the regularization technique ensures the stability of the scheme and allows us to significantly simplify the computational procedure. We investigate the stability of the computational scheme and prove the dependence of the stability on the discretization steps and error level of the measurement results. To obtain the experimental temperature error estimates, computational experiments were carried out. The computational results are consistent with the theoretical error estimates and confirm the efficiency and reliability of the proposed computational scheme.

Solar coronal loop heating by cross-field wave transport

NASA Technical Reports Server (NTRS)

Amendt, Peter; Benford, Gregory

1989-01-01

Solar coronal arches heated by turbulent ion-cyclotron waves may suffer significant cross-field transport by these waves. Nonlinear processes fix the wave-propagation speed at about a tenth of the ion thermal velocity, which seems sufficient to spread heat from a central core into a large cool surrounding cocoon. Waves heat cocoon ions both through classical ion-electron collisions and by turbulent stochastic ion motions. Plausible cocoon sizes set by wave damping are in roughly kilometers, although the wave-emitting core may be only 100 m wide. Detailed study of nonlinear stabilization and energy-deposition rates predicts that nearby regions can heat to values intermediate between the roughly electron volt foot-point temperatures and the about 100 eV core, which is heated by anomalous Ohmic losses. A volume of 100 times the core volume may be affected. This qualitative result may solve a persistent problem with current-driven coronal heating; that it affects only small volumes and provides no way to produce the extended warm structures perceptible to existing instruments.

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.

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Second harmonic generation of q-Gaussian laser beam in preformed collisional plasma channel with nonlinear absorption

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

Gupta, Naveen, E-mail: naveens222@rediffmail.com; Singh, Arvinder, E-mail: arvinder6@lycos.com; Singh, Navpreet, E-mail: navpreet.nit@gmail.com

2015-11-15

This paper presents a scheme for second harmonic generation of an intense q-Gaussian laser beam in a preformed parabolic plasma channel, where collisional nonlinearity is operative with nonlinear absorption. Due to nonuniform irradiance of intensity along the wavefront of the laser beam, nonuniform Ohmic heating of plasma electrons takes place. Due to this nonuniform heating of plasma, the laser beam gets self-focused and produces strong density gradients in the transverse direction. The generated density gradients excite an electron plasma wave at pump frequency that interacts with the pump beam to produce its second harmonics. The formulation is based on amore » numerical solution of the nonlinear Schrodinger wave equation in WKB approximation followed by moment theory approach. A second order nonlinear differential equation governing the propagation dynamics of the laser beam with distance of propagation has been obtained and is solved numerically by Runge Kutta fourth order technique. The effect of nonlinear absorption on self-focusing of the laser beam and conversion efficiency of its second harmonics has been investigated.« less

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.

MHD boundary layer slip flow and heat transfer of ferrofluid along a stretching cylinder with prescribed heat flux.

PubMed

Qasim, Muhammad; Khan, Zafar Hayat; Khan, Waqar Ahmad; Ali Shah, Inayat

2014-01-01

This study investigates the magnetohydrodynamic (MHD) flow of ferrofluid along a stretching cylinder. The velocity slip and prescribed surface heat flux boundary conditions are employed on the cylinder surface. Water as conventional base fluid containing nanoparticles of magnetite (Fe3O4) is used. Comparison between magnetic (Fe3O4) and non-magnetic (Al2O3) nanoparticles is also made. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations and then solved numerically using shooting method. Present results are compared with the available data in the limiting cases. The present results are found to be in an excellent agreement. It is observed that with an increase in the magnetic field strength, the percent difference in the heat transfer rate of magnetic nanoparticles with Al2O3 decreases. Surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases, i.e curvature helps to enhance the heat transfer.

Integral method for transient He II heat transfer in a semi-infinite domain

NASA Astrophysics Data System (ADS)

Baudouy, B.

2002-05-01

Integral methods are suited to solve a non-linear system of differential equations where the non-linearity can be found either in the differential equations or in the boundary conditions. Though they are approximate methods, they have proven to give simple solutions with acceptable accuracy for transient heat transfer in He II. Taking in account the temperature dependence of thermal properties, direct solutions are found without the need of adjusting a parameter. Previously, we have presented a solution for the clamped heat flux and in the present study this method is used to accommodate the clamped-temperature problem. In the case of constant thermal properties, this method yields results that are within a few percent of the exact solution for the heat flux at the axis origin. We applied this solution to analyze recovery from burnout and find an agreement within 10% at low heat flux, whereas at high heat flux the model deviates from the experimental data suggesting the need for a more refined thermal model.

Controllability of semi-infinite rod heating by a point source

NASA Astrophysics Data System (ADS)

Khurshudyan, A.

2018-04-01

The possibility of control over heating of a semi-infinite thin rod by a point source concentrated at an inner point of the rod, is studied. Quadratic and piecewise constant solutions of the problem are derived, and the possibilities of solving appropriate problems of optimal control are indicated. Determining of the parameters of the piecewise constant solution is reduced to a problem of nonlinear programming. Numerical examples are considered.

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.

Nonlinear unsteady convection on micro and nanofluids with Cattaneo-Christov heat flux

NASA Astrophysics Data System (ADS)

Mamatha Upadhya, S.; Raju, C. S. K.; Mahesha; Saleem, S.

2018-06-01

This is a theoretical study of unsteady nonlinear convection on magnetohydrodynamic fluid in a suspension of dust and graphene nanoparticles. For boosting the heat transport phenomena we consider the Cattaneo-Christov heat flux and thermal radiation. Dispersal of graphene nanoparticles in dusty fluids finds applications in biocompatibility, bio-imaging, biosensors, detection and cancer treatment, in monitoring stem cells differentiation etc. Initially the simulation is performed by amalgamation of dust (micron size) and nanoparticles into base fluid. Primarily existing partial differential system (PDEs) is changed to ordinary differential system (ODEs) with the support of usual similarity transformations. Consequently, the highly nonlinear ODEs are solved numerically through Runge-Kutta and Shooting method. The computational results for Non-dimensional temperature and velocity profiles are offered through graphs (ϕ = 0 and ϕ = 0.05) cases. Additionally, the numerical values of friction factor and heat transfer rate are tabulated numerically for various physical parameters obtained. We also validated the current outcomes with previously available study and found to be extremely acceptable. From this study we conclude that in the presence of nanofluid heat transfer rate and temperature distribution is higher compared to micro fluid.

Numerical study of heat transfer and fluid flow for steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Pohlman, Matthew Michael

The study of heat transfer and fluid flow in a vertical Bridgman device is motivated by current industrial difficulties in growing crystals with as few defects as possible. For example, Gallium Arsenide (GaAs) is of great interest to the semiconductor industry but remains an uneconomical alternative to silicon because of the manufacturing problems. This dissertation is a two dimensional study of the fluid in an idealized Bridgman device. The model nonlinear PDEs are discretized using second order finite differencing. Newton's method solves the resulting nonlinear discrete equations. The large sparse linear systems involving the Jacobian are solved iteratively using the Generalized Minimum Residual method (GMRES). By adapting fast direct solvers for elliptic equations with simple boundary conditions, a good preconditioner is developed which is essential for GMRES to converge quickly. Trends of the fluid flow and heat transfer for typical ranges of the physical parameters are determined. Also, the size of the terms in the mathematical model are found by numerical investigation, in order to find what terms are in balance as the physical parameters vary. The results suggest the plausibility of simpler asymptotic solutions.

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 optimal modified variational iteration method for the Lane-Emden equations with Neumann and Robin boundary conditions

NASA Astrophysics Data System (ADS)

Singh, Randhir; Das, Nilima; Kumar, Jitendra

2017-06-01

An effective analytical technique is proposed for the solution of the Lane-Emden equations. The proposed technique is based on the variational iteration method (VIM) and the convergence control parameter h . In order to avoid solving a sequence of nonlinear algebraic or complicated integrals for the derivation of unknown constant, the boundary conditions are used before designing the recursive scheme for solution. The series solutions are found which converges rapidly to the exact solution. Convergence analysis and error bounds are discussed. Accuracy, applicability of the method is examined by solving three singular problems: i) nonlinear Poisson-Boltzmann equation, ii) distribution of heat sources in the human head, iii) second-kind Lane-Emden equation.

Thermally stratified flow of second grade fluid with non-Fourier heat flux and temperature dependent thermal conductivity

NASA Astrophysics Data System (ADS)

Khan, M. Ijaz; Zia, Q. M. Zaigham; Alsaedi, A.; Hayat, T.

2018-03-01

This attempt explores stagnation point flow of second grade material towards an impermeable stretched cylinder. Non-Fourier heat flux and thermal stratification are considered. Thermal conductivity dependents upon temperature. Governing non-linear differential system is solved using homotopic procedure. Interval of convergence for the obtained series solutions is explicitly determined. Physical quantities of interest have been examined for the influential variables entering into the problems. It is examined that curvature parameter leads to an enhancement in velocity and temperature. Further temperature for non-Fourier heat flux model is less than Fourier's heat conduction law.

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

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.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

PubMed

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

Model and Comparative Study for Flow of Viscoelastic Nanofluids with Cattaneo-Christov Double Diffusion

PubMed Central

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-01-01

Here two classes of viscoelastic fluids have been analyzed in the presence of Cattaneo-Christov double diffusion expressions of heat and mass transfer. A linearly stretched sheet has been used to create the flow. Thermal and concentration diffusions are characterized firstly by introducing Cattaneo-Christov fluxes. Novel features regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system has been taken into place by using suitable transformations. The resulting nonlinear systems have been solved via convergent approach. Graphs have been sketched in order to investigate how the velocity, temperature and concentration profiles are affected by distinct physical flow parameters. Numerical values of skin friction coefficient and heat and mass transfer rates at the wall are also computed and discussed. Our observations demonstrate that the temperature and concentration fields are decreasing functions of thermal and concentration relaxation parameters. PMID:28046011

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

NASA Technical Reports Server (NTRS)

Chen, C.-J.; Naseri-Neshat, H.; Ho, K.-S.

1981-01-01

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Forced convective heat transfer in boundary layer flow of Sisko fluid over a nonlinear stretching sheet.

PubMed

Munir, Asif; Shahzad, Azeem; Khan, Masood

2014-01-01

The major focus of this article is to analyze the forced convective heat transfer in a steady boundary layer flow of Sisko fluid over a nonlinear stretching sheet. Two cases are studied, namely (i) the sheet with variable temperature (PST case) and (ii) the sheet with variable heat flux (PHF case). The heat transfer aspects are investigated for both integer and non-integer values of the power-law index. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically. The numerical results are obtained by the shooting method using adaptive Runge Kutta method with Broyden's method in the domain[Formula: see text]. The numerical results for the temperature field are found to be strongly dependent upon the power-law index, stretching parameter, wall temperature parameter, material parameter of the Sisko fluid and Prandtl number. In addition, the local Nusselt number versus wall temperature parameter is also graphed and tabulated for different values of pertaining parameters. Further, numerical results are validated by comparison with exact solutions as well as previously published results in the literature.

Thermal buoyancy on magneto hydrodynamic flow over a vertical saturated porous surface with viscous dissipation

NASA Astrophysics Data System (ADS)

Nirmala, P. H.; Saila Kumari, A.; Raju, C. S. K.

2018-04-01

In the present article, we studied the magnetohydro dynamic flow induced heat transfer from vertical surface embedded in a saturated porous medium in the presence of viscous dissipation. Appropriate similarity transformations are used to transmute the non-linear governing partial differential equations to non-linear ODE. To solve these ordinary differential equations (ODE) we used the well-known integral method of Von Karman type. A comparison has been done and originates to be in suitable agreement with the previous published results. The tabulated and graphical results are given to consider the physical nature of the problem. From this results we found that the magnetic field parameter depreciate the velocity profiles and improves the heat transfer rate of the flow.

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.

Unsteady heat transfer performance of heat pipe with axially swallow-tailed microgrooves

NASA Astrophysics Data System (ADS)

Zhang, R. P.

2017-04-01

A mathematical model is developed for predicting the transient heat transfer and fluid flow of heat pipe with axially swallow-tailed microgrooves. The effects of liquid convective heat transfer in the microgrooves, liquid-vapor interfacial phase-change heat transfer and liquid-vapor interfacial shear stress are accounted for in the present model. The coupled non-linear control equations are solved numerically. Mass flow rate at the interface is obtained from the application of kinetic theory. Time variation of wall temperature is studied from the initial startup to steady state. The numerical results are verified by experiments. Time constants for startup and shutdown operation are defined to determine how fast a heat pipe responds to an applied input heat flux, which slightly decreases with increasing heat load.

TORO II simulations of induction heating in ferromagnetic materials

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

Adkins, D.R.; Gartling, D.K.; Kelley, J.B.

TORO II is a finite element computer program that is used in the simulation of electric and magnetic fields. This code, which was developed at Sandia National Laboratories, has been coupled with a finite element thermal code, COYOTE II, to predict temperature profiles in inductively heated parts. The development of an effective technique to account for the nonlinear behavior of the magnetic permeability in ferromagnetic parts is one of the more difficult aspects of solving induction heating problems. In the TORO II code, nonlinear, spatially varying magnetic permeability is approximated by an effective permeability on an element-by-element basis that effectivelymore » provides the same energy deposition that is produced when the true permeability is used. This approximation has been found to give an accurate estimate of the volumetric heating distribution in the part, and predicted temperature distributions have been experimentally verified using a medium carbon steel and a 10kW industrial induction heating unit. Work on the model was funded through a Cooperative Research and Development Agreement (CRADA) between the Department of Energy and General Motors` Delphi Saginaw Steering Systems.« less

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

A revised model for Jeffrey nanofluid subject to convective condition and heat generation/absorption

PubMed Central

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-01-01

Here magnetohydrodynamic (MHD) boundary layer flow of Jeffrey nanofluid by a nonlinear stretching surface is addressed. Heat generation/absorption and convective surface condition effects are considered. Novel features of Brownian motion and thermophoresis are present. A non-uniform applied magnetic field is employed. Boundary layer and small magnetic Reynolds number assumptions are employed in the formulation. A newly developed condition with zero nanoparticles mass flux is imposed. The resulting nonlinear systems are solved. Convergence domains are explicitly identified. Graphs are analyzed for the outcome of sundry variables. Further local Nusselt number is computed and discussed. It is observed that the effects of Hartman number on the temperature and concentration distributions are qualitatively similar. Both temperature and concentration distributions are enhanced for larger Hartman number. PMID:28231298

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

Analysis of Heat Transfer Phenomenon in Magnetohydrodynamic Casson Fluid Flow Through Cattaneo-Christov Heat Diffusion Theory

NASA Astrophysics Data System (ADS)

Ramesh, G. K.; Gireesha, B. J.; Shehzad, S. A.; Abbasi, F. M.

2017-07-01

Heat transport phenomenon of two-dimensional magnetohydrodynamic Casson fluid flow by employing Cattaneo-Christov heat diffusion theory is described in this work. The term of heat absorption/generation is incorporated in the mathematical modeling of present flow problem. The governing mathematical expressions are solved for velocity and temperature profiles using RKF 45 method along with shooting technique. The importance of arising nonlinear quantities namely velocity, temperature, skin-friction and temperature gradient are elaborated via plots. It is explored that the Casson parameter retarded the liquid velocity while it enhances the fluid temperature. Further, we noted that temperature and thickness of temperature boundary layer are weaker in case of Cattaneo-Christov heat diffusion model when matched with the profiles obtained for Fourier’s theory of heat flux.

Analysis and design of an ultrahigh temperature hydrogen-fueled MHD generator

NASA Technical Reports Server (NTRS)

Moder, Jeffrey P.; Myrabo, Leik N.; Kaminski, Deborah A.

1993-01-01

A coupled gas dynamics/radiative heat transfer analysis of partially ionized hydrogen, in local thermodynamic equilibrium, flowing through an ultrahigh temperature (10,000-20,000 K) magnetohydrodynamic (MHD) generator is performed. Gas dynamics are modeled by a set of quasi-one-dimensional, nonlinear differential equations which account for friction, convective and radiative heat transfer, and the interaction between the ionized gas and applied magnetic field. Radiative heat transfer is modeled using nongray, absorbing-emitting 2D and 3D P-1 approximations which permit an arbitrary variation of the spectral absorption coefficient with frequency. Gas dynamics and radiative heat transfer are coupled through the energy equation and through the temperature- and density-dependent absorption coefficient. The resulting nonlinear elliptic problem is solved by iterative methods. Design of such MHD generators as onboard, open-cycle, electric power supplies for a particular advanced airbreathing propulsion concept produced an efficient and compact 128-MWe generator characterized by an extraction ratio of 35.5 percent, a power density of 10,500 MWe/cu m, and a specific (extracted) energy of 324 MJe/kg of hydrogen. The maximum wall heat flux and total wall heat load were 453 MW/sq m and 62 MW, respectively.

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.

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.

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.

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

NASA Astrophysics Data System (ADS)

Hayat, T.; Ahmad, Salman; Ijaz Khan, M.; Alsaedi, A.

2018-05-01

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODE’s. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.

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

NASA Technical Reports Server (NTRS)

Handschuh, Robert F.

1987-01-01

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

exponential finite difference technique for solving partial differential equations

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

Handschuh, R.F.

1987-01-01

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

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.

The effect of nonlinear propagation on heating of tissue: A numerical model of diagnostic ultrasound beams

NASA Astrophysics Data System (ADS)

Cahill, Mark D.; Humphrey, Victor F.; Doody, Claire

2000-07-01

Thermal safety indices for diagnostic ultrasound beams are calculated under the assumption that the sound propagates under linear conditions. A non-axisymmetric finite difference model is used to solve the KZK equation, and so to model the beam of a diagnostic scanner in pulsed Doppler mode. Beams from both a uniform focused rectangular source and a linear array are considered. Calculations are performed in water, and in attenuating media with tissue-like characteristics. Attenuating media are found to exhibit significant nonlinear effects for finite-amplitude beams. The resulting loss of intensity by the beam is then used as the source term in a model of tissue heating to estimate the maximum temperature rises. These are compared with the thermal indices, derived from the properties of the water-propagated beams.

Investigation of heat and mass transfer under the influence of variable diffusion coefficient and thermal conductivity

NASA Astrophysics Data System (ADS)

Mohyud Din, S. T.; Zubair, T.; Usman, M.; Hamid, M.; Rafiq, M.; Mohsin, S.

2018-04-01

This study is devoted to analyze the influence of variable diffusion coefficient and variable thermal conductivity on heat and mass transfer in Casson fluid flow. The behavior of concentration and temperature profiles in the presence of Joule heating and viscous dissipation is also studied. The dimensionless conversation laws with suitable BCs are solved via Modified Gegenbauer Wavelets Method (MGWM). It has been observed that increase in Casson fluid parameter (β ) and parameter ɛ enhances the Nusselt number. Moreover, Nusselt number of Newtonian fluid is less than that of the Casson fluid. The phenomenon of mass transport can be increased by solute of variable diffusion coefficient rather than solute of constant diffusion coefficient. A detailed analysis of results is appropriately highlighted. The obtained results, error estimates, and convergence analysis reconfirm the credibility of proposed algorithm. It is concluded that MGWM is an appropriate tool to tackle nonlinear physical models and hence may be extended to some other nonlinear problems of diversified physical nature also.

Stagnation point flow on bioconvection nanofluid over a stretching/shrinking surface with velocity and thermal slip effects

NASA Astrophysics Data System (ADS)

Chan, Sze Qi; Aman, Fazlina; Mansur, Syahira

2017-09-01

Nanofluid containing nanometer sized particles has become an ideal thermal conductivity medium for the flow and heat transfer in many industrial and engineering applications due to their high rate of heat transfer. However, swimming microorganisms are imposed into the nanofluid to overcome the instability of nanoparticles due to a bioconvection phenomenon. This paper investigates the stagnation point flow on bioconvection heat transfer of a nanofluid over a stretching/shrinking surface containing gyrotactic microorganisms. Velocity and thermal slip effects are the two conditions incorporated into the model. Similarity transformation is applied to reduce the governing nonlinear partial differential equations into the nonlinear ordinary differential equations. The transformed equations are then solved numerically. The results are displayed in the form of graphs and tables. The effects of these governing parameters on the skin friction coefficient, local Nusselt number, local Sherwood number and the local density of the motile microorganisms are analysed and discussed in details.

Variable viscosity on unsteady dissipative Carreau fluid over a truncated cone filled with titanium alloy nanoparticles

NASA Astrophysics Data System (ADS)

Raju, C. S. K.; Sekhar, K. R.; Ibrahim, S. M.; Lorenzini, G.; Viswanatha Reddy, G.; Lorenzini, E.

2017-05-01

In this study, we proposed a theoretical investigation on the temperature-dependent viscosity effect on magnetohydrodynamic dissipative nanofluid over a truncated cone with heat source/sink. The involving set of nonlinear partial differential equations is transforming to set of nonlinear ordinary differential equations by using self-similarity solutions. The transformed governing equations are solved numerically using Runge-Kutta-based Newton's technique. The effects of various dimensionless parameters on the skin friction coefficient and the local Nusselt number profiles are discussed and presented with the support of graphs. We also obtained the validation of the current solutions with existing solution under some special cases. The water-based titanium alloy has a lesser friction factor coefficient as compared with kerosene-based titanium alloy, whereas the rate of heat transfer is higher in water-based titanium alloy compared with kerosene-based titanium alloy. From this we can highlight that depending on the industrial needs cooling/heating chooses the water- or kerosene-based titanium alloys.

Use of multilevel modeling for determining optimal parameters of heat supply systems

NASA Astrophysics Data System (ADS)

Stennikov, V. A.; Barakhtenko, E. A.; Sokolov, D. V.

2017-07-01

The problem of finding optimal parameters of a heat-supply system (HSS) is in ensuring the required throughput capacity of a heat network by determining pipeline diameters and characteristics and location of pumping stations. Effective methods for solving this problem, i.e., the method of stepwise optimization based on the concept of dynamic programming and the method of multicircuit optimization, were proposed in the context of the hydraulic circuit theory developed at Melentiev Energy Systems Institute (Siberian Branch, Russian Academy of Sciences). These methods enable us to determine optimal parameters of various types of piping systems due to flexible adaptability of the calculation procedure to intricate nonlinear mathematical models describing features of used equipment items and methods of their construction and operation. The new and most significant results achieved in developing methodological support and software for finding optimal parameters of complex heat supply systems are presented: a new procedure for solving the problem based on multilevel decomposition of a heat network model that makes it possible to proceed from the initial problem to a set of interrelated, less cumbersome subproblems with reduced dimensionality; a new algorithm implementing the method of multicircuit optimization and focused on the calculation of a hierarchical model of a heat supply system; the SOSNA software system for determining optimum parameters of intricate heat-supply systems and implementing the developed methodological foundation. The proposed procedure and algorithm enable us to solve engineering problems of finding the optimal parameters of multicircuit heat supply systems having large (real) dimensionality, and are applied in solving urgent problems related to the optimal development and reconstruction of these systems. The developed methodological foundation and software can be used for designing heat supply systems in the Central and the Admiralty regions in St. Petersburg, the city of Bratsk, and the Magistral'nyi settlement.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

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

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

Tsai, C.H.

1981-01-01

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

Influence of Soret-Dufour and thermophoresis on hydromagnetic mixed convection heat and mass transfer over an inclined flat plate with non-uniform heat source/sink and chemical reaction

NASA Astrophysics Data System (ADS)

Pal, Dulal; Mondal, Hiranmoy

2018-03-01

The paper is devoted to the study of thermophoresis and Soret-Dufour effects on magnetohydrodynamic mixed convective heat and mass transfer over an inclined flat plate with non-uniform heat source/sink. Governing non-linear coupled ordinary differential equations are solved numerically using Runge-Kutta Fehlberg technique with shooting scheme. The effects of various physical parameters on the velocity, temperature, and concentration profiles are depicted graphically. The values of skin-friction coefficient, Nusselt number and Sherwood number are presented in a tabular form. It is found that increase in thermophoretic and chemical reaction parameters retard the velocity and concentration distributions in the boundary layer.

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.

MHD stagnation point flow and heat transfer of a nanofluid over a permeable nonlinear stretching/shrinking sheet with viscous dissipation effect

NASA Astrophysics Data System (ADS)

Jusoh, Rahimah; Nazar, Roslinda

2018-04-01

The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.

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

Transport processes in magnetically confined plasmas in the nonlinear regime.

PubMed

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

Slip Effects On MHD Three Dimensional Flow Of Casson Fluid Over An Exponentially Stretching Surface

NASA Astrophysics Data System (ADS)

Madhusudhana Rao, B.; Krishna Murthy, M.; Sivakumar, N.; Rushi Kumar, B.; Raju, C. S. K.

2018-04-01

Heat and mass transfer effects on MHD three dimensional flow of Casson fluid over an exponentially stretching surface with slip conditions is examined. The similarity transformations are used to convert the governing equations into a set of nonlinear ordinary differential equations and are solved numerically using fourth order Runge-Kutta method along with shooting technique. The effects of Casson parameter, Hartmann number, heat source/sink,chemical reaction and slip factors on velocity, temperature and concentration are shown graphically. The skin friction coefficient and the Nusselt number are examined numerically.

Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy.

PubMed

Awad, Faiz G; Motsa, Sandile; Khumalo, Melusi

2014-01-01

In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.

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 and Mass Transfer in Unsteady Rotating Fluid Flow with Binary Chemical Reaction and Activation Energy

PubMed Central

Awad, Faiz G.; Motsa, Sandile; Khumalo, Melusi

2014-01-01

In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations. PMID:25250830

THERMO-HYDRO-MECHANICAL MODELING OF WORKING FLUID INJECTION AND THERMAL ENERGY EXTRACTION IN EGS FRACTURES AND ROCK MATRIX

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

Robert Podgorney; Chuan Lu; Hai Huang

2012-01-01

Development of enhanced geothermal systems (EGS) will require creation of a reservoir of sufficient volume to enable commercial-scale heat transfer from the reservoir rocks to the working fluid. A key assumption associated with reservoir creation/stimulation is that sufficient rock volumes can be hydraulically fractured via both tensile and shear failure, and more importantly by reactivation of naturally existing fractures (by shearing), to create the reservoir. The advancement of EGS greatly depends on our understanding of the dynamics of the intimately coupled rock-fracture-fluid-heat system and our ability to reliably predict how reservoirs behave under stimulation and production. Reliable performance predictions ofmore » EGS reservoirs require accurate and robust modeling for strongly coupled thermal-hydrological-mechanical (THM) processes. Conventionally, these types of problems have been solved using operator-splitting methods, usually by coupling a subsurface flow and heat transport simulators with a solid mechanics simulator via input files. An alternative approach is to solve the system of nonlinear partial differential equations that govern multiphase fluid flow, heat transport, and rock mechanics simultaneously, using a fully coupled, fully implicit solution procedure, in which all solution variables (pressure, enthalpy, and rock displacement fields) are solved simultaneously. This paper describes numerical simulations used to investigate the poro- and thermal- elastic effects of working fluid injection and thermal energy extraction on the properties of the fractures and rock matrix of a hypothetical EGS reservoir, using a novel simulation software FALCON (Podgorney et al., 2011), a finite element based simulator solving fully coupled multiphase fluid flow, heat transport, rock deformation, and fracturing using a global implicit approach. Investigations are also conducted on how these poro- and thermal-elastic effects are related to fracture permeability evolution.« less

Unique Outcomes of Internal Heat Generation and Thermal Deposition on Viscous Dissipative Transport of Viscoplastic Fluid over a Riga-Plate

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Azhar, Ehtsham; Mehmood, Zaffar; Maraj, E. N.

2018-01-01

Boundary layer stagnation point flow of Casson fluid over a Riga plate of variable thickness is investigated in present article. Riga plate is an electromagnetic actuator consists of enduring magnets and gyrated aligned array of alternating electrodes mounted on a plane surface. Physical problem is modeled and simplified under appropriate transformations. Effects of thermal radiation and viscous dissipation are incorporated. These differential equations are solved by Keller Box Scheme using MATLAB. Comparison is given with shooting techniques along with Range-Kutta Fehlberg method of order 5. Graphical and tabulated analysis is drawn. The results reveal that Eckert number, radiation and fluid parameters enhance temperature whereas they contribute in lowering rate of heat transfer. The numerical outcomes of present analysis depicts that Keller Box Method is capable and consistent to solve proposed nonlinear problem with high accuracy.

Optimal homotopy asymptotic method for flow and heat transfer of a viscoelastic fluid in an axisymmetric channel with a porous wall.

PubMed

Mabood, Fazle; Khan, Waqar A; Ismail, Ahmad Izani Md

2013-01-01

In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.

CHAP-2 heat-transfer analysis of the Fort St. Vrain reactor core

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

Kotas, J.F.; Stroh, K.R.

1983-01-01

The Los Alamos National Laboratory is developing the Composite High-Temperature Gas-Cooled Reactor Analysis Program (CHAP) to provide advanced best-estimate predictions of postulated accidents in gas-cooled reactor plants. The CHAP-2 reactor-core model uses the finite-element method to initialize a two-dimensional temperature map of the Fort St. Vrain (FSV) core and its top and bottom reflectors. The code generates a finite-element mesh, initializes noding and boundary conditions, and solves the nonlinear Laplace heat equation using temperature-dependent thermal conductivities, variable coolant-channel-convection heat-transfer coefficients, and specified internal fuel and moderator heat-generation rates. This paper discusses this method and analyzes an FSV reactor-core accident thatmore » simulates a control-rod withdrawal at full power.« less

Optimal Homotopy Asymptotic Method for Flow and Heat Transfer of a Viscoelastic Fluid in an Axisymmetric Channel with a Porous Wall

PubMed Central

Mabood, Fazle; Khan, Waqar A.; Ismail, Ahmad Izani

2013-01-01

In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena. PMID:24376722

Control of non-linear actuator of artificial muscles for the use in low-cost robotics prosthetics limbs

NASA Astrophysics Data System (ADS)

Anis Atikah, Nurul; Yeng Weng, Leong; Anuar, Adzly; Chien Fat, Chau; Sahari, Khairul Salleh Mohamed; Zainal Abidin, Izham

2017-10-01

Currently, the methods of actuating robotic-based prosthetic limbs are moving away from bulky actuators to more fluid materials such as artificial muscles. The main disadvantages of these artificial muscles are their high cost of manufacturing, low-force generation, cumbersome and complex controls. A recent discovery into using super coiled polymer (SCP) proved to have low manufacturing costs, high force generation, compact and simple controls. Nevertheless, the non-linear controls still exists due to the nature of heat-based actuation, which is hysteresis. This makes position control difficult. Using electrically conductive devices allows for very quick heating, but not quick cooling. This research tries to solve the problem by using peltier devices, which can effectively heat and cool the SCP, hence giving way to a more precise control. The peltier device does not actively introduce more energy to a volume of space, which the coiled heating does; instead, it acts as a heat pump. Experiments were conducted to test the feasibility of using peltier as an actuating method on different diameters of nylon fishing strings. Based on these experiments, the performance characteristics of the strings were plotted, which could be used to control the actuation of the string efficiently in the future.

Axisymmetric flow of Casson fluid by a swirling cylinder

NASA Astrophysics Data System (ADS)

Javed, Muhammad Faisal; Khan, Muhammad Imran; Khan, Niaz Bahadur; Muhammad, Riaz; Rehman, Muftooh Ur; Khan, Sajjad Wali; Khan, Tufail A.

2018-06-01

The present communication aims to investigate the influence of heat generation/absorption on axisymmetric Casson liquid flow over a stretched cylinder. Flow is caused due to torsional motion of cylinder. The governing physical problem is modelled and transferred into set of coupled nonlinear ordinary differential equations. These equations are solved numerically using built-in-Shooting method. Influence of sundry variables on the swirling velocity, temperature, coefficient of skin friction and heat transfer rate are computed and analyzed in a physical manner. Magnitude of axial skin friction is enhances for larger Reynold number and magnetic parameter while local Nusselt number decays with the enhancement of Casson parameter, heat generation/absorption and magnetic parameter. Comparison with already existing results is also given in the limiting case.

Nonlinear, Incremental Structural Analysis of Olmsted Locks and Dams. Volume 1: Main Text

DTIC Science & Technology

1992-12-01

dependent functions, which are supplied as algebraic functions of time or as data arrays in ABAQUS user subroutines (Hibbitt, Karlsson, and Sorenson 1988...143.0 Thermal Prouerties 9. The heat transfer capability of ABAQUS uses the finite element method to numerically solve the governing differential...coefficient of linear thermal expansion which were conducted at WES for Olmsted mixtures 6 and 11 (Hammons et al. 1991). The different concrete mixture

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

Davis, C.G.

Starting with the initial understanding that pulsation in variable stars is caused by the heat engine of Hydrogen and Helium ionization in their atmospheres (A.S. Eddington in Cox 1980) it was soon realized that non-linear effects were responsible for the detailed features on their light and velocity curves. With the advent of the computer we were able to solve the coupled set of hydrodynamics and radiation diffusion equations to model these non-linear features. This paper describes some recent model results for long period (LP) Cepheids in an attempt to get another handle on Cepheid masses. Section II discusses these resultsmore » and Section III considers the implications of these model results on the problem of the Cepheid mass discrepancy.« less

Solution of second order quasi-linear boundary value problems by a wavelet method

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

Zhang, Lei; Zhou, Youhe; Wang, Jizeng, E-mail: jzwang@lzu.edu.cn

2015-03-10

A wavelet Galerkin method based on expansions of Coiflet-like scaling function bases is applied to solve second order quasi-linear boundary value problems which represent a class of typical nonlinear differential equations. Two types of typical engineering problems are selected as test examples: one is about nonlinear heat conduction and the other is on bending of elastic beams. Numerical results are obtained by the proposed wavelet method. Through comparing to relevant analytical solutions as well as solutions obtained by other methods, we find that the method shows better efficiency and accuracy than several others, and the rate of convergence can evenmore » reach orders of 5.8.« less

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.

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.

Entropy Analysis in Mixed Convection MHD flow of Nanofluid over a Non-linear Stretching Sheet

NASA Astrophysics Data System (ADS)

Matin, Meisam Habibi; Nobari, Mohammad Reza Heirani; Jahangiri, Pouyan

This article deals with a numerical study of entropy analysis in mixed convection MHD flow of nanofluid over a non-linear stretching sheet taking into account the effects of viscous dissipation and variable magnetic field. The nanofluid is made of such nano particles as SiO2 with pure water as a base fluid. To analyze the problem, at first the boundary layer equations are transformed into non-linear ordinary equations using a similarity transformation. The resultant equations are then solved numerically using the Keller-Box scheme based on the implicit finite-difference method. The effects of different non-dimensional governing parameters such as magnetic parameter, nanoparticles volume fraction, Nusselt, Richardson, Eckert, Hartman, Brinkman, Reynolds and entropy generation numbers are investigated in details. The results indicate that increasing the nano particles to the base fluids causes the reduction in shear forces and a decrease in stretching sheet heat transfer coefficient. Also, decreasing the magnetic parameter and increasing the Eckert number result in improves heat transfer rate. Furthermore, the surface acts as a strong source of irreversibility due to the higher entropy generation number near the surface.

Self-focusing and defocusing of Gaussian laser beams in collisional underdense magnetized plasmas with considering the nonlinear ohmic heating and ponderomotive force effects

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

Ettehadi Abari, Mehdi; Sedaghat, Mahsa; Shokri, Babak, E-mail: b-shokri@sbu.ac.ir

2015-10-15

The propagation characteristics of a Gaussian laser beam in collisional magnetized plasma are investigated by considering the ponderomotive and ohmic heating nonlinearities. Here, by taking into account the effect of the external magnetic field, the second order differential equation of the dimensionless beam width parameter is solved numerically. Furthermore, the nonlinear dielectric permittivity of the mentioned plasma medium in the paraxial approximation and its dependence on the propagation characteristics of the Gaussian laser pulse is obtained, and its variation in terms of the dimensionless plasma length is analyzed at different initial normalized plasma and cyclotron frequencies. The results show thatmore » the dimensionless beam width parameter is strongly affected by the initial plasma frequency, magnetic strength, and laser pulse intensity. Furthermore, it is found that there exists a certain intensity value below which the laser pulse tends to self focus, while the beam diverges above of this value. In addition, the results confirm that, by increasing the plasma and cyclotron frequencies (plasma density and magnetic strength), the self-focusing effect can occur intensively.« less

On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Ahmad, Bashir

2016-06-01

This research article addresses the magnetohydrodynamic (MHD) flow of second grade nanofluid over a nonlinear stretching sheet. Heat and mass transfer aspects are investigated through the thermophoresis and Brownian motion effects. Second grade fluid is assumed electrically conducting through a non-uniform applied magnetic field. Mathematical formulation is developed subject to small magnetic Reynolds number and boundary layer assumptions. Newly constructed condition having zero mass flux of nanoparticles at the boundary is incorporated. Transformations have been invoked for the reduction of partial differential systems into the set of nonlinear ordinary differential systems. The governing nonlinear systems have been solved for local behavior. Graphical results of different influential parameters are studied and discussed in detail. Computations for skin friction coefficient and local Nusselt number have been carried out. It is observed that the effects of thermophoresis parameter on the temperature and nanoparticles concentration distributions are qualitatively similar. The temperature and nanoparticles concentration distributions are enhanced for the larger magnetic parameter.

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.

Magnetohydrodynamic dissipative flow across the slendering stretching sheet with temperature dependent variable viscosity

NASA Astrophysics Data System (ADS)

Jayachandra Babu, M.; Sandeep, N.; Ali, M. E.; Nuhait, Abdullah O.

The boundary layer flow across a slendering stretching sheet has gotten awesome consideration due to its inexhaustible pragmatic applications in nuclear reactor technology, acoustical components, chemical and manufacturing procedures, for example, polymer extrusion, and machine design. By keeping this in view, we analyzed the two-dimensional MHD flow across a slendering stretching sheet within the sight of variable viscosity and viscous dissipation. The sheet is thought to be convectively warmed. Convective boundary conditions through heat and mass are employed. Similarity transformations used to change over the administering nonlinear partial differential equations as a group of nonlinear ordinary differential equations. Runge-Kutta based shooting technique is utilized to solve the converted equations. Numerical estimations of the physical parameters involved in the problem are calculated for the friction factor, local Nusselt and Sherwood numbers. Viscosity variation parameter and chemical reaction parameter shows the opposite impact to each other on the concentration profile. Heat and mass transfer Biot numbers are helpful to enhance the temperature and concentration respectively.

A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

Optimization of the functional domain of flat plate collectors

NASA Astrophysics Data System (ADS)

Ritoux, G.; Irigaray, J.-L.

1981-12-01

The variations of the extracted heat flux as function of the temperature of the heat transfer fluid in black and selective surface solar collectors are examined. The heat flux is calculated based on the difference of the initial to the stage of thermal equilibrium of the fluid. A nonlinear system of equations is developed and solved by a fast, iterative method to obtain the equilibrium temperatures. It is found that more flux can be extracted from the solar heat by a collector with only one glass cover than with more than one cover. The captured flux is proportional to the coefficient of transmission of the glass coverings, to the coefficient of absorption of the collector, and to the incident flux. Black painted surfaces were more absorbent than selective surfaces, and highest collection efficiencies were displayed by low temperature collectors. Charts of effective uses of the respective types of collectors for heating swimming pools, hot water, home heat, and for refrigeration and air-conditioning are provided.

Effects of Heat Source/Sink and Chemical Reaction on MHD Maxwell Nanofluid Flow Over a Convectively Heated Exponentially Stretching Sheet Using Homotopy Analysis Method

NASA Astrophysics Data System (ADS)

Sravanthi, C. S.; Gorla, R. S. R.

2018-02-01

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

Entropy generation in a second grade magnetohydrodynamic nanofluid flow over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation

NASA Astrophysics Data System (ADS)

Sithole, Hloniphile; Mondal, Hiranmoy; Sibanda, Precious

2018-06-01

This study addresses entropy generation in magnetohydrodynamic flow of a second grade nanofluid over a convectively heated stretching sheet with nonlinear thermal radiation and viscous dissipation. The second grade fluid is assumed to be electrically conducting and is permeated by an applied non-uniform magnetic field. We further consider the impact on the fluid properties and the Nusselt number of homogeneous-heterogeneous reactions and a convective boundary condition. The mathematical equations are solved using the spectral local linearization method. Computations for skin-friction coefficient and local Nusselt number are carried out and displayed in a table. It is observed that the effects of the thermophoresis parameter is to increase the temperature distributions throughout the boundary layer. The entropy generation is enhanced by larger magnetic parameters and increasing Reynolds number. The aim of this manuscript is to pay more attention of entropy generation analysis with heat and fluid flow on second grade nanofluids to improve the system performance. Also the fluid velocity and temperature in the boundary layer region rise significantly for increasing the values of the second grade nanofluid parameter.

Double stratification effects in chemically reactive squeezed Sutterby fluid flow with thermal radiation and mixed convection

NASA Astrophysics Data System (ADS)

Ahmad, S.; Farooq, M.; Javed, M.; Anjum, Aisha

2018-03-01

A current analysis is carried out to study theoretically the mixed convection characteristics in squeezing flow of Sutterby fluid in squeezed channel. The constitutive equation of Sutterby model is utilized to characterize the rheology of squeezing phenomenon. Flow characteristics are explored with dual stratification. In flowing fluid which contains heat and mass transport, the first order chemical reaction and radiative heat flux affect the transport phenomenon. The systems of non-linear governing equations have been modulating which then solved by mean of convergent approach (Homotopy Analysis Method). The graphs are reported and illustrated for emerging parameters. Through graphical explanations, drag force, rate of heat and mass transport are conversed for different pertinent parameters. It is found that heat and mass transport rate decays with dominant double stratified parameters and chemical reaction parameter. The present two-dimensional examination is applicable in some of the engineering processes and industrial fluid mechanics.

Numerical study of Free Convective Viscous Dissipative flow along Vertical Cone with Influence of Radiation using Network Simulation method

NASA Astrophysics Data System (ADS)

Kannan, R. M.; Pullepu, Bapuji; Immanuel, Y.

2018-04-01

A two dimensional mathematical model is formulated for the transient laminar free convective flow with heat transfer over an incompressible viscous fluid past a vertical cone with uniform surface heat flux with combined effects of viscous dissipation and radiation. The dimensionless boundary layer equations of the flow which are transient, coupled and nonlinear Partial differential equations are solved using the Network Simulation Method (NSM), a powerful numerical technique which demonstrates high efficiency and accuracy by employing the network simulator computer code Pspice. The velocity and temperature profiles have been investigated for various factors, namely viscous dissipation parameter ε, Prandtl number Pr and radiation Rd are analyzed graphically.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

The effects of strain heating in lithospheric stretching models

NASA Technical Reports Server (NTRS)

Stanton, M.; Hodge, D.; Cozzarelli, F.

1985-01-01

The deformation by stretching of a continental type lithosphere has been formulated so that the problem can be solved by a continuum mechanical approach. The deformation, stress state, and temperature distribution are constrained to satisfy the physical laws of conservation of mass, energy, momentum, and an experimentally defined rheological response. The conservation of energy equation including a term of strain energy dissipation is given. The continental lithosphere is assumed to have the rheology of an isotropic, incompressible, nonlinear viscous, two layered solid.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

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.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

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.

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

1990-01-01

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

NASA Technical Reports Server (NTRS)

Musielak, Z. E.

1992-01-01

In the area of solar physics, new calculations of the acoustic wave energy fluxes generated in the solar convective zone was performed. The original theory developed was corrected by including a new frequency factor describing temporal variations of the turbulent energy spectrum. We have modified the original Stein code by including this new frequency factor, and tested the code extensively. Another possible source of the mechanical energy generated in the solar convective zone is the excitation of magnetic flux tube waves which can carry energy along the tubes far away from the region. The problem as to how efficiently those waves are generated in the Sun was recently solved. The propagation of nonlinear magnetic tube waves in the solar atmosphere was calculated, and mode coupling, shock formation, and heating of the local medium was studied. The wave trapping problems and evaluation of critical frequencies for wave reflection in the solar atmosphere was studied. It was shown that the role played by Alfven waves in the wind accelerations and the coronal hole heating is dominant. Presently, we are performing calculations of wave energy fluxes generated in late-type dwarf stars and studying physical processes responsible for the heating of stellar chromospheres and coronae. In the area of physics of waves, a new analytical approach for studying linear Alfven waves in smoothly nonuniform media was recently developed. This approach is presently being extended to study the propagation of linear and nonlinear magnetohydrodynamic (MHD) waves in stratified, nonisothermal and solar atmosphere. The Lighthill theory of sound generation to nonisothermal media (with a special temperature distribution) was extended. Energy cascade by nonlinear MHD waves and possible chaos driven by these waves are presently considered.

Thermodynamic properties of asymptotically Reissner–Nordström black holes

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

Hendi, S.H., E-mail: hendi@shirazu.ac.ir

2014-07-15

Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariantmore » metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points. -- Highlights: •We examine the thermodynamical properties of black holes in Einstein gravity with nonlinear electrodynamics. •We investigate thermodynamic stability and discuss about the size of stable black holes. •We obtain analytical solutions of higher dimensional theory.« less

New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

Unsteady MHD blood flow through porous medium in a parallel plate channel

NASA Astrophysics Data System (ADS)

Latha, R.; Rushi Kumar, B.

2017-11-01

In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.

A Unified Approach for Solving Nonlinear Regular Perturbation Problems

ERIC Educational Resources Information Center

Khuri, S. A.

2008-01-01

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

Understanding of flux-limited behaviors of heat transport in nonlinear regime

NASA Astrophysics Data System (ADS)

Guo, Yangyu; Jou, David; Wang, Moran

2016-01-01

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

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.

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

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

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

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

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

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

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

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

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

DOE PAGES

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

2016-09-29

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

Fluctuation dynamo based on magnetic reconnections

NASA Astrophysics Data System (ADS)

Baggaley, A. W.; Shukurov, A.; Barenghi, C. F.; Subramanian, K.

2010-01-01

We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find that the flux rope dynamo is more than an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy released during reconnections has a power-law form with the slope -3, consistent with the solar corona heating by nanoflares. We also present a nonlinear extension of the model. This shows that a plausible saturation mechanism of the fluctuation dynamo is the suppression of turbulent magnetic diffusivity, due to suppression of random stretching at the location of the flux ropes. We confirm that the probability distribution function of the magnetic line curvature has a power-law form suggested by \\citet{Sheck:2002b}. We argue, however, using our results that this does not imply a persistent folded structure of magnetic field, at least in the nonlinear stage.

Thermal Image Sensing Model for Robotic Planning and Search.

PubMed

Castro Jiménez, Lídice E; Martínez-García, Edgar A

2016-08-08

This work presents a search planning system for a rolling robot to find a source of infra-red (IR) radiation at an unknown location. Heat emissions are observed by a low-cost home-made IR passive visual sensor. The sensor capability for detection of radiation spectra was experimentally characterized. The sensor data were modeled by an exponential model to estimate the distance as a function of the IR image's intensity, and, a polynomial model to estimate temperature as a function of IR intensities. Both theoretical models are combined to deduce a subtle nonlinear exact solution via distance-temperature. A planning system obtains feed back from the IR camera (position, intensity, and temperature) to lead the robot to find the heat source. The planner is a system of nonlinear equations recursively solved by a Newton-based approach to estimate the IR-source in global coordinates. The planning system assists an autonomous navigation control in order to reach the goal and avoid collisions. Trigonometric partial differential equations were established to control the robot's course towards the heat emission. A sine function produces attractive accelerations toward the IR source. A cosine function produces repulsive accelerations against the obstacles observed by an RGB-D sensor. Simulations and real experiments of complex indoor are presented to illustrate the convenience and efficacy of the proposed approach.

A coupled electro-thermal Discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Homsi, L.; Geuzaine, C.; Noels, L.

2017-11-01

This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems. In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method. The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H1-norm and in the L2-norm are shown to be optimal in the mesh size with the polynomial approximation degree.

Numerical treatment for Carreau nanofluid flow over a porous nonlinear stretching surface

NASA Astrophysics Data System (ADS)

Eid, Mohamed R.; Mahny, Kasseb L.; Muhammad, Taseer; Sheikholeslami, Mohsen

2018-03-01

The impact of magnetic field and nanoparticles on the two-phase flow of a generalized non-Newtonian Carreau fluid over permeable non-linearly stretching surface has been analyzed in the existence of all suction/injection and thermal radiation. The governing PDEs with congruous boundary condition are transformed into a system of non-linear ODEs with appropriate boundary conditions by using similarity transformation. It solved numerically by using 4th-5th order Runge-Kutta-Fehlberg method based on shooting technique. The impacts of non-dimensional controlling parameters on velocity, temperature, and nanoparticles volume concentration profiles are scrutinized with aid of graphs. The Nusselt and the Sherwood numbers are studied at the different situations of the governing parameters. The numerical computations are in excellent consent with previously reported studies. It is found that the heat transfer rate is reduced with an increment of thermal radiation parameter and on contrary of the rising of magnetic field. The opposite trend happens in the mass transfer rate.

Numerical simulation of two-dimensional Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Grigoriev, Vasiliy V.; Zakharov, Petr E.

2017-11-01

This paper considered Rayleigh-Benard convection (natural convection). This is a flow, which is formed in a viscous medium when heated from below and cooled from above. As a result, are formed vortices (convective cells). This process is described by a system of nonlinear differential equations in Oberbeck-Boussinesq approximation. As the governing parameters characterizing convection states Rayleigh number, Prandtl number are picked. The problem is solved by using finite element method with computational package FEniCS. Numerical results for different Rayleigh numbers are obtained. Studied integral characteristic (Nusselt number) depending on the Rayleigh number.

Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave

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

Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com

2014-07-15

The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the Lmore » and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.« less

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.

Ball bearing heat analysis program (BABHAP)

NASA Technical Reports Server (NTRS)

1978-01-01

The Ball Bearing Heat Analysis Program (BABHAP) is an attempt to assemble a series of equations, some of which are non-linear algebraic systems, in a logical order, which when solved, provide a complex analysis of load distribution among the balls, ball velocities, heat generation resulting from friction, applied load, and ball spinning, minimum lubricant film thickness, and many additional characteristics of ball bearing systems. Although initial design requirements for BABHAP were dictated by the core limitations of the PDP 11/45 computer, (approximately 8K of real words with limited number of instructions) the program dimensions can easily be expanded for large core computers such as the UNIVAC 1108. The PDP version of BABHAP is also operational on the UNIVAC system with the exception that the PDP uses 029 punch and the UNIVAC uses 026. A conversion program was written to allow transfer between machines.

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.

Melting heat transport of nanofluidic problem over a Riga plate with erratic thickness: Use of Keller Box scheme

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Azhar, Ehtsham; Mehmood, Zaffar; Maraj, E. N.

Present article is a study of stagnation point flow over Riga plate with erratic thickness. Riga plate is an electromagnetic surface in which electrodes are assembled alternatively. This arrangement generates electromagnetic hydrodynamic behavior in the fluid flow. This is an attempt to investigate influence of melting heat, thermal radiation and viscous dissipation effects on Riga plate. A traversal electric and magnetic fields are produced by Riga plate. It causes Lorentz force parallel to wall which contributes in directing flow pattern. Physical problem is modeled and reduced nonlinear system is solved numerically. Comparative analysis is carried out between solutions obtained by Keller Box Method and shooting technique with Runge-Kutta Fehlberg method of order 5. It is noted that melting heat transfer reduces temperature distribution whereas radiation parameter upsurge it. Velocity is accelerated by modified Hartman number and Eckert number contributes in raising temperature.

Numerical simulation for aspects of homogeneous and heterogeneous reactions in forced convection flow of nanofluid

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Shah, Faisal; Khan, Muhammad Ijaz; Alsaedi, Ahmed

2018-03-01

Mixed convection stagnation point flow of nanofluid by a vertical permeable circular cylinder has been addressed. Water is treated as ordinary liquid while nanoparticles include aluminium oxide, copper and titanium dioxide. Homogeneous-heterogeneous reactions are considered. The nonlinear higher order expressions are changed into first ordinary differential equations and then solved by built-in-Shooting method in mathematica. The results of velocity, temperature, concentration, skin friction and local Nusselt number are discussed. Our results demonstrate that surface drag force and heat transfer rate are enhanced linearly for higher estimation of curvature parameter. Further surface drag force decays for aluminium oxide and it enhances for copper nanoparticle. Heat transfer rate enhances with increasing all three types of nanoparticles. In addition, the lowest heat transfer rate is obtained in case of titanium dioxide when compared with copper and aluminium oxide.

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

Frequency-Domain Analysis of Diffusion-Cooled Hot-Electron Bolometer Mixers

NASA Technical Reports Server (NTRS)

Skalare, A.; McGrath, W. R.; Bumble, B.; LeDuc, H. G.

1998-01-01

A new theoretical model is introduced to describe heterodyne mixer conversion efficiency and noise (from thermal fluctuation effects) in diffusion-cooled superconducting hot-electron bolometers. The model takes into account the non-uniform internal electron temperature distribution generated by Wiedemann-Franz heat conduction, and accepts for input an arbitrary (analytical or experimental) superconducting resistance-versus- temperature curve. A non-linear large-signal solution is solved iteratively to calculate the temperature distribution, and a linear frequency-domain small-signal formulation is used to calculate conversion efficiency and noise. In the small-signal solution the device is discretized into segments, and matrix algebra is used to relate the heating modulation in the segments to temperature and resistance modulations. Matrix expressions are derived that allow single-sideband mixer conversion efficiency and coupled noise power to be directly calculated. The model accounts for self-heating and electrothermal feedback from the surrounding bias circuit.

Prediction of Experimental Surface Heat Flux of Thin Film Gauges using ANFIS

NASA Astrophysics Data System (ADS)

Sarma, Shrutidhara; Sahoo, Niranjan; Unal, Aynur

2018-05-01

Precise quantification of surface heat fluxes in highly transient environment is of paramount importance from the design point of view of several engineering equipment like thermal protection or cooling systems. Such environments are simulated in experimental facilities by exposing the surface with transient heat loads typically step/impulsive in nature. The surface heating rates are then determined from highly transient temperature history captured by efficient surface temperature sensors. The classical approach is to use thin film gauges (TFGs) in which temperature variations are acquired within milliseconds, thereby allowing calculation of surface heat flux, based on the theory of one-dimensional heat conduction on a semi-infinite body. With recent developments in the soft computing methods, the present study is an attempt for the application of intelligent system technique, called adaptive neuro fuzzy inference system (ANFIS) to recover surface heat fluxes from a given temperature history recorded by TFGs without having the need to solve lengthy analytical equations. Experiments have been carried out by applying known quantity of `impulse heat load' through laser beam on TFGs. The corresponding voltage signals have been acquired and surface heat fluxes are estimated through classical analytical approach. These signals are then used to `train' the ANFIS model, which later predicts output for `test' values. Results from both methods have been compared and these surface heat fluxes are used to predict the non-linear relationship between thermal and electrical properties of the gauges that are exceedingly pertinent to the design of efficient TFGs. Further, surface plots have been created to give an insight about dimensionality effect of the non-linear dependence of thermal/electrical parameters on each other. Later, it is observed that a properly optimized ANFIS model can predict the impulsive heat profiles with significant accuracy. This paper thus shows the appropriateness of soft computing technique as a practically constructive replacement for tedious analytical formulation and henceforth, effectively quantifies the modeling of TFGs.

Numerical study of MHD nanofluid flow and heat transfer past a bidirectional exponentially stretching sheet

NASA Astrophysics Data System (ADS)

Ahmad, Rida; Mustafa, M.; Hayat, T.; Alsaedi, A.

2016-06-01

Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite-Fe3O4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction.

Effect of radiation and magnetohydrodynamic free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid

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

Alkasasbeh, Hamzeh Taha, E-mail: zukikuj@yahoo.com; Sarif, Norhafizah Md, E-mail: zukikuj@yahoo.com; Salleh, Mohd Zuki, E-mail: zukikuj@yahoo.com

2015-02-03

In this paper, the effect of radiation on magnetohydrodynamic free convection boundary layer flow on a solid sphere with Newtonian heating in a micropolar fluid, in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The transformed boundary layer equations in the form of nonlinear partial differential equations are solved numerically using an implicit finite difference scheme known as the Keller-box method. Numerical solutions are obtained for the local wall temperature and the local skin friction coefficient, as well as the velocity, angular velocity and temperature profiles. The features of the flow andmore » heat transfer characteristics for various values of the Prandtl number Pr, micropolar parameter K, magnetic parameter M, radiation parameter N{sub R}, the conjugate parameter γ and the coordinate running along the surface of the sphere, x are analyzed and discussed.« less

Solving Nonlinear Differential Equations in the Engineering Curriculum

ERIC Educational Resources Information Center

Auslander, David M.

1977-01-01

Described is the Dynamic System Simulation Language (SIM) mini-computer system utilized at the University of California, Los Angeles. It is used by engineering students for solving nonlinear differential equations. (SL)

Nonlinear asymmetric tearing mode evolution in cylindrical geometry

DOE PAGES

Teng, Qian; Ferraro, N.; Gates, David A.; ...

2016-10-27

The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w). For a low beta plasma without external heating, Δ'(w) can be approximately described by two terms, Δ' ql(w), Δ'A(w). In this work, we present a simple method to calculate the quasilinear stability index Δ'ql rigorously, for poloidal mode number m ≥ 2. Δ' ql is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ' 0, w, wlnw, and w2.more » Δ' A is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δ' ql and Δ' A is consistent with the more accurate expression calculated perturbatively. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. Lastly, it is also confirmed by the simulation that the Δ' A has to be considered in calculating island saturation.« less

Size effects in non-linear heat conduction with flux-limited behaviors

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

Solving intuitionistic fuzzy multi-objective nonlinear programming problem

NASA Astrophysics Data System (ADS)

Anuradha, D.; Sobana, V. E.

2017-11-01

This paper presents intuitionistic fuzzy multi-objective nonlinear programming problem (IFMONLPP). All the coefficients of the multi-objective nonlinear programming problem (MONLPP) and the constraints are taken to be intuitionistic fuzzy numbers (IFN). The IFMONLPP has been transformed into crisp one and solved by using Kuhn-Tucker condition. Numerical example is provided to illustrate the approach.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

Thermodynamics of bread baking: A two-state model

NASA Astrophysics Data System (ADS)

Zürcher, Ulrich

2014-03-01

Bread baking can be viewed as a complex physico-chemical process. It is governed by transport of heat and is accompanied by changes such as gelation of starch, the expansion of air cells within dough, and others. We focus on the thermodynamics of baking and investigate the heat flow through dough and find that the evaporation of excess water in dough is the rate-limiting step. We consider a simplified one-dimensional model of bread, treating the excess water content as a two-state variable that is zero for baked bread and a fixed constant for unbaked dough. We arrive at a system of coupled, nonlinear ordinary differential equations, which are solved using a standard Runge-Kutta integration method. The calculated baking times are consistent with common baking experience.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

On Diffusive Climatological Models.

NASA Astrophysics Data System (ADS)

Griffel, D. H.; Drazin, P. G.

1981-11-01

A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.

Variational algorithms for nonlinear smoothing applications

NASA Technical Reports Server (NTRS)

Bach, R. E., Jr.

1977-01-01

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun Yuan; Young, D. H.

1991-01-01

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Analytical study of temperature distribution in a rectangular porous fin considering both insulated and convective tip

NASA Astrophysics Data System (ADS)

Deshamukhya, Tuhin; Bhanja, Dipankar; Nath, Sujit; Maji, Ambarish; Choubey, Gautam

2017-07-01

The following study is concerned with determination of temperature distribution of porous fins under convective and insulated tip conditions. The authors have made an effort to study the effect of various important parameters involved in the transfer of heat through porous fins as well as the temperature distribution along the fin length subjected to both convective as well as insulated ends. The non-linear equation obtained has been solved by Adomian Decomposition method and validated with a numerical scheme called Finite Difference method by using a central difference scheme and Gauss Siedel Iterative method.

Thermal Image Sensing Model for Robotic Planning and Search

PubMed Central

Castro Jiménez, Lídice E.; Martínez-García, Edgar A.

2016-01-01

This work presents a search planning system for a rolling robot to find a source of infra-red (IR) radiation at an unknown location. Heat emissions are observed by a low-cost home-made IR passive visual sensor. The sensor capability for detection of radiation spectra was experimentally characterized. The sensor data were modeled by an exponential model to estimate the distance as a function of the IR image’s intensity, and, a polynomial model to estimate temperature as a function of IR intensities. Both theoretical models are combined to deduce a subtle nonlinear exact solution via distance-temperature. A planning system obtains feed back from the IR camera (position, intensity, and temperature) to lead the robot to find the heat source. The planner is a system of nonlinear equations recursively solved by a Newton-based approach to estimate the IR-source in global coordinates. The planning system assists an autonomous navigation control in order to reach the goal and avoid collisions. Trigonometric partial differential equations were established to control the robot’s course towards the heat emission. A sine function produces attractive accelerations toward the IR source. A cosine function produces repulsive accelerations against the obstacles observed by an RGB-D sensor. Simulations and real experiments of complex indoor are presented to illustrate the convenience and efficacy of the proposed approach. PMID:27509510

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

On a nonlinear state of the electromagnetic ion/ion cyclotron instability

NASA Astrophysics Data System (ADS)

Cremer, M.; Scholer, M.

We have investigated the nonlinear properties of the electromagnetic ion/ion cyclotron instability (EMIIC) by means of hybrid simulations (macroparticle ions, massless electron fluid). The instability is driven by the relative (super-Alfvénic) streaming of two field-aligned ion beams in a low beta plasma (ion thermal pressure to magnetic field pressure) and may be of importance in the plasma sheet boundary layer. As shown in previously reported simulations the waves propagate obliquely to the magnetic field and heat the ions in the perpendicular direction as the relative beam velocity decreases. By running the simulation to large times it can be shown that the large temperature anisotropy leads to the ion cyclotron instability (IC) with parallel propagating Alfvén ion cyclotron waves. This is confirmed by numerically solving the electromagnetic dispersion relation. An application of this property to the plasma sheet boundary layer is discussed.

Nonlinear problems of the theory of heterogeneous slightly curved shells

NASA Technical Reports Server (NTRS)

Kantor, B. Y.

1973-01-01

An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.

Quadratic Convective Flow of a Micropolar Fluid along an Inclined Plate in a Non-Darcy Porous Medium with Convective Boundary Condition

NASA Astrophysics Data System (ADS)

RamReddy, Ch.; Naveen, P.; Srinivasacharya, D.

2017-06-01

The objective of the present study is to investigate the effect of nonlinear variation of density with temperature and concentration on the mixed convective flow of a micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of the convective boundary condition. In order to analyze all the essential features, the governing non-dimensional partial differential equations are transformed into a system of ordinary differential equations using a local non-similarity procedure and then the resulting boundary value problem is solved using a successive linearisation method (SLM). By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the micropolar parameter and non-Darcy parameter tend to increase the skin friction and the reverse change is observed in wall couple stress, mass and heat transfer rates. The influence of the nonlinear concentration parameter is more prominent on all the physical characteristics of the present model, compared with that of nonlinear temperature parameter.

Unsteady Heat and Mass Transfer of Chemically Reacting Micropolar Fluid in a Porous Channel with Hall and Ion Slip Currents

PubMed Central

2014-01-01

This paper presents an incompressible two-dimensional heat and mass transfer of an electrically conducting micropolar fluid flow in a porous medium between two parallel plates with chemical reaction, Hall and ion slip effects. Let there be periodic injection or suction at the lower and upper plates and the nonuniform temperature and concentration at the plates are varying periodically with time. The flow field equations are reduced to nonlinear ordinary differential equations using similarity transformations and then solved numerically by quasilinearization technique. The profiles of velocity components, microrotation, temperature distribution and concentration are studied for different values of fluid and geometric parameters such as Hartmann number, Hall and ion slip parameters, inverse Darcy parameter, Prandtl number, Schmidt number, and chemical reaction rate and shown in the form of graphs. PMID:27419211

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

TRUMP. Transient & S-State Temperature Distribution

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

Elrod, D.C.; Turner, W.D.

1992-03-03

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables, temperature, pressure, or field strength. Initial conditions may vary with spatial position,more » and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.« less

Application of an enriched FEM technique in thermo-mechanical contact problems

NASA Astrophysics Data System (ADS)

Khoei, A. R.; Bahmani, B.

2018-02-01

In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton-Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature.

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

Elrod, D.C.; Turner, W.D.

TRUMP solves a general nonlinear parabolic partial differential equation describing flow in various kinds of potential fields, such as fields of temperature, pressure, or electricity and magnetism; simultaneously, it will solve two additional equations representing, in thermal problems, heat production by decomposition of two reactants having rate constants with a general Arrhenius temperature dependence. Steady-state and transient flow in one, two, or three dimensions are considered in geometrical configurations having simple or complex shapes and structures. Problem parameters may vary with spatial position, time, or primary dependent variables, temperature, pressure, or field strength. Initial conditions may vary with spatial position,more » and among the criteria that may be specified for ending a problem are upper and lower limits on the size of the primary dependent variable, upper limits on the problem time or on the number of time-steps or on the computer time, and attainment of steady state.« less

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Churchill, S. W.

1975-01-01

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Multiple solutions in MHD flow and heat transfer of Sisko fluid containing nanoparticles migration with a convective boundary condition: Critical points

NASA Astrophysics Data System (ADS)

Dhanai, Ruchika; Rana, Puneet; Kumar, Lokendra

2016-05-01

The motivation behind the present analysis is to focus on magneto-hydrodynamic flow and heat transfer characteristics of non-Newtonian fluid (Sisko fluid) past a permeable nonlinear shrinking sheet utilizing nanoparticles involving convective boundary condition. The non-homogenous nanofluid transport model considering the effect of Brownian motion, thermophoresis, suction/injection and no nanoparticle flux at the sheet with convective boundary condition has been solved numerically by the RKF45 method with shooting technique. Critical points for various pertinent parameters are evaluated in this study. The dual solutions (both first and second solutions) are captured in certain range of material constant (nc< n < ∞) , mass transfer parameter (sc < s < ∞) and shrinking parameter (χc < χ < 0) . For both the branches (upper and lower branch), the rate of heat transfer is an increasing function of the power-law index, Prandtl number and Biot number, whereas it is a decreasing function of the material constant and thermophoresis parameter.

Two-phase magnetoconvection flow of magnetite (Fe3O4) nanoparticles in a horizontal composite porous annulus

NASA Astrophysics Data System (ADS)

Abbas, Zaheer; Hasnain, Jafar

A numerical study is performed to examine the two-phase magnetoconvection and heat transfer phenomena of Fe3O4 -kerosene nanofluid flow in a horizontal composite porous annulus with an external magnetic field. The annulus is filled with immiscible fluids flowing between two concentric cylinders. The governing equations of the flow problem are obtained using Darcy-Brinkman model. Heat transfer is analyzed in the presence of viscous and Darcian dissipation terms. The shooting method is used as a tool to solve the obtained non-linear ordinary differential equations for the velocity and temperature profiles. The velocity and temperature distributions are analyzed and discussed under the influence of involved flow parameters with the aid of graphs. It is found that both velocity and temperature of fluid are decreased with ferroparticle volume fraction. In addition to that, it is also presented that the existence of magnetic field decreases the benefit of ferrofluids in heat transfer progression.

Chemical reaction and heat generation/absorption aspects in MHD nonlinear convective flow of third grade nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Alsaedi, Ahmed

Nonlinear thermal radiation and chemical reaction in magnetohydrodynamic (MHD) flow of third grade nanofluid over a stretching sheet with variable thickness are addressed. Heat generation/absorption and nonlinear convection are considered. The sheet moves with nonlinear velocity. Sheet is convectively heated. In addition zero mass flux condition for nanoparticle concentration is imposed. Results for velocity, temperature, concentration, skin friction and local Nusselt number are presented and examined. It is found that velocity and boundary layer thickness are increasing for Reynolds number. Temperature is a increasing function of the heat generation/absorption parameter while it causes a decrease in the heat transfer rate. Moreover effect of Brownian motion and chemical reaction on the concentration are quite reverse.

Non-linear dual-phase-lag model for analyzing heat transfer phenomena in living tissues during thermal ablation.

PubMed

Kumar, P; Kumar, Dinesh; Rai, K N

2016-08-01

In this article, a non-linear dual-phase-lag (DPL) bio-heat transfer model based on temperature dependent metabolic heat generation rate is derived to analyze the heat transfer phenomena in living tissues during thermal ablation treatment. The numerical solution of the present non-linear problem has been done by finite element Runge-Kutta (4,5) method which combines the essence of Runge-Kutta (4,5) method together with finite difference scheme. Our study demonstrates that at the thermal ablation position temperature predicted by non-linear and linear DPL models show significant differences. A comparison has been made among non-linear DPL, thermal wave and Pennes model and it has been found that non-linear DPL and thermal wave bio-heat model show almost same nature whereas non-linear Pennes model shows significantly different temperature profile at the initial stage of thermal ablation treatment. The effect of Fourier number and Vernotte number (relaxation Fourier number) on temperature profile in presence and absence of externally applied heat source has been studied in detail and it has been observed that the presence of externally applied heat source term highly affects the efficiency of thermal treatment method. Copyright © 2016 Elsevier Ltd. All rights reserved.

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

NASA Astrophysics Data System (ADS)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

Nonlinear Convective Flows in a Laterally Heated Two-Layer System with a Temperature-Dependent Heat Release/Consumption at the Interface

NASA Astrophysics Data System (ADS)

Simanovskii, Ilya; Viviani, Antonio; Dubois, Frank; Queeckers, Patrick

2018-01-01

Nonlinear convective flows developed under the joint action of buoyant and thermocapillary effects in a laterally heated two-layer system filling the closed cavity, have been investigated. The influence of a temperature-dependent interfacial heat release/consumption on nonlinear steady and oscillatory regimes, has been studied. It is shown that sufficiently strong temperature dependence of interfacial heat sinks and heat sources can change the sequence of bifurcations and lead to the development of specific oscillatory regimes in the system.

A family of conjugate gradient methods for large-scale nonlinear equations.

PubMed

Feng, Dexiang; Sun, Min; Wang, Xueyong

2017-01-01

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method.

Thermally induced delay and reversal of liquid film dewetting on chemically patterned surfaces.

PubMed

Kalpathy, Sreeram K; Francis, Lorraine F; Kumar, Satish

2013-10-15

A thin liquid film resting on a solid substrate that is heated or cooled from below experiences surface tension gradients, which lead to Marangoni flows. We explore the behavior of such a film on a chemically patterned substrate which drives film dewetting in order to determine how surface patterning and applied temperature gradients can be designed to influence the behavior of thin-film coatings. A nonlinear partial differential equation for the film height based on lubrication theory is solved numerically for a broad range of problem parameters. Uniform cooling of the substrate is found to significantly delay dewetting that is driven by wettability gradients. Uniform heating speeds up dewetting but can destroy the near-perfect templating imposed by the surface patterning. However, localized heating and cooling together can accelerate dewetting while maintaining templating quality. Localized heating and cooling can also be used to drive liquid onto areas that it would dewet from in the absence of heating. Overall, these results indicate that applied temperature gradients can significantly influence dewetting driven by surface patterning, and suggest strategies for the creation of spatially patterned thin-film coatings and flow control in microfluidic devices. Copyright © 2013 Elsevier Inc. All rights reserved.

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Nonlinear thermotics: nonlinearity enhancement and harmonic generation in thermal metasurfaces

NASA Astrophysics Data System (ADS)

Dai, Gaole; Shang, Jin; Wang, Ruizhe; Huang, Jiping

2018-03-01

We propose and investigate a class of structural surfaces (metasurfaces). We develop the perturbation theory and the effective medium theory to study the thermal properties of the metasurface. We report that the coefficient of temperature-dependent (nonlinear) item in thermal conductivity can be enhanced under certain conditions. Furthermore, the existence of nonlinear item helps to generate high-order harmonic frequencies of heat flux in the presence of a heat source with periodic temperature. This work paves a different way to control and manipulate the transfer of heat, and it also makes it possible to develop nonlinear thermotics in the light of nonlinear optics.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

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

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Complexity in Nature and Society: Complexity Management in the Age of Globalization

NASA Astrophysics Data System (ADS)

Mainzer, Klaus

The theory of nonlinear complex systems has become a proven problem-solving approach in the natural sciences from cosmic and quantum systems to cellular organisms and the brain. Even in modern engineering science self-organizing systems are developed to manage complex networks and processes. It is now recognized that many of our ecological, social, economic, and political problems are also of a global, complex, and nonlinear nature. What are the laws of sociodynamics? Is there a socio-engineering of nonlinear problem solving? What can we learn from nonlinear dynamics for complexity management in social, economic, financial and political systems? Is self-organization an acceptable strategy to handle the challenges of complexity in firms, institutions and other organizations? It is a main thesis of the talk that nature and society are basically governed by nonlinear and complex information dynamics. How computational is sociodynamics? What can we hope for social, economic and political problem solving in the age of globalization?.

Linear and Non-Linear Visual Feature Learning in Rat and Humans

PubMed Central

Bossens, Christophe; Op de Beeck, Hans P.

2016-01-01

The visual system processes visual input in a hierarchical manner in order to extract relevant features that can be used in tasks such as invariant object recognition. Although typically investigated in primates, recent work has shown that rats can be trained in a variety of visual object and shape recognition tasks. These studies did not pinpoint the complexity of the features used by these animals. Many tasks might be solved by using a combination of relatively simple features which tend to be correlated. Alternatively, rats might extract complex features or feature combinations which are nonlinear with respect to those simple features. In the present study, we address this question by starting from a small stimulus set for which one stimulus-response mapping involves a simple linear feature to solve the task while another mapping needs a well-defined nonlinear combination of simpler features related to shape symmetry. We verified computationally that the nonlinear task cannot be trivially solved by a simple V1-model. We show how rats are able to solve the linear feature task but are unable to acquire the nonlinear feature. In contrast, humans are able to use the nonlinear feature and are even faster in uncovering this solution as compared to the linear feature. The implications for the computational capabilities of the rat visual system are discussed. PMID:28066201

Efficient simulation of press hardening process through integrated structural and CFD analyses

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

Palaniswamy, Hariharasudhan; Mondalek, Pamela; Wronski, Maciek

Press hardened steel parts are being increasingly used in automotive structures for their higher strength to meet safety standards while reducing vehicle weight to improve fuel consumption. However, manufacturing of sheet metal parts by press hardening process to achieve desired properties is extremely challenging as it involves complex interaction of plastic deformation, metallurgical change, thermal distribution, and fluid flow. Numerical simulation is critical for successful design of the process and to understand the interaction among the numerous process parameters to control the press hardening process in order to consistently achieve desired part properties. Until now there has been no integratedmore » commercial software solution that can efficiently model the complete process from forming of the blank, heat transfer between the blank and tool, microstructure evolution in the blank, heat loss from tool to the fluid that flows through water channels in the tools. In this study, a numerical solution based on Altair HyperWorks® product suite involving RADIOSS®, a non-linear finite element based structural analysis solver and AcuSolve®, an incompressible fluid flow solver based on Galerkin Least Square Finite Element Method have been utilized to develop an efficient solution for complete press hardening process design and analysis. RADIOSS is used to handle the plastic deformation, heat transfer between the blank and tool, and microstructure evolution in the blank during cooling. While AcuSolve is used to efficiently model heat loss from tool to the fluid that flows through water channels in the tools. The approach is demonstrated through some case studies.« less

Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data.

PubMed

Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun

2017-03-01

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

NASA Technical Reports Server (NTRS)

Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.

1995-01-01

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Numerical Modeling of Nonlinear Thermodynamics in SMA Wires

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

Reynolds, D R; Kloucek, P

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associatedmore » with such materials.« less

A non-Fourier approach towards the analysis of heat transfer enhancement with water based nanofluids through a channel

NASA Astrophysics Data System (ADS)

Dil, Taimoor; Khan, M. Sabeel

2018-05-01

In this article, a non-Fourier approach to model the heat transfer phenomenon in nanofluids having application to automotive industry is studied. In this respect, a recently proposed hyperbolic heat flux equation is embedded into the heat energy equation and thereby incorporating the effect of thermal relaxation time. Nanofluids are formed by considering copper oxide (CuO), Titanium dioxide (TiO2) and Aluminum oxide (Al2O3) nano-solid particles in the base fluid. The flow governing system of PDEs along with boundary conditions is transformed into its respective coupled system of nonlinear ODEs using suitable similarity functions. Runge-Kutta-Fehlberg (RK-5) numerical scheme embedded with shooting method is implemented and used to solve the obtained boundary value problem. Numerical simulations are performed and tabulated to analyze the influence of solid volume fraction on local coefficient of skin-friction and Nusselt number. A comparison is made between the results by Fourier and present heat flux model. We conclude that the presented new approach is more general and thus allows predicting the influence of thermal relaxation time on the heat transfer characteristics. Moreover, consideration of present model over the Fourier model helps to predict the actual temporal behavior of solution.

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.

Mixed convective peristaltic flow of carbon nanotubes submerged in water using different thermal conductivity models.

PubMed

Hayat, T; Ahmed, Bilal; Abbasi, F M; Ahmad, B

2016-10-01

Single Walled Carbon Nanotubes (SWCNTs) are the advanced product of nanotechnology having notable mechanical and physical properties. Peristalsis of SWCNTs suspended in water through an asymmetric channel is examined. Such mechanism is studied in the presence of viscous dissipation, velocity slip, mixed convection, temperature jump and heat generation/absorption. Mathematical modeling is carried out under the low Reynolds number and long wavelength approximation. Resulting nonlinear system is solved using the perturbation technique for small Brinkman's number. Physical analysis and comparison of the results in light of three different thermal conductivity models is also provided. It is reported that the heat transfer rate at the boundary increases with an increase in the nanotubes volume fraction. The addition of nanotubes affects the pressure gradient during the peristaltic flow. Moreover, the maximum velocity of the fluid decreases due to addition of the nanotubes. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Peristalsis of nonconstant viscosity Jeffrey fluid with nanoparticles

NASA Astrophysics Data System (ADS)

Alvi, N.; Latif, T.; Hussain, Q.; Asghar, S.

Mixed convective peristaltic activity of variable viscosity nanofluids is addressed. Unlike the conventional consideration of constant viscosity; the viscosity is taken as temperature dependent. Constitutive relations for linear viscoelastic Jeffrey fluid are employed and uniform magnetic field is applied in the transverse direction. For nanofluids, the formulation is completed in presence of Brownian motion, thermophoresis, viscous dissipation and Joule heating. Consideration of temperature dependence of viscosity is not a choice but the realistic requirement of the wall temperature and the heat generated due to the viscous dissipation. Well established large wavelength and small Reynolds number approximations are invoked. Non-linear coupled system is analytically solved for the convergent series solutions identifying the interval of convergence explicitly. A comparative study between analytical and numerical solution is made for certainty. Influence of the parameters undertaken for the description of the problem is pointed out and its physics explained.

Collective effects and dynamics of non-adiabatic flame balls

NASA Astrophysics Data System (ADS)

D'Angelo, Yves; Joulin, Guy

2001-03-01

The dynamics of a homogeneous, polydisperse collection of non-adiabatic flame balls (FBs) is investigated by analytical/numerical means. A strongly temperature-dependent Arrhenius reaction rate is assumed, along with a light enough reactant characterized by a markedly less than unity Lewis number (Le). Combining activation-energy asymptotics with a mean-field type of treatment, the analysis yields a nonlinear integro-differential evolution equation (EE) for the FB population. The EE accounts for heat losses inside each FB and unsteadiness around it, as well as for its interactions with the entire FB population, namely mutual heating and faster (Le<1) consumption of the reactant pool. The initial FB number density and size distribution enter the EE explicitly. The latter is studied analytically at early times, then for small total FB number densities; it is subsequently solved numerically, yielding the whole population evolution and its lifetime. Generalizations and open questions relating to `spotty' turbulent combustion are finally evoked.

Computational Simulation of Thermal and Spattering Phenomena and Microstructure in Selective Laser Melting of Inconel 625

NASA Astrophysics Data System (ADS)

Özel, Tuğrul; Arısoy, Yiğit M.; Criales, Luis E.

Computational modelling of Laser Powder Bed Fusion (L-PBF) processes such as Selective laser Melting (SLM) can reveal information that is hard to obtain or unobtainable by in-situ experimental measurements. A 3D thermal field that is not visible by the thermal camera can be obtained by solving the 3D heat transfer problem. Furthermore, microstructural modelling can be used to predict the quality and mechanical properties of the product. In this paper, a nonlinear 3D Finite Element Method based computational code is developed to simulate the SLM process with different process parameters such as laser power and scan velocity. The code is further improved by utilizing an in-situ thermal camera recording to predict spattering which is in turn included as a stochastic heat loss. Then, thermal gradients extracted from the simulations applied to predict growth directions in the resulting microstructure.

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.

Unsteady MHD Mixed Convection Slip Flow of Casson Fluid over Nonlinearly Stretching Sheet Embedded in a Porous Medium with Chemical Reaction, Thermal Radiation, Heat Generation/Absorption and Convective Boundary Conditions

PubMed Central

Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas

2016-01-01

Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail. PMID:27776174

Theoretical analysis of non-linear Joule heating effects over an electro-thermal patterned flow

NASA Astrophysics Data System (ADS)

Sanchez, Salvador; Ascanio, Gabriel; Mendez, Federico; Bautista, Oscar

2017-11-01

In this work, non-linear Joule heating effects for electro-thermal patterned flows driven inside of a slit microchannel are analyzed. Here, the movement of fluids is controlled by placing electro-thermal forces, which are generated through an imposed longitudinal electric field, E0, and the wall electric potential produced by electrodes inserted along the surface of the microchannel wall, ζ. For this analysis, viscosity and electrical conductivity of fluids are included as known functions, which depend on the temperature; therefore, in order to determine the flow, temperature and electric potential fields together with its simultaneous interactions, the equations of continuity, momentum, energy, charges distribution and electrical current have to be solved in a coupled manner. The main results obtained in the study reveal that with the presence of thermal gradients along of the microchannel, local electro-thermal forces, Fχ, are affected in a sensible manner, and consequently, the flow field is modified substantially, causing the interruption or intensification of recirculations along of the microchannel. This work was supported by the Fondo SEP-CONACYT through research Grants No. 220900 and 20171181 from SIP-IPN. F. Mendez acknowledges support from PAPIIT-UNAM under Contract Number IN112215. S. Sanchez thanks to DGAPA-UNAM for the postdoctoral fellowship.

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

The convergence study of the homotopy analysis method for solving nonlinear Volterra-Fredholm integrodifferential equations.

PubMed

Ghanbari, Behzad

2014-01-01

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

A Heuristic Fast Method to Solve the Nonlinear Schroedinger Equation in Fiber Bragg Gratings with Arbitrary Shape Input Pulse

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

Emami, F.; Hatami, M.; Keshavarz, A. R.

2009-08-13

Using a combination of Runge-Kutta and Jacobi iterative method, we could solve the nonlinear Schroedinger equation describing the pulse propagation in FBGs. By decomposing the electric field to forward and backward components in fiber Bragg grating and utilizing the Fourier series analysis technique, the boundary value problem of a set of coupled equations governing the pulse propagation in FBG changes to an initial condition coupled equations which can be solved by simple Runge-Kutta method.

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1991-01-01

The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.

Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm

NASA Astrophysics Data System (ADS)

Kania, Adhe; Sidarto, Kuntjoro Adji

2016-02-01

Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.

A Differential Evolution Algorithm Based on Nikaido-Isoda Function for Solving Nash Equilibrium in Nonlinear Continuous Games

PubMed Central

He, Feng; Zhang, Wei; Zhang, Guoqiang

2016-01-01

A differential evolution algorithm for solving Nash equilibrium in nonlinear continuous games is presented in this paper, called NIDE (Nikaido-Isoda differential evolution). At each generation, parent and child strategy profiles are compared one by one pairwisely, adapting Nikaido-Isoda function as fitness function. In practice, the NE of nonlinear game model with cubic cost function and quadratic demand function is solved, and this method could also be applied to non-concave payoff functions. Moreover, the NIDE is compared with the existing Nash Domination Evolutionary Multiplayer Optimization (NDEMO), the result showed that NIDE was significantly better than NDEMO with less iterations and shorter running time. These numerical examples suggested that the NIDE method is potentially useful. PMID:27589229

Nonlinear analysis of composite thin-walled helicopter blades

NASA Astrophysics Data System (ADS)

Kalfon, J. P.; Rand, O.

Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

An adaptive grid algorithm for one-dimensional nonlinear equations

NASA Technical Reports Server (NTRS)

Gutierrez, William E.; Hills, Richard G.

1990-01-01

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

NASA Astrophysics Data System (ADS)

Mamehrashi, K.; Yousefi, S. A.

2017-02-01

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

Mixed convection flow of a nanofluid containing gyrotactic microorganisms over a stretching/shrinking sheet in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Aman, Fazlina; Mohamad Khazim, Wan Nor Hafizah Wan; Mansur, Syahira

2017-09-01

Interaction of motile microorganisms and nanoparticles along with buoyancy forces will produce nanofluid bioconvection. Bioconvection happened because of the microorganisms are imposed into the nanofluid to stabilize the nanoparticles to suspend. In this paper, we investigated the problem of mixed convection flow of a nanofluid combined with gyrotactic microorganisms over a stretching/shrinking sheet under the influence of magnetic field. The nonlinear partial differential equations are transformed into a set of five similarities nonlinear ordinary differential equations by using similarity transformation, before being solved numerically. Some of the governing parameters involve in this problem are magnetic parameter, stretching/shrinking parameter, Brownian motion parameter, thermophoresis parameter and Prandtl number. Using tables and graphs, the consequences of numerous parameters on the flow and heat transfer features are examined and discussed. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms are strongly affected by the governing parameters.

Numerical solution of mixed convection flow of an MHD Jeffery fluid over an exponentially stretching sheet in the presence of thermal radiation and chemical reaction

NASA Astrophysics Data System (ADS)

Shateyi, Stanford; Marewo, Gerald T.

2018-05-01

We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Recent developments of artificial intelligence in drying of fresh food: A review.

PubMed

Sun, Qing; Zhang, Min; Mujumdar, Arun S

2018-03-01

Intellectualization is an important direction of drying development and artificial intelligence (AI) technologies have been widely used to solve problems of nonlinear function approximation, pattern detection, data interpretation, optimization, simulation, diagnosis, control, data sorting, clustering, and noise reduction in different food drying technologies due to the advantages of self-learning ability, adaptive ability, strong fault tolerance and high degree robustness to map the nonlinear structures of arbitrarily complex and dynamic phenomena. This article presents a comprehensive review on intelligent drying technologies and their applications. The paper starts with the introduction of basic theoretical knowledge of ANN, fuzzy logic and expert system. Then, we summarize the AI application of modeling, predicting, and optimization of heat and mass transfer, thermodynamic performance parameters, and quality indicators as well as physiochemical properties of dried products in artificial biomimetic technology (electronic nose, computer vision) and different conventional drying technologies. Furthermore, opportunities and limitations of AI technique in drying are also outlined to provide more ideas for researchers in this area.

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.

Resonant Vibrations and Vibrational Heating of Physically Nonlinear Viscoelastic Shells and Their Damping Using Piezoelectric Sensor and Actuator

NASA Astrophysics Data System (ADS)

Kirichok, I. F.

2017-09-01

Forced axisymmetric resonant vibrations and vibrational heating of viscoelastic, physically nonlinear, closed, spherical, and infinitely long cylindrical shells and ring with piezoelectric sensor and actuator are considered. The effect of physical nonlinearity of passive material on the vibration amplitude and vibrational heating temperature is studied. The possibility of active damping of vibrations by piezoelectric sensors and actuators is demonstrated.

Solving a System of Nonlinear Algebraic Equations You Only Get Error Messages--What to Do Next?

ERIC Educational Resources Information Center

Shacham, Mordechai; Brauner, Neima

2017-01-01

Chemical engineering problems often involve the solution of systems of nonlinear algebraic equations (NLE). There are several software packages that can be used for solving NLE systems, but they may occasionally fail, especially in cases where the mathematical model contains discontinuities and/or regions where some of the functions are undefined.…

Solving Nonlinear Euler Equations with Arbitrary Accuracy

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2005-01-01

A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

Cumulants of heat transfer across nonlinear quantum systems

NASA Astrophysics Data System (ADS)

Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

2013-12-01

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

Thermophysical effects of carbon nanotubes on MHD flow over a stretching surface

NASA Astrophysics Data System (ADS)

Ul Haq, Rizwan; Khan, Zafar Hayat; Khan, Waqar Ahmed

2014-09-01

This article is intended for investigating the effects of magnetohydrodynamics (MHD) and volume fraction of carbon nanotubes (CNTs) on the flow and heat transfer in two lateral directions over a stretching sheet. For this purpose, three types of base fluids specifically water, ethylene glycol and engine oil with single and multi-walled carbon nanotubes are used in the analysis. The convective boundary condition in the presence of CNTs is presented first time and not been explored so far. The transformed nonlinear differential equations are solved by the Runge-Kutta-Fehlberg method with a shooting technique. The dimensionless velocity and shear stress are obtained in both directions. The dimensionless heat transfer is determined on the surface. Three different models of thermal conductivity are comparable for both CNTs and it is found that the Xue [1] model gives the best approach to guess the superb thermal conductivity in comparison with the Maxwell [2] and Hamilton and Crosser [3] models. And finally, another finding suggests the engine oil provides the highest skin friction and heat transfer rates.

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.

Modeling the heat transfer problem for the novel combined cryosurgery and hyperthermia system.

PubMed

Zhao, Gang; Bai, Xue-Fei; Luo, Da-Wei; Gao, Da-Yong

2006-01-01

A multidimensional, finite element analysis (FEA) for the freezing, holding, rewarming and heating processes of biological tissues during the cryosurgery process of the new Combined Cryosurgery/Hyperthermia System is presented to theoretically test its validity. The tissues are treated as nonideal materials freezing over a temperature range, and the thermophysical properties of which are temperature dependent. The enthalpy method is applied to solve the highly nonlinear problem. It was found that when the same boundary condition and the same target tissue presented, the novel Cryosurgery/Hyperthermia System could supply the target tissue an approximative cooling rate, a much lower minimal temperature, a much greater warming rate, and a much greater thermal gradients compared with that of the simplified Endocare system. The numerical simulation indicates that the novel combined cryosurgery and hyperthermia system can provide an excellent curative effect in the corresponding cryotherapy. And the most attractive feature of this FEA framework is that it can be easily mastered by the surgeon without in-depth theory of heat transfer to analyze the cryosurgery process beforehand due to the friendly GUI (graphical user interface) of Ansys software.

Mathematical simulation and optimization of cutting mode in turning of workpieces made of nickel-based heat-resistant alloy

NASA Astrophysics Data System (ADS)

Bogoljubova, M. N.; Afonasov, A. I.; Kozlov, B. N.; Shavdurov, D. E.

2018-05-01

A predictive simulation technique of optimal cutting modes in the turning of workpieces made of nickel-based heat-resistant alloys, different from the well-known ones, is proposed. The impact of various factors on the cutting process with the purpose of determining optimal parameters of machining in concordance with certain effectiveness criteria is analyzed in the paper. A mathematical model of optimization, algorithms and computer programmes, visual graphical forms reflecting dependences of the effectiveness criteria – productivity, net cost, and tool life on parameters of the technological process - have been worked out. A nonlinear model for multidimensional functions, “solution of the equation with multiple unknowns”, “a coordinate descent method” and heuristic algorithms are accepted to solve the problem of optimization of cutting mode parameters. Research shows that in machining of workpieces made from heat-resistant alloy AISI N07263, the highest possible productivity will be achieved with the following parameters: cutting speed v = 22.1 m/min., feed rate s=0.26 mm/rev; tool life T = 18 min.; net cost – 2.45 per hour.

On radiative heat transfer in stagnation point flow of MHD Carreau fluid over a stretched surface

NASA Astrophysics Data System (ADS)

Khan, Masood; Sardar, Humara; Mudassar Gulzar, M.

2018-03-01

This paper investigates the behavior of MHD stagnation point flow of Carreau fluid in the presence of infinite shear rate viscosity. Additionally heat transfer analysis in the existence of non-linear radiation with convective boundary condition is performed. Moreover effects of Joule heating is observed and mathematical analysis is presented in the presence of viscous dissipation. The suitable transformations are employed to alter the leading partial differential equations to a set of ordinary differential equations. The subsequent non-straight common ordinary differential equations are solved numerically by an effective numerical approach specifically Runge-Kutta Fehlberg method alongside shooting technique. It is found that the higher values of Hartmann number (M) correspond to thickening of the thermal and thinning of momentum boundary layer thickness. The analysis further reveals that the fluid velocity is diminished by increasing the viscosity ratio parameter (β∗) and opposite trend is observed for temperature profile for both hydrodynamic and hydromagnetic flows. In addition the momentum boundary layer thickness is increased with velocity ratio parameter (α) and opposite is true for thermal boundary layer thickness.

Robustness analysis of an air heating plant and control law by using polynomial chaos

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

Colón, Diego; Ferreira, Murillo A. S.; Bueno, Átila M.

2014-12-10

This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputsmore » (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.« less

An advanced model of heat and mass transfer in the protective clothing - verification

NASA Astrophysics Data System (ADS)

Łapka, P.; Furmański, P.

2016-09-01

The paper presents an advanced mathematical and numerical models of heat and mass transfer in the multi-layers protective clothing and in elements of the experimental stand subjected to either high surroundings temperature or high radiative heat flux emitted by hot objects. The model included conductive-radiative heat transfer in the hygroscopic porous fabrics and air gaps as well as conductive heat transfer in components of the stand. Additionally, water vapour diffusion in the pores and air spaces as well as phase transition of the bound water in the fabric fibres (sorption and desorption) were accounted for. The thermal radiation was treated in the rigorous way e.g.: semi-transparent absorbing, emitting and scattering fabrics were assumed a non-grey and all optical phenomena at internal or external walls were modelled. The air was assumed transparent. Complex energy and mass balance as well as optical conditions at internal or external interfaces were formulated in order to find exact values of temperatures, vapour densities and radiation intensities at these interfaces. The obtained highly non-linear coupled system of discrete equation was solve by the in-house iterative algorithm which was based on the Finite Volume Method. The model was then successfully partially verified against the results obtained from commercial software for simplified cases.

Transverse transport of Fe3O4-H2O with viscosity variation under pure internal heating

NASA Astrophysics Data System (ADS)

Mehmood, Rashid; Tabassum, R.

2018-05-01

Smart fluids are the fluids whose properties can be changed by applying an electric or a magnetic field. Such type of fluid finds tremendous applications in electronic devices, semi-active dampers, magnetic resonance imaging, in space craft propulsion and many more. This communication addresses water based magneto ferrofluid striking at a stretching surface in an oblique manner. In order to present physically realistic analysis, viscosity is assumed to be dependent upon temperature as well as volume fraction of magnetite nanoparticle. The flow governing problem is altered into nonlinear coupled system of ordinary differential equations via scaling transformation which is then solved numerically by means of Runge-kutta Fehlberg scheme. Impact of sundry parameters such as magnetic field parameter, nanoparticle volume fraction, heat generation parameter and variable viscosity parameter on velocity and temperature profile of magneto ferrofluid is presented graphically and discussed in a physical manner. Practical measures of interest namely skin friction and heat flux at the surface are computed. Streamline patterns are traced out to examine the flow pattern. It is found that skin friction and rate of heat transfer at the wall enhances by strengthening the applied magnetic field. Local heat flux can also be enhanced with increasing the volume fraction of magnetite nanoparticles.

Similar solutions of double-diffusive dissipative layers along free surfaces

NASA Astrophysics Data System (ADS)

Napolitano, L. G.; Viviani, A.; Savino, R.

1990-10-01

Free convection due to buoyant forces (natural convection) and surface tension gradients (Marangoni convection) generated by temperature and concentration gradients is discussed together with the formation of double-diffusive boundary layers along liquid-gas interfaces. Similarity solutions for each class of free convection are derived and the resulting nonlinear two-point problems are solved numerically using the quasi-linearization method. Velocity, temperature, concentration profiles, interfacial velocity, heat and mass transfer bulk coefficients for various Prandtl and Schmidt numbers, and different values of the similarity parameters are determined. The convective flows are of particular interest because they are considered to influence the processes of crystal growth, both on earth and in a microgravity environment.

Numerical investigation of velocity slip and temperature jump effects on unsteady flow over a stretching permeable surface

NASA Astrophysics Data System (ADS)

Hosseini, E.; Loghmani, G. B.; Heydari, M.; Rashidi, M. M.

2017-02-01

In this paper, the boundary layer flow and heat transfer of unsteady flow over a porous accelerating stretching surface in the presence of the velocity slip and temperature jump effects are investigated numerically. A new effective collocation method based on rational Bernstein functions is applied to solve the governing system of nonlinear ordinary differential equations. This method solves the problem on the semi-infinite domain without truncating or transforming it to a finite domain. In addition, the presented method reduces the solution of the problem to the solution of a system of algebraic equations. Graphical and tabular results are presented to investigate the influence of the unsteadiness parameter A , Prandtl number Pr, suction parameter fw, velocity slip parameter γ and thermal slip parameter φ on the velocity and temperature profiles of the fluid. The numerical experiments are reported to show the accuracy and efficiency of the novel proposed computational procedure. Comparisons of present results are made with those obtained by previous works and show excellent agreement.

Demonstration of leapfrogging for implementing nonlinear model predictive control on a heat exchanger.

PubMed

Sridhar, Upasana Manimegalai; Govindarajan, Anand; Rhinehart, R Russell

2016-01-01

This work reveals the applicability of a relatively new optimization technique, Leapfrogging, for both nonlinear regression modeling and a methodology for nonlinear model-predictive control. Both are relatively simple, yet effective. The application on a nonlinear, pilot-scale, shell-and-tube heat exchanger reveals practicability of the techniques. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

The U.S. Geological Survey Modular Ground-Water Model - PCGN: A Preconditioned Conjugate Gradient Solver with Improved Nonlinear Control

USGS Publications Warehouse

Naff, Richard L.; Banta, Edward R.

2008-01-01

The preconditioned conjugate gradient with improved nonlinear control (PCGN) package provides addi-tional means by which the solution of nonlinear ground-water flow problems can be controlled as compared to existing solver packages for MODFLOW. Picard iteration is used to solve nonlinear ground-water flow equations by iteratively solving a linear approximation of the nonlinear equations. The linear solution is provided by means of the preconditioned conjugate gradient algorithm where preconditioning is provided by the modi-fied incomplete Cholesky algorithm. The incomplete Cholesky scheme incorporates two levels of fill, 0 and 1, in which the pivots can be modified so that the row sums of the preconditioning matrix and the original matrix are approximately equal. A relaxation factor is used to implement the modified pivots, which determines the degree of modification allowed. The effects of fill level and degree of pivot modification are briefly explored by means of a synthetic, heterogeneous finite-difference matrix; results are reported in the final section of this report. The preconditioned conjugate gradient method is coupled with Picard iteration so as to efficiently solve the nonlinear equations associated with many ground-water flow problems. The description of this coupling of the linear solver with Picard iteration is a primary concern of this document.

Enhancement of ohmic and stochastic heating by resonance effects in capacitive radio frequency discharges: a theoretical approach.

PubMed

Mussenbrock, T; Brinkmann, R P; Lieberman, M A; Lichtenberg, A J; Kawamura, E

2008-08-22

In low-pressure capacitive radio frequency discharges, two mechanisms of electron heating are dominant: (i) Ohmic heating due to collisions of electrons with neutrals of the background gas and (ii) stochastic heating due to momentum transfer from the oscillating boundary sheath. In this work we show by means of a nonlinear global model that the self-excitation of the plasma series resonance which arises in asymmetric capacitive discharges due to nonlinear interaction of plasma bulk and sheath significantly affects both Ohmic heating and stochastic heating. We observe that the series resonance effect increases the dissipation by factors of 2-5. We conclude that the nonlinear plasma dynamics should be taken into account in order to describe quantitatively correct electron heating in asymmetric capacitive radio frequency discharges.

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

Xie, Dexuan

1996-01-01

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

NASA Astrophysics Data System (ADS)

Vasant, Pandian

2011-06-01

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

A Method to Solve Interior and Exterior Camera Calibration Parameters for Image Resection

NASA Technical Reports Server (NTRS)

Samtaney, Ravi

1999-01-01

An iterative method is presented to solve the internal and external camera calibration parameters, given model target points and their images from one or more camera locations. The direct linear transform formulation was used to obtain a guess for the iterative method, and herein lies one of the strengths of the present method. In all test cases, the method converged to the correct solution. In general, an overdetermined system of nonlinear equations is solved in the least-squares sense. The iterative method presented is based on Newton-Raphson for solving systems of nonlinear algebraic equations. The Jacobian is analytically derived and the pseudo-inverse of the Jacobian is obtained by singular value decomposition.

Heat Transfer in Complex Fluids

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

Mehrdad Massoudi

Amongst the most important constitutive relations in Mechanics, when characterizing the behavior of complex materials, one can identify the stress tensor T, the heat flux vector q (related to heat conduction) and the radiant heating (related to the radiation term in the energy equation). Of course, the expression 'complex materials' is not new. In fact, at least since the publication of the paper by Rivlin & Ericksen (1955), who discussed fluids of complexity (Truesdell & Noll, 1992), to the recently published books (Deshpande et al., 2010), the term complex fluids refers in general to fluid-like materials whose response, namely themore » stress tensor, is 'non-linear' in some fashion. This non-linearity can manifest itself in variety of forms such as memory effects, yield stress, creep or relaxation, normal-stress differences, etc. The emphasis in this chapter, while focusing on the constitutive modeling of complex fluids, is on granular materials (such as coal) and non-linear fluids (such as coal-slurries). One of the main areas of interest in energy related processes, such as power plants, atomization, alternative fuels, etc., is the use of slurries, specifically coal-water or coal-oil slurries, as the primary fuel. Some studies indicate that the viscosity of coal-water mixtures depends not only on the volume fraction of solids, and the mean size and the size distribution of the coal, but also on the shear rate, since the slurry behaves as shear-rate dependent fluid. There are also studies which indicate that preheating the fuel results in better performance, and as a result of such heating, the viscosity changes. Constitutive modeling of these non-linear fluids, commonly referred to as non-Newtonian fluids, has received much attention. Most of the naturally occurring and synthetic fluids are non-linear fluids, for example, polymer melts, suspensions, blood, coal-water slurries, drilling fluids, mud, etc. It should be noted that sometimes these fluids show Newtonian (linear) behavior for a given range of parameters or geometries; there are many empirical or semi-empirical constitutive equations suggested for these fluids. There have also been many non-linear constitutive relations which have been derived based on the techniques of continuum mechanics. The non-linearities oftentimes appear due to higher gradient terms or time derivatives. When thermal and or chemical effects are also important, the (coupled) momentum and energy equations can give rise to a variety of interesting problems, such as instability, for example the phenomenon of double-diffusive convection in a fluid layer. In Conclusion, we have studied the flow of a compressible (density gradient type) non-linear fluid down an inclined plane, subject to radiation boundary condition. The heat transfer is also considered where a source term, similar to the Arrhenius type reaction, is included. The non-dimensional forms of the equations are solved numerically and the competing effects of conduction, dissipation, heat generation and radiation are discussed. It is observed that the velocity increases rapidly in the region near the inclined surface and is slower in the region near the free surface. Since R{sub 7} is a measure of the heat generation due to chemical reaction, when the reaction is frozen (R{sub 7}=0.0) the temperature distributions would depend only on R{sub 1}, and R{sub 2}, representing the effects of the pressure force developed in the material due to the distribution, R{sub 3} and R{sub 4} viscous dissipation, R{sub 5} the normal stress coefficient, R{sub 6} the measure of the emissivity of the particles to the thermal conductivity, etc. When the flow is not frozen (RP{sub 7} > 0) the temperature inside the flow domain is much higher than those at the inclined and free surfaces. As a result, heat is transferred away from the flow toward both the inclined surface and the free surface with a rate that increases as R{sub 7} increases. For a given temperature, an increase in {zeta} implies that the activation energy is smaller and thus, the reaction rate is increased leading to an increase in the heat of the reaction. As a result the flow is chemically heated and its temperature increase. The results shown here indicate that for all values of {zeta} used the chemical effects are significant and the temperature is always higher than both the surface temperature and the free surface temperature. The heat transfer is always from the flow toward both the inclined surface and the free stream. It is also noticed that for all values of m chosen in this study, the temperature is higher than the surface and the free stream temperature. The heat transfer at the inclined surface and at the free stream increase slowly for negative values of m to about m=0.5, but it begins to significantly increase for m greater than 0.5.« less

The program FANS-3D (finite analytic numerical simulation 3-dimensional) and its applications

NASA Technical Reports Server (NTRS)

Bravo, Ramiro H.; Chen, Ching-Jen

1992-01-01

In this study, the program named FANS-3D (Finite Analytic Numerical Simulation-3 Dimensional) is presented. FANS-3D was designed to solve problems of incompressible fluid flow and combined modes of heat transfer. It solves problems with conduction and convection modes of heat transfer in laminar flow, with provisions for radiation and turbulent flows. It can solve singular or conjugate modes of heat transfer. It also solves problems in natural convection, using the Boussinesq approximation. FANS-3D was designed to solve heat transfer problems inside one, two and three dimensional geometries that can be represented by orthogonal planes in a Cartesian coordinate system. It can solve internal and external flows using appropriate boundary conditions such as symmetric, periodic and user specified.

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma

NASA Astrophysics Data System (ADS)

Tolba, R. E.; El-Bedwehy, N. A.; Moslem, W. M.; El-Labany, S. K.; Yahia, M. E.

2016-01-01

Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.

Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma

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

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com; Moslem, W. M., E-mail: wmmoslem@hotmail.com

2016-01-15

Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

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.

Krylov subspace methods - Theory, algorithms, and applications

NASA Technical Reports Server (NTRS)

Sad, Youcef

1990-01-01

Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

Wave-Kinetic Simulations of the Nonlinear Generation of Electromagnetic VLF Waves through Velocity Ring Instabilities

NASA Astrophysics Data System (ADS)

Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.

2014-12-01

Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].

Implicit time-integration method for simultaneous solution of a coupled non-linear system

NASA Astrophysics Data System (ADS)

Watson, Justin Kyle

Historically large physical problems have been divided into smaller problems based on the physics involved. This is no different in reactor safety analysis. The problem of analyzing a nuclear reactor for design basis accidents is performed by a handful of computer codes each solving a portion of the problem. The reactor thermal hydraulic response to an event is determined using a system code like TRAC RELAP Advanced Computational Engine (TRACE). The core power response to the same accident scenario is determined using a core physics code like Purdue Advanced Core Simulator (PARCS). Containment response to the reactor depressurization in a Loss Of Coolant Accident (LOCA) type event is calculated by a separate code. Sub-channel analysis is performed with yet another computer code. This is just a sample of the computer codes used to solve the overall problems of nuclear reactor design basis accidents. Traditionally each of these codes operates independently from each other using only the global results from one calculation as boundary conditions to another. Industry's drive to uprate power for reactors has motivated analysts to move from a conservative approach to design basis accident towards a best estimate method. To achieve a best estimate calculation efforts have been aimed at coupling the individual physics models to improve the accuracy of the analysis and reduce margins. The current coupling techniques are sequential in nature. During a calculation time-step data is passed between the two codes. The individual codes solve their portion of the calculation and converge to a solution before the calculation is allowed to proceed to the next time-step. This thesis presents a fully implicit method of simultaneous solving the neutron balance equations, heat conduction equations and the constitutive fluid dynamics equations. It discusses the problems involved in coupling different physics phenomena within multi-physics codes and presents a solution to these problems. The thesis also outlines the basic concepts behind the nodal balance equations, heat transfer equations and the thermal hydraulic equations, which will be coupled to form a fully implicit nonlinear system of equations. The coupling of separate physics models to solve a larger problem and improve accuracy and efficiency of a calculation is not a new idea, however implementing them in an implicit manner and solving the system simultaneously is. Also the application to reactor safety codes is new and has not be done with thermal hydraulics and neutronics codes on realistic applications in the past. The coupling technique described in this thesis is applicable to other similar coupled thermal hydraulic and core physics reactor safety codes. This technique is demonstrated using coupled input decks to show that the system is solved correctly and then verified by using two derivative test problems based on international benchmark problems the OECD/NRC Three mile Island (TMI) Main Steam Line Break (MSLB) problem (representative of pressurized water reactor analysis) and the OECD/NRC Peach Bottom (PB) Turbine Trip (TT) benchmark (representative of boiling water reactor analysis).

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

2017-11-01

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

PubMed

Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

2017-09-01

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Adaptive Neural Networks Prescribed Performance Control Design for Switched Interconnected Uncertain Nonlinear Systems.

PubMed

Li, Yongming; Tong, Shaocheng

2017-06-28

In this paper, an adaptive neural networks (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) Collocation Method for Solving Linear and Nonlinear Fokker-Planck Equations

NASA Astrophysics Data System (ADS)

Parand, K.; Latifi, S.; Moayeri, M. M.; Delkhosh, M.

2018-05-01

In this study, we have constructed a new numerical approach for solving the time-dependent linear and nonlinear Fokker-Planck equations. In fact, we have discretized the time variable with Crank-Nicolson method and for the space variable, a numerical method based on Generalized Lagrange Jacobi Gauss-Lobatto (GLJGL) collocation method is applied. It leads to in solving the equation in a series of time steps and at each time step, the problem is reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. One can observe that the proposed method is simple and accurate. Indeed, one of its merits is that it is derivative-free and by proposing a formula for derivative matrices, the difficulty aroused in calculation is overcome, along with that it does not need to calculate the General Lagrange basis and matrices; they have Kronecker property. Linear and nonlinear Fokker-Planck equations are given as examples and the results amply demonstrate that the presented method is very valid, effective, reliable and does not require any restrictive assumptions for nonlinear terms.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Mechanisms of double stratification and magnetic field in flow of third grade fluid over a slendering stretching surface with variable thermal conductivity

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir

2018-03-01

This article addresses the magnetohydrodynamic (MHD) stagnation point flow of third grade fluid towards a nonlinear stretching sheet. Energy expression is based through involvement of variable thermal conductivity. Heat and mass transfer aspects are described within the frame of double stratification effects. Boundary layer partial differential systems are deduced. Governing systems are then converted into ordinary differential systems by invoking appropriate variables. The transformed expressions are solved through homotopic technique. Impact of embedded variables on velocity, thermal and concentration fields are displayed and argued. Numerical computations are presented to obtain the results of skin friction coefficient and local Nusselt and Sherwood numbers. It is revealed that larger values of magnetic parameter reduces the velocity field while reverse situation is noticed due to wall thickness variable. Temperature field and local Nusselt number are quite reverse for heat generation/absorption parameter. Moreover qualitative behaviors of concentration field and local Sherwood number are similar for solutal stratification parameter.

Flow and Heat Transfer in Sisko Fluid with Convective Boundary Condition

PubMed Central

Malik, Rabia; Khan, Masood; Munir, Asif; Khan, Waqar Azeem

2014-01-01

In this article, we have studied the flow and heat transfer in Sisko fluid with convective boundary condition over a non-isothermal stretching sheet. The flow is influenced by non-linearly stretching sheet in the presence of a uniform transverse magnetic field. The partial differential equations governing the problem have been reduced by similarity transformations into the ordinary differential equations. The transformed coupled ordinary differential equations are then solved analytically by using the homotopy analysis method (HAM) and numerically by the shooting method. Effects of different parameters like power-law index , magnetic parameter , stretching parameter , generalized Prandtl number Pr and generalized Biot number are presented graphically. It is found that temperature profile increases with the increasing value of and whereas it decreases for . Numerical values of the skin-friction coefficient and local Nusselt number are tabulated at various physical situations. In addition, a comparison between the HAM and exact solutions is also made as a special case and excellent agreement between results enhance a confidence in the HAM results. PMID:25285822

Self-consistent description of a system of interacting phonons

NASA Astrophysics Data System (ADS)

Poluektov, Yu. M.

2015-11-01

A proposal for a method of self-consistent description of phonon systems. This method generalizes the Debye model to account for phonon-phonon interaction. The idea of "self-consistent" phonons is introduced; their speed depends on the temperature and is determined by solving a non-linear equation. The Debye energy is also a function of the temperature within the framework of the proposed approach. The thermodynamics of "self-consistent" phonon gas are built. It is shown that at low temperatures the cubic law temperature dependence of specific heat acquires an additional term that is proportional to the seventh power of the temperature. This seems to explain the reason why the cubic law for specific heat is observed only at relatively low temperatures. At high temperatures, the theory predicts a linear deviation with respect to temperature from the Dulong-Petit law, which is observed experimentally. A modification to the melting criteria is considered, to account for the phonon-phonon interaction.

Analysis of unsteady compressible viscous layers

NASA Technical Reports Server (NTRS)

Power, G. D.; Verdon, J. M.; Kousen, K. A.

1990-01-01

The development of an analysis to predict the unsteady compressible flows in blade boundary layers and wakes is presented. The equations that govern the flows in these regions are transformed using an unsteady turbulent generalization of the Levy-Lees transformation. The transformed equations are solved using a finite difference technique in which the solution proceeds by marching in time and in the streamwise direction. Both laminar and turbulent flows are studied, the latter using algebraic turbulence and transition models. Laminar solutions for a flat plate are shown to approach classical asymptotic results for both high and low frequency unsteady motions. Turbulent flat-plate results are in qualitative agreement with previous predictions and measurements. Finally, the numerical technique is also applied to the stator and rotor of a low-speed turbine stage to determine unsteady effects on surface heating. The results compare reasonably well with measured heat transfer data and indicate that nonlinear effects have minimal impact on the mean and unsteady components of the flow.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

PubMed

Li, Yongming; Tong, Shaocheng

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

NASA Astrophysics Data System (ADS)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Computer codes for thermal analysis of a solid rocket motor nozzle

NASA Technical Reports Server (NTRS)

Chauhan, Rajinder Singh

1988-01-01

A number of computer codes are available for performing thermal analysis of solid rocket motor nozzles. Aerotherm Chemical Equilibrium (ACE) computer program can be used to perform one-dimensional gas expansion to determine the state of the gas at each location of a nozzle. The ACE outputs can be used as input to a computer program called Momentum/Energy Integral Technique (MEIT) for predicting boundary layer development development, shear, and heating on the surface of the nozzle. The output from MEIT can be used as input to another computer program called Aerotherm Charring Material Thermal Response and Ablation Program (CMA). This program is used to calculate oblation or decomposition response of the nozzle material. A code called Failure Analysis Nonlinear Thermal and Structural Integrated Code (FANTASTIC) is also likely to be used for performing thermal analysis of solid rocket motor nozzles after the program is duly verified. A part of the verification work on FANTASTIC was done by using one and two dimension heat transfer examples with known answers. An attempt was made to prepare input for performing thermal analysis of the CCT nozzle using the FANTASTIC computer code. The CCT nozzle problem will first be solved by using ACE, MEIT, and CMA. The same problem will then be solved using FANTASTIC. These results will then be compared for verification of FANTASTIC.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

A Jacobi collocation approximation for nonlinear coupled viscous Burgers' equation

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohamed A.; Hafez, Ramy M.

2014-02-01

This article presents a numerical approximation of the initial-boundary nonlinear coupled viscous Burgers' equation based on spectral methods. A Jacobi-Gauss-Lobatto collocation (J-GL-C) scheme in combination with the implicit Runge-Kutta-Nyström (IRKN) scheme are employed to obtain highly accurate approximations to the mentioned problem. This J-GL-C method, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled viscous Burgers' equation to a system of nonlinear ordinary differential equation which is far easier to solve. The given examples show, by selecting relatively few J-GL-C points, the accuracy of the approximations and the utility of the approach over other analytical or numerical methods. The illustrative examples demonstrate the accuracy, efficiency, and versatility of the proposed algorithm.

Drift-Alfven eigenmodes in inhomogeneous plasma

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

Vranjes, J.; Poedts, S.

2006-03-15

A set of three nonlinear equations describing drift-Alfven waves in a nonuniform magnetized plasma is derived and discussed both in linear and nonlinear limits. In the case of a cylindric radially bounded plasma with a Gaussian density distribution in the radial direction the linearized equations are solved exactly yielding general solutions for modes with quantized frequencies and with radially dependent amplitudes. The full set of nonlinear equations is also solved yielding particular solutions in the form of rotating radially limited structures. The results should be applicable to the description of electromagnetic perturbations in solar magnetic structures and in astrophysical column-likemore » objects including cosmic tornados.« less

Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

DOE PAGES

Willert, Jeffrey; Park, H.; Taitano, William

2015-11-01

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

PubMed

Wang, Xinghu; Hong, Yiguang; Ji, Haibo

2016-07-01

The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

NR-code: Nonlinear reconstruction code

NASA Astrophysics Data System (ADS)

Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

2018-04-01

NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

Nonlinear radiated MHD flow of nanoliquids due to a rotating disk with irregular heat source and heat flux condition

NASA Astrophysics Data System (ADS)

Mahanthesh, B.; Gireesha, B. J.; Shehzad, S. A.; Rauf, A.; Kumar, P. B. Sampath

2018-05-01

This research is made to visualize the nonlinear radiated flow of hydromagnetic nano-fluid induced due to rotation of the disk. The considered nano-fluid is a mixture of water and Ti6Al4V or AA7072 nano-particles. The various shapes of nanoparticles like lamina, column, sphere, tetrahedron and hexahedron are chosen in the analysis. The irregular heat source and nonlinear radiative terms are accounted in the law of energy. We used the heat flux condition instead of constant surface temperature condition. Heat flux condition is more relativistic and according to physical nature of the problem. The problem is made dimensionless with the help of suitable similarity constraints. The Runge-Kutta-Fehlberg scheme is adopted to find the numerical solutions of governing nonlinear ordinary differential systems. The solutions are plotted by considering the various values of emerging physical constraints. The effects of various shapes of nanoparticles are drawn and discussed.

Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary

NASA Astrophysics Data System (ADS)

Khan, W. A.; Khan, Z. H.; Rahi, M.

2014-06-01

Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302-307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Modeling water vapor and heat transfer in the normal and the intubated airways.

PubMed

Tawhai, Merryn H; Hunter, Peter J

2004-04-01

Intubation of the artificially ventilated patient with an endotracheal tube bypasses the usual conditioning regions of the nose and mouth. In this situation any deficit in heat or moisture in the air is compensated for by evaporation and thermal transfer from the pulmonary airway walls. To study the dynamics of heat and water transport in the intubated airway, a coupled system of nonlinear equations is solved in airway models with symmetric geometry and anatomically based geometry. Radial distribution of heat, water vapor, and velocity in the airway are described by power-law equations. Solution of the time-dependent system of equations yields dynamic airstream and mucosal temperatures and air humidity. Comparison of model results with two independent experimental studies in the normal and intubated airway shows a close correlation over a wide range of minute ventilation. Using the anatomically based model a range of spatially distributed temperature paths is demonstrated, which highlights the model's ability to predict thermal behavior in airway regions currently inaccessible to measurement. Accurate representation of conducting airway geometry is shown to be necessary for simulating mouth-breathing at rates between 15 and 100 l x min(-1), but symmetric geometry is adequate for the low minute ventilation and warm inspired air conditions that are generally supplied to the intubated patient.

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

2018-04-01

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

A note on the generation of phase plane plots on a digital computer. [for solution of nonlinear differential equations

NASA Technical Reports Server (NTRS)

Simon, M. K.

1980-01-01

A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated.

Solving Nonlinear Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

NASA Astrophysics Data System (ADS)

Kakhktsyan, V. M.; Khachatryan, A. Kh.

2013-07-01

A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

Computational aspects in high intensity ultrasonic surgery planning.

PubMed

Pulkkinen, A; Hynynen, K

2010-01-01

Therapeutic ultrasound treatment planning is discussed and computational aspects regarding it are reviewed. Nonlinear ultrasound simulations were solved with a combined frequency domain Rayleigh and KZK model. Ultrasonic simulations were combined with thermal simulations and were used to compute heating of muscle tissue in vivo for four different focused ultrasound transducers. The simulations were compared with measurements and good agreement was found for large F-number transducers. However, at F# 1.9 the simulated rate of temperature rise was approximately a factor of 2 higher than the measured ones. The power levels used with the F# 1 transducer were too low to show any nonlinearity. The simulations were used to investigate the importance of nonlinarities generated in the coupling water, and also the importance of including skin in the simulations. Ignoring either of these in the model would lead to larger errors. Most notably, the nonlinearities generated in the water can enhance the focal temperature by more than 100%. The simulations also demonstrated that pulsed high power sonications may provide an opportunity to significantly (up to a factor of 3) reduce the treatment time. In conclusion, nonlinear propagation can play an important role in shaping the energy distribution during a focused ultrasound treatment and it should not be ignored in planning. However, the current simulation methods are accurate only with relatively large F-numbers and better models need to be developed for sharply focused transducers. Copyright 2009 Elsevier Ltd. All rights reserved.

Investigating physical field effects on the size-dependent dynamic behavior of inhomogeneous nanoscale plates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Reza Barati, Mohammad

2017-02-01

This article investigates the thermo-mechanical vibration frequencies of magneto-electro-thermo-elastic functionally graded (METE-FG) nanoplates in the framework of refined four-unknown shear deformation plate theory. The present nanoplate is subjected to various kinds of thermal loads with uniform, linear and nonlinear distributions. The nonlinear distribution is considered as heat conduction and sinusoidal temperature rise. The present refined theory captures the influences of shear deformations without the need for shear correction factors. Thermo-magneto-electro-elastic coefficients of the FG nanoplate vary gradually along the thickness according to the power-law form. The scale coefficient is taken into consideration implementing the nonlocal elasticity of Eringen. The governing equations are derived through Hamilton's principle and are solved analytically. The frequency response is compared with those of previously published data. The obtained results are presented for the thermo-mechanical vibrations of the FG nanobeams to investigate the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

A similarity solution of time dependent MHD liquid film flow over stretching sheet with variable physical properties

NASA Astrophysics Data System (ADS)

Idrees, M.; Rehman, Sajid; Shah, Rehan Ali; Ullah, M.; Abbas, Tariq

2018-03-01

An analysis is performed for the fluid dynamics incorporating the variation of viscosity and thermal conductivity on an unsteady two-dimensional free surface flow of a viscous incompressible conducting fluid taking into account the effect of a magnetic field. Surface tension quadratically vary with temperature while fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The boundary layer partial differential equations in cartesian coordinates are transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformation. The developed nonlinear equations are solved analytically by Homotopy Analysis Method (HAM) while numerically by using the shooting method. The Effects of natural parameters such as the variable viscosity parameter A, variable thermal conductivity parameter N, Hartmann number Ma, film Thickness, unsteadiness parameter S, Thermocapillary number M and Prandtl number Pr on the velocity and temperature profiles are investigated. The results for the surface skin friction coefficient f″ (0) , Nusselt number (heat flux) -θ‧ (0) and free surface temperature θ (1) are presented graphically and in tabular form.

Design and Validation of a Ten-Port Waveguide Reflectometer Sensor: Application to Efficiency Measurement and Optimization of Microwave-Heating Ovens

PubMed Central

Pedreño-Molina, Juan L.; Monzó-Cabrera, Juan; Lozano-Guerrero, Antonio; Toledo-Moreo, Ana

2008-01-01

This work presents the design, manufacturing process, calibration and validation of a new microwave ten-port waveguide reflectometer based on the use of neural networks. This low-cost novel device solves some of the shortcomings of previous reflectometers such as non-linear behavior of power sensors, noise presence and the complexity of the calibration procedure, which is often based on complex mathematical equations. These problems, which imply the reduction of the reflection coefficient measurement accuracy, have been overcome by using a higher number of probes than usual six-port configurations and by means of the use of Radial Basis Function (RBF) neural networks in order to reduce the influence of noise and non-linear processes over the measurements. Additionally, this sensor can be reconfigured whenever some of the eight coaxial power detectors fail, still providing accurate values in real time. The ten-port performance has been compared against a high-cost measurement instrument such as a vector network analyzer and applied to the measurement and optimization of energy efficiency of microwave ovens, with good results. PMID:27873961

Effect of multiple slip on a chemically reactive MHD non-Newtonian nanofluid power law fluid flow over a stretching sheet with microorganism

NASA Astrophysics Data System (ADS)

Basir, Mohammad Faisal Mohd; Ismail, Fazreen Amira; Amirsom, Nur Ardiana; Latiff, Nur Amalina Abdul; Ismail, Ahmad Izani Md.

2017-04-01

The effect of multiple slip on a chemically reactive magnetohydrodynamic (MHD) non-Newtonian power law fluid flow over a stretching sheet with microorganism was numerically investigated. The governing partial differential equations were transformed into nonlinear ordinary differential equations using the similarity transformations developed by Lie group analysis. The reduced governing nonlinear ordinary differential equations were then numerically solved using the Runge-Kutta-Fehlberg fourth-fifth order method. Good agreement was found between the present numerical solutions with the existing published results to support the validity and the accuracy of the numerical computations. The influences of the velocity, thermal, mass and microorganism slips, the magnetic field parameter and the chemical reaction parameter on the dimensionless velocity, temperature, nanoparticle volume fraction, microorganism concentration, the distribution of the density of motile microorganisms have been illustrated graphically. The effects of the governing parameters on the physical quantities, namely, the local heat transfer rate, the local mass transfer rate and the local microorganism transfer rate were analyzed and discussed.

Convective hydromagnetic instabilities of a power-law liquid saturating a porous medium: Flux conditions

NASA Astrophysics Data System (ADS)

Chahtour, C.; Ben Hamed, H.; Beji, H.; Guizani, A.; Alimi, W.

2018-01-01

We investigate how an external imposed magnetic field affects thermal instability in a horizontal shallow porous cavity saturated by a non-Newtonian power-law liquid. The magnetic field is assumed to be constant and parallel to the gravity. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. We use linear stability analysis to find expressions for the critical Rayleigh number as a function of the power-law index and the intensity of the magnetic field. We use nonlinear parallel flow theory to find some explicit solutions of the problem, and we use finite difference numerical simulations to solve the full nonlinear equations. We show how the presence of magnetic field alters the known hydrodynamical result of Newtonian flows and power-law flows and how it causes the presence of subcritical finite amplitude convection for both pseudoplastic and dilatant fluids. We also show that in the limit of very strong magnetic field, the dissipation of energy by Joule effect dominates the dissipation of energy by shear stress and gives to the liquid an inviscid character.

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

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

Xu, X Q

We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. Withmore » our 4D ({psi}, {theta}, {epsilon}, {mu}) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.« less

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

NASA Astrophysics Data System (ADS)

Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.; Pop, Ioan

2018-06-01

The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

Theoretical investigation of the force and dynamically coupled torsional-axial-lateral dynamic response of eared rotors

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1982-01-01

Difficulties in solution methodology to be used to deal with the potentially higher nonlinear rotor equations when dynamic coupling is included. A solution methodology is selected to solve the nonlinear differential equations. The selected method was verified to give good results even at large nonlinearity levels. The transfer matrix methodology is extended to the solution of nonlinear problems.

Square-integrable solutions to a family of nonlinear schrödinger equations from nonlinear quantum theory

NASA Astrophysics Data System (ADS)

Teismann, Holger

2005-10-01

We consider nonlinear Schrödinger equations which have been proposed as fundamental equations of nonlinear quantum theories. The equations are singular in that the wave function ψ appears in the denominator of rational expressions. To avoid the problem of zeros of ψ it is natural to make the ansatz ψ = e ν. This ansatz, however, conflicts with the—physically motivated—requirement that the solutions ψ be square integrable. We show that this conflict can be resolved by considering an unusual function space whose definition involves the derivative ∇ ν of ν. This function space turns out to be dense subset of L2 and the equations can be solved in the L2-sense (as desired) by first solving an evolutionary system for ∇ ν and then transforming back to ψ.

Stabilization of the SIESTA MHD Equilibrium Code Using Rapid Cholesky Factorization

NASA Astrophysics Data System (ADS)

Hirshman, S. P.; D'Azevedo, E. A.; Seal, S. K.

2016-10-01

The SIESTA MHD equilibrium code solves the discretized nonlinear MHD force F ≡ J X B - ∇p for a 3D plasma which may contain islands and stochastic regions. At each nonlinear evolution step, it solves a set of linearized MHD equations which can be written r ≡ Ax - b = 0, where A is the linearized MHD Hessian matrix. When the solution norm | x| is small enough, the nonlinear force norm will be close to the linearized force norm | r| 0 obtained using preconditioned GMRES. In many cases, this procedure works well and leads to a vanishing nonlinear residual (equilibrium) after several iterations in SIESTA. In some cases, however, | x|>1 results and the SIESTA code has to be restarted to obtain nonlinear convergence. In order to make SIESTA more robust and avoid such restarts, we have implemented a new rapid QR factorization of the Hessian which allows us to rapidly and accurately solve the least-squares problem AT r = 0, subject to the condition | x|<1. This avoids large contributions to the nonlinear force terms and in general makes the convergence sequence of SIESTA much more stable. The innovative rapid QR method is based on a pairwise row factorization of the tri-diagonal Hessian. It provides a complete Cholesky factorization while preserving the memory allocation of A. This work was supported by the U.S. D.O.E. contract DE-AC05-00OR22725.

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

NASA Astrophysics Data System (ADS)

van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

2017-12-01

A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

Non-linear eigensolver-based alternative to traditional SCF methods

NASA Astrophysics Data System (ADS)

Gavin, B.; Polizzi, E.

2013-05-01

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem, i.e., H({ψ})ψ = Eψ. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the non-linearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the density functional theory-Kohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixing-scheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.

Investigation of the transport shortfall in Alcator C-Mod L-mode plasmas

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

Howard, N. T.; White, A. E.; Greenwald, M.

2013-03-15

A so-called 'transport shortfall,' where ion and electron heat fluxes and turbulence are underpredicted by gyrokinetic codes, has been robustly identified in DIII-D L-mode plasmas for {rho}>0.55[T. L. Rhodes et al., Nucl. Fusion 51(6), 063022 (2011); and C. Holland et al., Phys. Plasmas 16(5), 052301 (2009)]. To probe the existence of a transport shortfall across different tokamaks, a dedicated scan of auxiliary heated L-mode discharges in Alcator C-Mod are studied in detail with nonlinear gyrokinetic simulations for the first time. Two discharges, only differing by the amount of auxiliary heating are investigated using both linear and nonlinear simulation of themore » GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)]. Nonlinear gyrokinetic simulation of the low and high input power discharges reveals a discrepancy between simulation and experiment in only the electron heat flux channel of the low input power discharge. However, both discharges demonstrate excellent agreement in the ion heat flux channel, and the high input power discharge demonstrates simultaneous agreement with experiment in both the electron and ion heat flux channels. A summary of linear and nonlinear gyrokinetic results and a discussion of possible explanations for the agreement/disagreement in each heat flux channel is presented.« less

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

Numerical Simulation of Illumination and Thermal Conditions at the Lunar Poles Using LOLA DTMs

NASA Technical Reports Server (NTRS)

Glaser, P.; Glaser, D.; Oberst, J.; Neumann, G. A.; Mazarico, E.; Siegler, M. A.

2017-01-01

We are interested in illumination conditions and the temperature distribution within the upper two meters of regolith near the lunar poles. Here, areas exist receiving almost constant illumination near areas in permanent shadow, which were identified as potential exploration sites for future missions. For our study a numerical simulation of the illumination and thermal environment for lunar near-polar regions is needed. Our study is based on high-resolution, twenty meters per pixel and 400 x 400 km large polar Digital Terrain Models (DTMs), which were derived from Lunar Orbiter Laser Altimeter (LOLA) data. Illumination conditions were simulated by synthetically illuminating the LOLA DTMs using the horizon method considering the Sun as an extended source. We model polar illumination for the central 50 x 50 km subset and use it as an input at each time-step (2 h) to evaluate the heating of the lunar surface and subsequent conduction in the sub-surface. At surface level we balance the incoming insolation with the subsurface conduction and radiation into space, whereas in the sub-surface we consider conduction with an additional constant radiogenic heat source at the bottom of our two-meter layer. Density is modeled as depth-dependent, the specific heat parameter as temperature-dependent and the thermal conductivity as depth- and temperature-dependent. We implemented a fully implicit finite-volume method in space and backward Euler scheme in time to solve the one-dimensional heat equation at each pixel in our 50 x 50 km DTM. Due to the non-linear dependencies of the parameters mentioned above, Newton's method is employed as the non-linear solver together with the Gauss-Seidel method as the iterative linear solver in each Newton iteration. The software is written in OpenCL and runs in parallel on the GPU cores, which allows for fast computation of large areas and long time scales.

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

Building Flexible User Interfaces for Solving PDEs

NASA Astrophysics Data System (ADS)

Logg, Anders; Wells, Garth N.

2010-09-01

FEniCS is a collection of software tools for the automated solution of differential equations by finite element methods. In this note, we describe how FEniCS can be used to solve a simple nonlinear model problem with varying levels of automation. At one extreme, FEniCS provides tools for the fully automated and adaptive solution of nonlinear partial differential equations. At the other extreme, FEniCS provides a range of tools that allow the computational scientist to experiment with novel solution algorithms.

Computation of nonlinear ultrasound fields using a linearized contrast source method.

PubMed

Verweij, Martin D; Demi, Libertario; van Dongen, Koen W A

2013-08-01

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

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.

Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations

NASA Astrophysics Data System (ADS)

Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.

2018-03-01

Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.

A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Karel, S.

1975-01-01

An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.

New Galerkin operational matrices for solving Lane-Emden type equations

NASA Astrophysics Data System (ADS)

Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

2016-04-01

Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Modelling fully-coupled Thermo-Hydro-Mechanical (THM) processes in fractured reservoirs using GOLEM: a massively parallel open-source simulator

NASA Astrophysics Data System (ADS)

Jacquey, Antoine; Cacace, Mauro

2017-04-01

Utilization of the underground for energy-related purposes have received increasing attention in the last decades as a source for carbon-free energy and for safe storage solutions. Understanding the key processes controlling fluid and heat flow around geological discontinuities such as faults and fractures as well as their mechanical behaviours is therefore of interest in order to design safe and sustainable reservoir operations. These processes occur in a naturally complex geological setting, comprising natural or engineered discrete heterogeneities as faults and fractures, span a relatively large spectrum of temporal and spatial scales and they interact in a highly non-linear fashion. In this regard, numerical simulators have become necessary in geological studies to model coupled processes and complex geological geometries. In this study, we present a new simulator GOLEM, using multiphysics coupling to characterize geological reservoirs. In particular, special attention is given to discrete geological features such as faults and fractures. GOLEM is based on the Multiphysics Object-Oriented Simulation Environment (MOOSE). The MOOSE framework provides a powerful and flexible platform to solve multiphysics problems implicitly and in a tightly coupled manner on unstructured meshes which is of interest for the considered non-linear context. Governing equations in 3D for fluid flow, heat transfer (conductive and advective), saline transport as well as deformation (elastic and plastic) have been implemented into the GOLEM application. Coupling between rock deformation and fluid and heat flow is considered using theories of poroelasticity and thermoelasticity. Furthermore, considering material properties such as density and viscosity and transport properties such as porosity as dependent on the state variables (based on the International Association for the Properties of Water and Steam models) increase the coupling complexity of the problem. The GOLEM application aims therefore at integrating more physical processes observed in the field or in the laboratory to simulate more realistic scenarios. The use of high-level nonlinear solver technology allow us to tackle these complex multiphysics problems in three dimensions. Basic concepts behing the GOLEM simulator will be presented in this study as well as a few application examples to illustrate its main features.

High-order Two-way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

NASA Technical Reports Server (NTRS)

Fibich, Gadi; Tsynkov, Semyon

2000-01-01

When solving linear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, by linear superposition, the original problem is reduced to one that involves only the scattered waves driven by the values of the impinging field at the surface of the obstacles. In addition, when the original domain is unbounded, special artificial boundary conditions (ABCs) that would guarantee the reflectionless propagation of waves have to be set at the outer boundary of the finite computational domain. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed, should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call this type of boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation that models the laser beam propagation in a medium with nonlinear index of refraction. In this case, the forward propagation is accompanied by backscattering, i.e., generation of waves in the direction opposite to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained for a fourth-order accurate discretization to the Helmholtz operator; the fourth-order grid convergence is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition, allows for direct calculation of the magnitude of backscattering.

Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics

NASA Astrophysics Data System (ADS)

Rangan, Aaditya V.; Cai, David; Tao, Louis

2007-02-01

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear boundary conditions. The PDEs themselves are self-consistently specified by parameters which are functions of the boundary values of the solution. The moment equations can be stiff in space and time. Numerical methods are presented here for efficiently and accurately solving these moment equations. The essential ingredients in our numerical methods include: (i) the system is discretized in time with an implicit Euler method within a spectral deferred correction framework, therefore, the PDEs of the kinetic theory are reduced to a sequence, in time, of boundary value problems (BVPs) with nonlinear boundary conditions; (ii) a set of auxiliary parameters is introduced to recast the original BVP with nonlinear boundary conditions as BVPs with linear boundary conditions - with additional algebraic constraints on the auxiliary parameters; (iii) a careful combination of two Newton's iterates for the nonlinear BVP with linear boundary condition, interlaced with a Newton's iterate for solving the associated algebraic constraints is constructed to achieve quadratic convergence for obtaining the solutions with self-consistent parameters. It is shown that a simple fixed-point iteration can only achieve a linear convergence for the self-consistent parameters. The practicability and efficiency of our numerical methods for solving the moment equations of the kinetic theory are illustrated with numerical examples. It is further demonstrated that the moment equations derived from the kinetic theory of neuronal network dynamics can very well capture the coarse-grained dynamical properties of integrate-and-fire neuronal networks.

SIERRA Multimechanics Module: Aria User Manual Version 4.44

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

Sierra Thermal /Fluid Team

2017-04-01

Aria is a Galerkin fnite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process fows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of eithermore » arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

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

Sierra Thermal/Fluid Team

Aria is a Galerkin fnite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process fows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of eithermore » arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

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

Sierra Thermal /Fluid Team

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re %3C 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrarymore » Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

Alfvén wave dynamics at the neighborhood of a 2.5D magnetic null-point

NASA Astrophysics Data System (ADS)

Sabri, S.; Vasheghani Farahani, S.; Ebadi, H.; Hosseinpour, M.; Fazel, Z.

2018-05-01

The aim of the present study is to highlight the energy transfer via the interaction of magnetohydrodynamic waves with a 2.5D magnetic null-point in a finite plasma-β regime of the solar corona. An initially symmetric Alfvén pulse at a specific distance from a magnetic null-point is kicked towards the isothermal null-point. A shock-capturing Godunov-type PLUTO code is used to solve the ideal magnetohydrodynamic set equations in the context of wave-plasma energy transfer. As the Alfvén wave propagates towards the magnetic null-point it experiences speed lowering which ends up in releasing energy along the separatrices. In this line owing to the Alfvén wave, a series of events take place that contribute towards coronal heating. Nonlinear induced waves are by products of the torsional Alfvén interaction with magnetic null-points. The energy of these induced waves which are fast magnetoacoustic (transverse) and slow magnetoacoustic (longitudinal) waves are supplied by the Alfvén wave. The nonlinearly induced density perturbations are proportional to the Alfvén wave energy loss. This supplies energy for the propagation of fast and slow magnetoacoustic waves, where in contrast to the fast wave the slow wave experiences a continuous energy increase. As such, the slow wave may transfer its energy to the medium at later times, maintaining a continuous heating mechanism at the neighborhood of a magnetic null-point.

Solving nonlinear equilibrium equations of deformable systems by method of embedded polygons

NASA Astrophysics Data System (ADS)

Razdolsky, A. G.

2017-09-01

Solving of nonlinear algebraic equations is an obligatory stage of studying the equilibrium paths of nonlinear deformable systems. The iterative method for solving a system of nonlinear algebraic equations stated in an explicit or implicit form is developed in the present work. The method consists of constructing a sequence of polygons in Euclidean space that converge into a single point that displays the solution of the system. Polygon vertices are determined on the assumption that individual equations of the system are independent from each other and each of them is a function of only one variable. Initial positions of vertices for each subsequent polygon are specified at the midpoints of certain straight segments determined at the previous iteration. The present algorithm is applied for analytical investigation of the behavior of biaxially compressed nonlinear-elastic beam-column with an open thin-walled cross-section. Numerical examples are made for the I-beam-column on the assumption that its material follows a bilinear stress-strain diagram. A computer program based on the shooting method is developed for solving the problem. The method is reduced to numerical integration of a system of differential equations and to the solution of a system of nonlinear algebraic equations between the boundary values of displacements at the ends of the beam-column. A stress distribution at the beam-column cross-sections is determined by subdividing the cross-section area into many small cells. The equilibrium path for the twisting angle and the lateral displacements tend to the stationary point when the load is increased. Configuration of the path curves reveals that the ultimate load is reached shortly once the maximal normal stresses at the beam-column fall outside the limit of the elastic region. The beam-column has a unique equilibrium state for each value of the load, that is, there are no equilibrium states once the maximum load is reached.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

The Effect of Using an Explicit General Problem Solving Teaching Approach on Elementary Pre-Service Teachers' Ability to Solve Heat Transfer Problems

ERIC Educational Resources Information Center

Mataka, Lloyd M.; Cobern, William W.; Grunert, Megan L.; Mutambuki, Jacinta; Akom, George

2014-01-01

This study investigate the effectiveness of adding an "explicit general problem solving teaching strategy" (EGPS) to guided inquiry (GI) on pre-service elementary school teachers' ability to solve heat transfer problems. The pre-service elementary teachers in this study were enrolled in two sections of a chemistry course for pre-service…

Validation of a High-Order Prefactored Compact Scheme on Nonlinear Flows with Complex Geometries

NASA Technical Reports Server (NTRS)

Hixon, Ray; Mankbadi, Reda R.; Povinelli, L. A. (Technical Monitor)

2000-01-01

Three benchmark problems are solved using a sixth-order prefactored compact scheme employing an explicit 10th-order filter with optimized fourth-order Runge-Kutta time stepping. The problems solved are the following: (1) propagation of sound waves through a transonic nozzle; (2) shock-sound interaction; and (3) single airfoil gust response. In the first two problems, the spatial accuracy of the scheme is tested on a stretched grid, and the effectiveness of boundary conditions is shown. The solution stability and accuracy near a shock discontinuity is shown as well. Also, 1-D nonlinear characteristic boundary conditions will be evaluated. In the third problem, a nonlinear Euler solver will be used that solves the equations in generalized curvilinear coordinates using the chain rule transformation. This work, continuing earlier work on flat-plate cascades and Joukowski airfoils, will focus mainly on the effect of the grid and boundary conditions on the accuracy of the solution. The grids were generated using a commercially available grid generator, GridPro/az3000.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

USGS Publications Warehouse

Cooley, R.L.; Hill, M.C.

1992-01-01

Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

NASA Astrophysics Data System (ADS)

See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

2018-04-01

This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

A Bivariate Chebyshev Spectral Collocation Quasilinearization Method for Nonlinear Evolution Parabolic Equations

PubMed Central

Motsa, S. S.; Magagula, V. M.; Sibanda, P.

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

PubMed

Motsa, S S; Magagula, V M; Sibanda, P

2014-01-01

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

Adaptive Fuzzy Output Feedback Control for Switched Nonlinear Systems With Unmodeled Dynamics.

PubMed

Tong, Shaocheng; Li, Yongming

2017-02-01

This paper investigates a robust adaptive fuzzy control stabilization problem for a class of uncertain nonlinear systems with arbitrary switching signals that use an observer-based output feedback scheme. The considered switched nonlinear systems possess the unstructured uncertainties, unmodeled dynamics, and without requiring the states being available for measurement. A state observer which is independent of switching signals is designed to solve the problem of unmeasured states. Fuzzy logic systems are used to identify unknown lumped nonlinear functions so that the problem of unstructured uncertainties can be solved. By combining adaptive backstepping design principle and small-gain approach, a novel robust adaptive fuzzy output feedback stabilization control approach is developed. The stability of the closed-loop system is proved via the common Lyapunov function theory and small-gain theorem. Finally, the simulation results are given to demonstrate the validity and performance of the proposed control strategy.

Application of the Homotopy Perturbation Method to the Nonlinear Pendulum

ERIC Educational Resources Information Center

Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.

2007-01-01

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…

Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

NASA Astrophysics Data System (ADS)

Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

2018-07-01

This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

NASA Astrophysics Data System (ADS)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

New computer program solves wide variety of heat flow problems

NASA Technical Reports Server (NTRS)

Almond, J. C.

1966-01-01

Boeing Engineering Thermal Analyzer /BETA/ computer program uses numerical methods to provide accurate heat transfer solutions to a wide variety of heat flow problems. The program solves steady-state and transient problems in almost any situation that can be represented by a resistance-capacitance network.

Unsteady mixed convection flow of Casson fluid past an inclined stretching sheet in the presence of nanoparticles

NASA Astrophysics Data System (ADS)

Rawi, N. A.; Ilias, M. R.; Lim, Y. J.; Isa, Z. M.; Shafie, S.

2017-09-01

The influence of nanoparticles on the unsteady mixed convection flow of Casson fluid past an inclined stretching sheet is investigated in this paper. The effect of gravity modulation on the flow is also considered. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as nanoparticles. The basic governing nonlinear partial differential equations are transformed using appropriate similarity transformation and solved numerically using an implicit finite difference scheme by means of the Keller-box method. The effect of nanoparticles volume fraction together with the effect of inclination angle and Casson parameter on the enhancement of heat transfer of Casson nanofluid is discussed in details. The velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number are presented and analyzed.

Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

NASA Astrophysics Data System (ADS)

Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

2018-01-01

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

Numerical techniques for solving nonlinear instability problems in smokeless tactical solid rocket motors. [finite difference technique

NASA Technical Reports Server (NTRS)

Baum, J. D.; Levine, J. N.

1980-01-01

The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.

A high-accuracy algorithm for solving nonlinear PDEs with high-order spatial derivatives in 1 + 1 dimensions

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

Yao, Jian Hua; Gooding, R.J.

1994-06-01

We propose an algorithm to solve a system of partial differential equations of the type u[sub t](x,t) = F(x, t, u, u[sub x], u[sub xx], u[sub xxx], u[sub xxxx]) in 1 + 1 dimensions using the method of lines with piecewise ninth-order Hermite polynomials, where u and F and N-dimensional vectors. Nonlinear boundary conditions are easily incorporated with this method. We demonstrate the accuracy of this method through comparisons of numerically determine solutions to the analytical ones. Then, we apply this algorithm to a complicated physical system involving nonlinear and nonlocal strain forces coupled to a thermal field. 4 refs.,more » 5 figs., 1 tab.« less

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

Bai, Zhaojun; Yang, Chao

What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcasemore » some of the cutting edge results from both communities and to discuss the challenges they are still facing. The minisymposium consisted of eight talks divided into two sessions. The first three talks focused on a type of nonlinear eigenvalue problem arising from electronic structure calculations. In this type of problem, the matrix Hamiltonian H depends, in a non-trivial way, on the set of eigenvectors X to be computed. The invariant subspace spanned by these eigenvectors also minimizes a total energy function that is highly nonlinear with respect to X on a manifold defined by a set of orthonormality constraints. In other applications, the nonlinearity of the matrix eigenvalue problem is restricted to the dependency of the matrix on the eigenvalues to be computed. These problems are often called polynomial or rational eigenvalue problems In the second session, Christian Mehl from Technical University of Berlin described numerical techniques for solving a special type of polynomial eigenvalue problem arising from vibration analysis of rail tracks excited by high-speed trains.« less

Using Microcomputers to Teach Non-Linear Equations at Sixth Form Level.

ERIC Educational Resources Information Center

Cheung, Y. L.

1984-01-01

Promotes the use of the microcomputer in mathematics instruction, reviewing approaches to teaching nonlinear equations. Examples of computer diagrams are illustrated and compared to textbook samples. An example of a problem-solving program is included. (ML)

Flexible parallel implicit modelling of coupled thermal-hydraulic-mechanical processes in fractured rocks

NASA Astrophysics Data System (ADS)

Cacace, Mauro; Jacquey, Antoine B.

2017-09-01

Theory and numerical implementation describing groundwater flow and the transport of heat and solute mass in fully saturated fractured rocks with elasto-plastic mechanical feedbacks are developed. In our formulation, fractures are considered as being of lower dimension than the hosting deformable porous rock and we consider their hydraulic and mechanical apertures as scaling parameters to ensure continuous exchange of fluid mass and energy within the fracture-solid matrix system. The coupled system of equations is implemented in a new simulator code that makes use of a Galerkin finite-element technique. The code builds on a flexible, object-oriented numerical framework (MOOSE, Multiphysics Object Oriented Simulation Environment) which provides an extensive scalable parallel and implicit coupling to solve for the multiphysics problem. The governing equations of groundwater flow, heat and mass transport, and rock deformation are solved in a weak sense (either by classical Newton-Raphson or by free Jacobian inexact Newton-Krylow schemes) on an underlying unstructured mesh. Nonlinear feedbacks among the active processes are enforced by considering evolving fluid and rock properties depending on the thermo-hydro-mechanical state of the system and the local structure, i.e. degree of connectivity, of the fracture system. A suite of applications is presented to illustrate the flexibility and capability of the new simulator to address problems of increasing complexity and occurring at different spatial (from centimetres to tens of kilometres) and temporal scales (from minutes to hundreds of years).

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.

A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.

Three dimensional radiative flow of magnetite-nanofluid with homogeneous-heterogeneous reactions

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Rashid, Madiha; Alsaedi, Ahmed

2018-03-01

Present communication deals with the effects of homogeneous-heterogeneous reactions in flow of nanofluid by non-linear stretching sheet. Water based nanofluid containing magnetite nanoparticles is considered. Non-linear radiation and non-uniform heat sink/source effects are examined. Non-linear differential systems are computed by Optimal homotopy analysis method (OHAM). Convergent solutions of nonlinear systems are established. The optimal data of auxiliary variables is obtained. Impact of several non-dimensional parameters for velocity components, temperature and concentration fields are examined. Graphs are plotted for analysis of surface drag force and heat transfer rate.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1994-01-01

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

PubMed

Meair, Jonathan; Jacquod, Philippe

2013-02-27

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

NASA Astrophysics Data System (ADS)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

NASA Astrophysics Data System (ADS)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

A diffuse-interface method for two-phase flows with soluble surfactants

PubMed Central

Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

2010-01-01

A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

Machining Chatter Analysis for High Speed Milling Operations

NASA Astrophysics Data System (ADS)

Sekar, M.; Kantharaj, I.; Amit Siddhappa, Savale

2017-10-01

Chatter in high speed milling is characterized by time delay differential equations (DDE). Since closed form solution exists only for simple cases, the governing non-linear DDEs of chatter problems are solved by various numerical methods. Custom codes to solve DDEs are tedious to build, implement and not error free and robust. On the other hand, software packages provide solution to DDEs, however they are not straight forward to implement. In this paper an easy way to solve DDE of chatter in milling is proposed and implemented with MATLAB. Time domain solution permits the study and model of non-linear effects of chatter vibration with ease. Time domain results are presented for various stable and unstable conditions of cut and compared with stability lobe diagrams.

Steady boundary layer slip flow along with heat and mass transfer over a flat porous plate embedded in a porous medium.

PubMed

Aziz, Asim; Siddique, J I; Aziz, Taha

2014-01-01

In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile.

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.

Steady Boundary Layer Slip Flow along with Heat and Mass Transfer over a Flat Porous Plate Embedded in a Porous Medium

PubMed Central

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

2014-01-01

In this paper, a simplified model of an incompressible fluid flow along with heat and mass transfer past a porous flat plate embedded in a Darcy type porous medium is investigated. The velocity, thermal and mass slip conditions are utilized that has not been discussed in the literature before. The similarity transformations are used to transform the governing partial differential equations (PDEs) into a nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then reduced to a system of first order differential equations which was solved numerically by using Matlab bvp4c code. The effects of permeability, suction/injection parameter, velocity parameter and slip parameter on the structure of velocity, temperature and mass transfer rates are examined with the aid of several graphs. Moreover, observations based on Schmidt number and Soret number are also presented. The result shows, the increase in permeability of the porous medium increase the velocity and decrease the temperature profile. This happens due to a decrease in drag of the fluid flow. In the case of heat transfer, the increase in permeability and slip parameter causes an increase in heat transfer. However for the case of increase in thermal slip parameter there is a decrease in heat transfer. An increase in the mass slip parameter causes a decrease in the concentration field. The suction and injection parameter has similar effect on concentration profile as for the case of velocity profile. PMID:25531301

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

Solving nonlinear evolution equation system using two different methods

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.

2015-12-01

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Solution of a Nonlinear Heat Conduction Equation for a Curvilinear Region with Dirichlet Conditions by the Fast-Expansion Method

NASA Astrophysics Data System (ADS)

Chernyshov, A. D.

2018-05-01

The analytical solution of the nonlinear heat conduction problem for a curvilinear region is obtained with the use of the fast-expansion method together with the method of extension of boundaries and pointwise technique of computing Fourier coefficients.

L1-Based Approximations of PDEs and Applications

DTIC Science & Technology

2012-09-05

the analysis of the Navier-Stokes equations. The early versions of artificial vis- cosities being overly dissipative, the interest for these technique ...Guermond, and B. Popov. Stability analysis of explicit en- tropy viscosity methods for non-linear scalar conservation equations. Math. Comp., 2012... methods for solv- ing mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems

A hybrid approach for nonlinear computational aeroacoustics predictions

NASA Astrophysics Data System (ADS)

Sassanis, Vasileios; Sescu, Adrian; Collins, Eric M.; Harris, Robert E.; Luke, Edward A.

2017-01-01

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier-Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier-Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.

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.

Combined Influence of Hall Current and Soret Effect on Chemically Reacting Magnetomicropolar Fluid Flow from Radiative Rotating Vertical Surface with Variable Suction in Slip-Flow Regime

PubMed Central

Jain, Preeti

2014-01-01

An analysis study is presented to study the effects of Hall current and Soret effect on unsteady hydromagnetic natural convection of a micropolar fluid in a rotating frame of reference with slip-flow regime. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the micropolar fluid with variable suction velocity. The effects of heat absorption, chemical reaction, and thermal radiation are discussed and for this Rosseland approximation is used to describe the radiative heat flux in energy equation. The entire system rotates with uniform angular velocity Ω about an axis normal to the plate. The nonlinear coupled partial differential equations are solved by perturbation techniques. In order to get physical insight, the numerical results of translational velocity, microrotation, fluid temperature, and species concentration for different physical parameters entering into the analysis are discussed and explained graphically. Also, the results of the skin-friction coefficient, the couple stress coefficient, Nusselt number, and Sherwood number are discussed with the help of figures for various values of flow pertinent flow parameters. PMID:27350957

Verification and validation of an advanced model of heat and mass transfer in the protective clothing

NASA Astrophysics Data System (ADS)

Łapka, Piotr; Furmański, Piotr

2018-04-01

The paper presents verification and validation of an advanced numerical model of heat and moisture transfer in the multi-layer protective clothing and in components of the experimental stand subjected to either high surroundings temperature or high radiative heat flux emitted by hot objects. The developed model included conductive-radiative heat transfer in the hygroscopic porous fabrics and air gaps as well as conductive heat transfer in components of the stand. Additionally, water vapour diffusion in the pores and air spaces as well as phase transition of the bound water in the fabric fibres (sorption and desorption) were accounted for. All optical phenomena at internal or external walls were modelled and the thermal radiation was treated in the rigorous way, i.e., semi-transparent absorbing, emitting and scattering fabrics with the non-grey properties were assumed. The air was treated as transparent. Complex energy and mass balances as well as optical conditions at internal or external interfaces were formulated in order to find values of temperatures, vapour densities and radiation intensities at these interfaces. The obtained highly non-linear coupled system of discrete equations was solved by the Finite Volume based in-house iterative algorithm. The developed model passed discretisation convergence tests and was successfully verified against the results obtained applying commercial software for simplified cases. Then validation was carried out using experimental measurements collected during exposure of the protective clothing to high radiative heat flux emitted by the IR lamp. Satisfactory agreement of simulated and measured temporal variation of temperature at external and internal surfaces of the multi-layer clothing was attained.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Comprehensive drought characteristics analysis based on a nonlinear multivariate drought index

NASA Astrophysics Data System (ADS)

Yang, Jie; Chang, Jianxia; Wang, Yimin; Li, Yunyun; Hu, Hui; Chen, Yutong; Huang, Qiang; Yao, Jun

2018-02-01

It is vital to identify drought events and to evaluate multivariate drought characteristics based on a composite drought index for better drought risk assessment and sustainable development of water resources. However, most composite drought indices are constructed by the linear combination, principal component analysis and entropy weight method assuming a linear relationship among different drought indices. In this study, the multidimensional copulas function was applied to construct a nonlinear multivariate drought index (NMDI) to solve the complicated and nonlinear relationship due to its dependence structure and flexibility. The NMDI was constructed by combining meteorological, hydrological, and agricultural variables (precipitation, runoff, and soil moisture) to better reflect the multivariate variables simultaneously. Based on the constructed NMDI and runs theory, drought events for a particular area regarding three drought characteristics: duration, peak, and severity were identified. Finally, multivariate drought risk was analyzed as a tool for providing reliable support in drought decision-making. The results indicate that: (1) multidimensional copulas can effectively solve the complicated and nonlinear relationship among multivariate variables; (2) compared with single and other composite drought indices, the NMDI is slightly more sensitive in capturing recorded drought events; and (3) drought risk shows a spatial variation; out of the five partitions studied, the Jing River Basin as well as the upstream and midstream of the Wei River Basin are characterized by a higher multivariate drought risk. In general, multidimensional copulas provides a reliable way to solve the nonlinear relationship when constructing a comprehensive drought index and evaluating multivariate drought characteristics.

Exploring inductive linearization for pharmacokinetic-pharmacodynamic systems of nonlinear ordinary differential equations.

PubMed

Hasegawa, Chihiro; Duffull, Stephen B

2018-02-01

Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Nonlinear radiative heat flux and heat source/sink on entropy generation minimization rate

NASA Astrophysics Data System (ADS)

Hayat, T.; Khan, M. Waleed Ahmed; Khan, M. Ijaz; Alsaedi, A.

2018-06-01

Entropy generation minimization in nonlinear radiative mixed convective flow towards a variable thicked surface is addressed. Entropy generation for momentum and temperature is carried out. The source for this flow analysis is stretching velocity of sheet. Transformations are used to reduce system of partial differential equations into ordinary ones. Total entropy generation rate is determined. Series solutions for the zeroth and mth order deformation systems are computed. Domain of convergence for obtained solutions is identified. Velocity, temperature and concentration fields are plotted and interpreted. Entropy equation is studied through nonlinear mixed convection and radiative heat flux. Velocity and temperature gradients are discussed through graphs. Meaningful results are concluded in the final remarks.

Testing Born-Infeld electrodynamics in waveguides.

PubMed

Ferraro, Rafael

2007-12-07

Waveguides can be employed to test nonlinear effects in electrodynamics. We solve Born-Infeld equations for TE waves in a rectangular waveguide. We show that the energy velocity acquires a dependence on the amplitude, and harmonic components appear as a consequence of the nonlinear behavior.

A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems

NASA Astrophysics Data System (ADS)

Negrello, Camille; Gosselet, Pierre; Rey, Christian

2018-05-01

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

NASA Astrophysics Data System (ADS)

Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.

2012-11-01

Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)

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.

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

Ochiai, Yoshihiro

Heat-conduction analysis under steady state without heat generation can easily be treated by the boundary element method. However, in the case with heat conduction with heat generation can approximately be solved without a domain integral by an improved multiple-reciprocity boundary element method. The convention multiple-reciprocity boundary element method is not suitable for complicated heat generation. In the improved multiple-reciprocity boundary element method, on the other hand, the domain integral in each step is divided into point, line, and area integrals. In order to solve the problem, the contour lines of heat generation, which approximate the actual heat generation, are used.

Numerical simulation of ultrasound-thermotherapy combining nonlinear wave propagation with broadband soft-tissue absorption.

PubMed

Ginter, S

2000-07-01

Ultrasound (US) thermotherapy is used to treat tumours, located deep in human tissue, by heat. It features by the application of high intensity focused ultrasound (HIFU), high local temperatures of about 90 degrees C and short treating time of a few seconds. Dosage of the therapy remains a problem. To get it under control, one has to know the heat source, i.e. the amount of absorbed US power, which shows nonlinear influences. Therefore, accurate simulations are essential. In this paper, an improved simulation model is introduced which enables accurate investigations of US thermotherapy. It combines nonlinear US propagation effects, which lead to generation of higher harmonics, with a broadband frequency-power law absorption typical for soft tissue. Only the combination of both provides a reliable calculation of the generated heat. Simulations show the influence of nonlinearities and broadband damping for different source signals on the absorbed US power density distribution.

Transition Helmholtz free energy, entropy, and heat capacity of free-standing smectic films in water: A mean-field treatment

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

Śliwa, Izabela, E-mail: izasliwa@ifmpan.poznan.pl; Zakharov, A. V., E-mail: alexandre.zakharov@yahoo.ca

Using the extended McMillan's mean field approach with anisotropic forces a study of both the structural and thermodynamic properties of free-standing smectic film (FSSF) in water on heating to the isotropic temperature is carried out numerically. By solving the self-consistent nonlinear equations for the order parameters, we obtained that the smectic-A-isotropic (AI) transition occurs through the series of layer-thinning transitions causing the films to thin in the stepwise manner as the temperature is increased above the bulk smectic-A-isotropic temperature T{sub AI}(bulk). With enhanced pair interactions in the bounding layers, the smectic-isotropic transition corresponds to smectic melting of the central layers.more » The effects of surface “enhanced” pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy and entropy, as well as the temperature dependence of the heat capacity of FSSFs, have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained – by means of optical microscopy and ellipsometry techniques – data of the temperature when the thin decylcyanobiphenyl smectic film immersing in water ruptures has been obtained.« less

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

NASA Astrophysics Data System (ADS)

Javed, Tariq; Ahmed, B.; Sajid, M.

2018-04-01

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin’s weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.

Nonlinear dynamics analysis of a low-temperature-differential kinematic Stirling heat engine

NASA Astrophysics Data System (ADS)

Izumida, Yuki

2018-03-01

The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature difference. The rotational state and the stationary state of the engine are described as a stable limit cycle and a stable fixed point of the dynamical equations, respectively. These two states coexist under a sufficient temperature difference, whereas the stable limit cycle does not exist under a temperature difference that is too small. Using a nonlinear bifurcation analysis, we show that the disappearance of the stable limit cycle occurs via a homoclinic bifurcation, with the temperature difference being the bifurcation parameter.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

FPPAC94: A two-dimensional multispecies nonlinear Fokker-Planck package for UNIX systems

NASA Astrophysics Data System (ADS)

Mirin, A. A.; McCoy, M. G.; Tomaschke, G. P.; Killeen, J.

1994-07-01

FPPAC94 solves the complete nonlinear multispecies Fokker-Planck collison operator for a plasma in two-dimensional velocity space. The operator is expressed in terms of spherical coordinates (speed and pitch angle) under the assumption of azimuthal symmetry. Provision is made for additional physics contributions (e.g. rf heating, electric field acceleration). The charged species, referred to as general species, are assumed to be in the presence of an arbitrary number of fixed Maxwellian species. The electrons may be treated either as one of these Maxwellian species or as a general species. Coulomb interactions among all charged species are considered This program is a new version of FPPAC. FPPAC was last published in Computer Physics Communications in 1988. This new version is identical in scope to the previous version. However, it is written in standard Fortran 77 and is able to execute on a variety of Unix systems. The code has been tested on the Cray-C90, HP-755 and Sun Sparc-1. The answers agree on all platforms where the code has been tested. The test problems are the same as those provided in 1988. This version also corrects a bug in the 1988 version.

Chemoviscosity modeling for thermosetting resins - I

NASA Technical Reports Server (NTRS)

Hou, T. H.

1984-01-01

A new analytical model for chemoviscosity variation during cure of thermosetting resins was developed. This model is derived by modifying the widely used WLF (Williams-Landel-Ferry) Theory in polymer rheology. Major assumptions involved are that the rate of reaction is diffusion controlled and is linearly inversely proportional to the viscosity of the medium over the entire cure cycle. The resultant first order nonlinear differential equation is solved numerically, and the model predictions compare favorably with experimental data of EPON 828/Agent U obtained on a Rheometrics System 4 Rheometer. The model describes chemoviscosity up to a range of six orders of magnitude under isothermal curing conditions. The extremely non-linear chemoviscosity profile for a dynamic heating cure cycle is predicted as well. The model is also shown to predict changes of glass transition temperature for the thermosetting resin during cure. The physical significance of this prediction is unclear at the present time, however, and further research is required. From the chemoviscosity simulation point of view, the technique of establishing an analytical model as described here is easily applied to any thermosetting resin. The model thus obtained is used in real-time process controls for fabricating composite materials.

A two steps solution approach to solving large nonlinear models: application to a problem of conjunctive use.

PubMed

Vieira, J; Cunha, M C

2011-01-01

This article describes a solution method of solving large nonlinear problems in two steps. The two steps solution approach takes advantage of handling smaller and simpler models and having better starting points to improve solution efficiency. The set of nonlinear constraints (named as complicating constraints) which makes the solution of the model rather complex and time consuming is eliminated from step one. The complicating constraints are added only in the second step so that a solution of the complete model is then found. The solution method is applied to a large-scale problem of conjunctive use of surface water and groundwater resources. The results obtained are compared with solutions determined with the direct solve of the complete model in one single step. In all examples the two steps solution approach allowed a significant reduction of the computation time. This potential gain of efficiency of the two steps solution approach can be extremely important for work in progress and it can be particularly useful for cases where the computation time would be a critical factor for having an optimized solution in due time.

Nonlinear dynamics and control of a vibrating rectangular plate

NASA Technical Reports Server (NTRS)

Shebalin, J. V.

1983-01-01

The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

NASA Astrophysics Data System (ADS)

Akbulut, Arzu; Taşcan, Filiz

2018-04-01

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

GHM method for obtaining rationalsolutions of nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

2015-01-01

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

Non-linear vibrations of sandwich viscoelastic shells

NASA Astrophysics Data System (ADS)

Benchouaf, Lahcen; Boutyour, El Hassan; Daya, El Mostafa; Potier-Ferry, Michel

2018-04-01

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

Heat perturbation spreading in the Fermi-Pasta-Ulam-β system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity

NASA Astrophysics Data System (ADS)

Xiong, Daxing

2017-06-01

We employ the heat perturbation correlation function to study thermal transport in the one-dimensional Fermi-Pasta-Ulam-β lattice with both nearest-neighbor and next-nearest-neighbor couplings. We find that such a system bears a peculiar phonon dispersion relation, and thus there exists a competition between phonon dispersion and nonlinearity that can strongly affect the heat correlation function's shape and scaling property. Specifically, for small and large anharmoncities, the scaling laws are ballistic and superdiffusive types, respectively, which are in good agreement with the recent theoretical predictions; whereas in the intermediate range of the nonlinearity, we observe an unusual multiscaling property characterized by a nonmonotonic delocalization process of the central peak of the heat correlation function. To understand these multiscaling laws, we also examine the momentum perturbation correlation function and find a transition process with the same turning point of the anharmonicity as that shown in the heat correlation function. This suggests coupling between the momentum transport and the heat transport, in agreement with the theoretical arguments of mode cascade theory.

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

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

Paul, Prokash; Bhattacharyya, Debangsu; Turton, Richard

Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimizationmore » problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.« less

Newton's method: A link between continuous and discrete solutions of nonlinear problems

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

PubMed Central

Batra, Romesh C.; Porfiri, Maurizio; Spinello, Davide

2008-01-01

We study the influence of von Kármán nonlinearity, van der Waals force, and thermal stresses on pull-in instability and small vibrations of electrostatically actuated microplates. We use the Galerkin method to develop a tractable reduced-order model for electrostatically actuated clamped rectangular microplates in the presence of van der Waals forces and thermal stresses. More specifically, we reduce the governing two-dimensional nonlinear transient boundary-value problem to a single nonlinear ordinary differential equation. For the static problem, the pull-in voltage and the pull-in displacement are determined by solving a pair of nonlinear algebraic equations. The fundamental vibration frequency corresponding to a deflected configuration of the microplate is determined by solving a linear algebraic equation. The proposed reduced-order model allows for accurately estimating the combined effects of van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflection profile with an extremely limited computational effort. PMID:27879752

Applications of IBSOM and ETEM for solving the nonlinear chains of atoms with long-range interactions

NASA Astrophysics Data System (ADS)

Foroutan, Mohammadreza; Zamanpour, Isa; Manafian, Jalil

2017-10-01

This paper presents a number of new solutions obtained for solving a complex nonlinear equation describing dynamics of nonlinear chains of atoms via the improved Bernoulli sub-ODE method (IBSOM) and the extended trial equation method (ETEM). The proposed solutions are kink solitons, anti-kink solitons, soliton solutions, hyperbolic solutions, trigonometric solutions, and bellshaped soliton solutions. Then our new results are compared with the well-known results. The methods used here are very simple and succinct and can be also applied to other nonlinear models. The balance number of these methods is not constant contrary to other methods. The proposed methods also allow us to establish many new types of exact solutions. By utilizing the Maple software package, we show that all obtained solutions satisfy the conditions of the studied model. More importantly, the solutions found in this work can have significant applications in Hamilton's equations and generalized momentum where solitons are used for long-range interactions.

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

DOE PAGES

Paul, Prokash; Bhattacharyya, Debangsu; Turton, Richard; ...

2017-06-06

Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimizationmore » problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.« less

Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

NASA Astrophysics Data System (ADS)

Eshmatov, B. Kh.

2007-03-01

This paper describes the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. The models are based on the Kirchhoff-Love (K.L.) hypothesis and Reissner-Mindlin (R.M.) generalized theory (with the incorporation of shear deformation and rotatory inertia) in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Koltunov-Rzhanitsyn type kernel, with three rheological parameters. In addition, the implication of each relaxation kernel parameter has been studied. To solve problems of viscoelastic systems with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Bubnov-Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic orthotropic rectangular plates have been solved, according to the K.L. and R.M. hypotheses. A comparison of the results obtained via these theories is also presented. In all problems, the convergence of the Bubnov-Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

NASA Astrophysics Data System (ADS)

Nazemizadeh, M.; Rahimi, H. N.; Amini Khoiy, K.

2012-03-01

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange's principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

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.

Kerr nonlinearity and nonlinear absorption coefficient in a four-level M-model cylindrical quantum dot under the phenomenon of electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Behroozian, B.; Askari, H. R.

2018-07-01

The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1993-01-01

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

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

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

Numerical solution of distributed order fractional differential equations

NASA Astrophysics Data System (ADS)

Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Optimization of Friction Stir Welding Tool Advance Speed via Monte-Carlo Simulation of the Friction Stir Welding Process

PubMed Central

Fraser, Kirk A.; St-Georges, Lyne; Kiss, Laszlo I.

2014-01-01

Recognition of the friction stir welding process is growing in the aeronautical and aero-space industries. To make the process more available to the structural fabrication industry (buildings and bridges), being able to model the process to determine the highest speed of advance possible that will not cause unwanted welding defects is desirable. A numerical solution to the transient two-dimensional heat diffusion equation for the friction stir welding process is presented. A non-linear heat generation term based on an arbitrary piecewise linear model of friction as a function of temperature is used. The solution is used to solve for the temperature distribution in the Al 6061-T6 work pieces. The finite difference solution of the non-linear problem is used to perform a Monte-Carlo simulation (MCS). A polynomial response surface (maximum welding temperature as a function of advancing and rotational speed) is constructed from the MCS results. The response surface is used to determine the optimum tool speed of advance and rotational speed. The exterior penalty method is used to find the highest speed of advance and the associated rotational speed of the tool for the FSW process considered. We show that good agreement with experimental optimization work is possible with this simplified model. Using our approach an optimal weld pitch of 0.52 mm/rev is obtained for 3.18 mm thick AA6061-T6 plate. Our method provides an estimate of the optimal welding parameters in less than 30 min of calculation time. PMID:28788627

Optimization of Friction Stir Welding Tool Advance Speed via Monte-Carlo Simulation of the Friction Stir Welding Process.

PubMed

Fraser, Kirk A; St-Georges, Lyne; Kiss, Laszlo I

2014-04-30

Recognition of the friction stir welding process is growing in the aeronautical and aero-space industries. To make the process more available to the structural fabrication industry (buildings and bridges), being able to model the process to determine the highest speed of advance possible that will not cause unwanted welding defects is desirable. A numerical solution to the transient two-dimensional heat diffusion equation for the friction stir welding process is presented. A non-linear heat generation term based on an arbitrary piecewise linear model of friction as a function of temperature is used. The solution is used to solve for the temperature distribution in the Al 6061-T6 work pieces. The finite difference solution of the non-linear problem is used to perform a Monte-Carlo simulation (MCS). A polynomial response surface (maximum welding temperature as a function of advancing and rotational speed) is constructed from the MCS results. The response surface is used to determine the optimum tool speed of advance and rotational speed. The exterior penalty method is used to find the highest speed of advance and the associated rotational speed of the tool for the FSW process considered. We show that good agreement with experimental optimization work is possible with this simplified model. Using our approach an optimal weld pitch of 0.52 mm/rev is obtained for 3.18 mm thick AA6061-T6 plate. Our method provides an estimate of the optimal welding parameters in less than 30 min of calculation time.

Nonlinear hyperbolic theory of thermal waves in metals

NASA Technical Reports Server (NTRS)

Wilhelm, H. E.; Choi, S. H.

1975-01-01

A closed-form solution for cylindrical thermal waves in metals is given based on the nonlinear hyperbolic system of energy-conservation and heat-flux relaxation equations. It is shown that heat released from a line source propagates radially outward with finite speed in the form of a thermal wave which exhibits a discontinuous wave front. Unique nonlinear thermal-wave solutions exist up to a critical amount of driving energy, i.e., for larger energy releases, the thermal flow becomes multivalued (occurrence of shock waves). By comparison, it is demonstrated that the parabolic thermal-wave theory gives, in general, a misleading picture of the profile and propagation of thermal waves and leads to physical (infinite speed of heat propagation) and mathematical (divergent energy integrals) difficulties. Attention is drawn to the importance of temporal heat-flux relaxation for the physical understanding of fast transient processes such as thermal waves and more general explosions and implosions.

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

Frayce, D.; Khayat, R.E.; Derdouri, A.

The dual reciprocity boundary element method (DRBEM) is implemented to solve three-dimensional transient heat conduction problems in the presence of arbitrary sources, typically as these problems arise in materials processing. The DRBEM has a major advantage over conventional BEM, since it avoids the computation of volume integrals. These integrals stem from transient, nonlinear, and/or source terms. Thus there is no need to discretize the inner domain, since only a number of internal points are needed for the computation. The validity of the method is assessed upon comparison with results from benchmark problems where analytical solutions exist. There is generally goodmore » agreement. Comparison against finite element results is also favorable. Calculations are carried out in order to assess the influence of the number and location of internal nodes. The influence of the ratio of the numbers of internal to boundary nodes is also examined.« less

Short-term climatic fluctuations forced by thermal anomalies

NASA Technical Reports Server (NTRS)

Hanna, A. F.

1982-01-01

A two level, global, spectral model using pressure as a vertical coordinate was developed. The system of equations describing the model is nonlinear and quasi-geostrophic (linear balance). Static stability is variable in the model. A moisture budget is calculated in the lower layer only. Convective adjustment is used to avoid supercritical temperature lapse rates. The mechanical forcing of topography is introduced as a vertical velocity at the lower boundary. Solar forcing is specified assuming a daily mean zenith angle. The differential diabatic heating between land and sea is paramterized. On land and sea ice surfaces, a steady state thermal energy equation is solved to calculate the surface temperature. On the oceans, the sea surface temperature is specified as the climatological average for January. The model is used to simulate the January, February and March circulations.

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

PubMed

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Estimation of Surface Temperature and Heat Flux by Inverse Heat Transfer Methods Using Internal Temperatures Measured While Radiantly Heating a Carbon/Carbon Specimen up to 1920 F

NASA Technical Reports Server (NTRS)

Pizzo, Michelle; Daryabeigi, Kamran; Glass, David

2015-01-01

The ability to solve the heat conduction equation is needed when designing materials to be used on vehicles exposed to extremely high temperatures; e.g. vehicles used for atmospheric entry or hypersonic flight. When using test and flight data, computational methods such as finite difference schemes may be used to solve for both the direct heat conduction problem, i.e., solving between internal temperature measurements, and the inverse heat conduction problem, i.e., using the direct solution to march forward in space to the surface of the material to estimate both surface temperature and heat flux. The completed research first discusses the methods used in developing a computational code to solve both the direct and inverse heat transfer problems using one dimensional, centered, implicit finite volume schemes and one dimensional, centered, explicit space marching techniques. The developed code assumed the boundary conditions to be specified time varying temperatures and also considered temperature dependent thermal properties. The completed research then discusses the results of analyzing temperature data measured while radiantly heating a carbon/carbon specimen up to 1920 F. The temperature was measured using thermocouple (TC) plugs (small carbon/carbon material specimens) with four embedded TC plugs inserted into the larger carbon/carbon specimen. The purpose of analyzing the test data was to estimate the surface heat flux and temperature values from the internal temperature measurements using direct and inverse heat transfer methods, thus aiding in the thermal and structural design and analysis of high temperature vehicles.

VALIDATION OF ANSYS FINITE ELEMENT ANALYSIS SOFTWARE

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

HAMM, E.R.

2003-06-27

This document provides a record of the verification and Validation of the ANSYS Version 7.0 software that is installed on selected CH2M HILL computers. The issues addressed include: Software verification, installation, validation, configuration management and error reporting. The ANSYS{reg_sign} computer program is a large scale multi-purpose finite element program which may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS Full Mechanical Version 7.0 installed on selected CH2M Hill Hanford Group (CH2M HILL) Intel processor based computers include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency andmore » buckling eigenvalue problems, static or time-varying magnetic analyses and various types of field and coupled-field applications. The program contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and thermal radiation. The ANSYS program has been in commercial use since 1970, and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil and steel industries.« less

A New Family of Schroder's Method and Its Variants Based on Power Means for Multiple Roots of Nonlinear Equations

ERIC Educational Resources Information Center

Kanwar, V.; Sharma, Kapil K.; Behl, Ramandeep

2010-01-01

In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

PubMed Central

Qiao, Shan; Jackson, Edward; Coussios, Constantin C.; Cleveland, Robin O.

2016-01-01

Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools. PMID:27914432

A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation.

PubMed

Demi, L; van Dongen, K W A; Verweij, M D

2011-03-01

Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation. © 2011 Acoustical Society of America

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code.

PubMed

Qiao, Shan; Jackson, Edward; Coussios, Constantin C; Cleveland, Robin O

2016-09-01

Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools.

Nonlinear acoustics in biomedical ultrasound

NASA Astrophysics Data System (ADS)

Cleveland, Robin O.

2015-10-01

Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.

Simulation of nonlinear convective thixotropic liquid with Cattaneo-Christov heat flux

NASA Astrophysics Data System (ADS)

Zubair, M.; Waqas, M.; Hayat, T.; Ayub, M.; Alsaedi, A.

2018-03-01

In this communication we utilized a modified Fourier approach featuring thermal relaxation effect in nonlinear convective flow by a vertical exponentially stretchable surface. Temperature-dependent thermal conductivity describes the heat transfer process. Thixotropic liquid is modeled. Convergent local similar solutions by homotopic approach are obtained. Graphical results for emerging parameters of interest are analyzed. Skin friction is calculated and interpreted. Consideration of larger local buoyancy and nonlinear convection parameters yields an enhancement in velocity distribution. Temperature and thermal layer thickness are reduced for larger thermal relaxation factor.

A new solution method for wheel/rail rolling contact.

PubMed

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

NASA Astrophysics Data System (ADS)

Vasant, P.; Ganesan, T.; Elamvazuthi, I.

2012-11-01

A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.

Nonlinear structure formation in ion-temperature-gradient driven drift waves in pair-ion plasma with nonthermal electron distribution

NASA Astrophysics Data System (ADS)

Razzaq, Javaria; Haque, Q.; Khan, Majid; Bhatti, Adnan Mehmood; Kamran, M.; Mirza, Arshad M.

2018-02-01

Nonlinear structure formation in ion-temperature-gradient (ITG) driven waves is investigated in pair-ion plasma comprising ions and nonthermal electrons (kappa, Cairns). By using the transport equations of the Braginskii model, a new set of nonlinear equations are derived. A linear dispersion relation is obtained and discussed analytically as well as numerically. It is shown that the nonthermal population of electrons affects both the linear and nonlinear characteristics of the ITG mode in pair-ion plasma. This work will be useful in tokamaks and stellarators where non-Maxwellian population of electrons may exist due to resonant frequency heating, electron cyclotron heating, runaway electrons, etc.

TRUST84. Sat-Unsat Flow in Deformable Media

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

Narasimhan, T.N.

1984-11-01

TRUST84 solves for transient and steady-state flow in variably saturated deformable media in one, two, or three dimensions. It can handle porous media, fractured media, or fractured-porous media. Boundary conditions may be an arbitrary function of time. Sources or sinks may be a function of time or of potential. The theoretical model considers a general three-dimensional field of flow in conjunction with a one-dimensional vertical deformation field. The governing equation expresses the conservation of fluid mass in an elemental volume that has a constant volume of solids. Deformation of the porous medium may be nonelastic. Permeability and the compressibility coefficientsmore » may be nonlinearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may be characterized by hysteresis. The relation between pore pressure change and effective stress change may be a function of saturation. The basic calculational model of the conductive heat transfer code TRUMP is applied in TRUST84 to the flow of fluids in porous media. The model combines an integrated finite difference algorithm for numerically solving the governing equation with a mixed explicit-implicit iterative scheme in which the explicit changes in potential are first computed for all elements in the system, after which implicit corrections are made only for those elements for which the stable time-step is less than the time-step being used. Time-step sizes are automatically controlled to optimize the number of iterations, to control maximum change to potential during a time-step, and to obtain desired output information. Time derivatives, estimated on the basis of system behavior during the two previous time-steps, are used to start the iteration process and to evaluate nonlinear coefficients. Both heterogeneity and anisotropy can be handled.« less

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

NASA Astrophysics Data System (ADS)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

Improvements to embedded shock wave calculations for transonic flow-applications to wave drag and pressure rise predictions

NASA Technical Reports Server (NTRS)

Seebass, A. R.

1974-01-01

The numerical solution of a single, mixed, nonlinear equation with prescribed boundary data is discussed. A second order numerical procedure for solving the nonlinear equation and a shock fitting scheme was developed to treat the discontinuities that appear in the solution.

Element-by-element Solution Procedures for Nonlinear Structural Analysis

NASA Technical Reports Server (NTRS)

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

1984-01-01

Element-by-element approximate factorization procedures are proposed for solving the large finite element equation systems which arise in nonlinear structural mechanics. Architectural and data base advantages of the present algorithms over traditional direct elimination schemes are noted. Results of calculations suggest considerable potential for the methods described.

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

NASA Astrophysics Data System (ADS)

Ding, Hu; Lim, C. W.; Chen, Li-Qun

2018-06-01

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations

NASA Astrophysics Data System (ADS)

Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati

2016-10-01

The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.

Finite difference time domain calculation of transients in antennas with nonlinear loads

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent

1991-01-01

In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Method of operating a thermal engine powered by a chemical reaction

DOEpatents

Ross, John; Escher, Claus

1988-01-01

The invention involves a novel method of increasing the efficiency of a thermal engine. Heat is generated by a non-linear chemical reaction of reactants, said heat being transferred to a thermal engine such as Rankine cycle power plant. The novel method includes externally perturbing one or more of the thermodynamic variables of said non-linear chemical reaction.

Method of operating a thermal engine powered by a chemical reaction

DOEpatents

Ross, J.; Escher, C.

1988-06-07

The invention involves a novel method of increasing the efficiency of a thermal engine. Heat is generated by a non-linear chemical reaction of reactants, said heat being transferred to a thermal engine such as Rankine cycle power plant. The novel method includes externally perturbing one or more of the thermodynamic variables of said non-linear chemical reaction. 7 figs.

Entropy generation minimization (EGM) of nanofluid flow by a thin moving needle with nonlinear thermal radiation

NASA Astrophysics Data System (ADS)

Waleed Ahmed Khan, M.; Ijaz Khan, M.; Hayat, T.; Alsaedi, A.

2018-04-01

Entropy generation minimization (EGM) and heat transport in nonlinear radiative flow of nanomaterials over a thin moving needle has been discussed. Nonlinear thermal radiation and viscous dissipation terms are merged in the energy expression. Water is treated as ordinary fluid while nanomaterials comprise titanium dioxide, copper and aluminum oxide. The nonlinear governing expressions of flow problems are transferred to ordinary ones and then tackled for numerical results by Built-in-shooting technique. In first section of this investigation, the entropy expression is derived as a function of temperature and velocity gradients. Geometrical and physical flow field variables are utilized to make it nondimensionalized. An entropy generation analysis is utilized through second law of thermodynamics. The results of temperature, velocity, concentration, surface drag force and heat transfer rate are explored. Our outcomes reveal that surface drag force and Nusselt number (heat transfer) enhanced linearly for higher nanoparticle volume fraction. Furthermore drag force decays for aluminum oxide and it enhances for copper nanoparticles. In addition, the lowest heat transfer rate is achieved for higher radiative parameter. Temperature field is enhanced with increase in temperature ratio parameter.

Problems in Nonlinear Acoustics: Pulsed Finite Amplitude Sound Beams, Nonlinear Propagation of Sound in Layered Media, Time Domain Solutions for Focused Sound Beams, Focusing of Sound with an Ellipsoidal Mirror, and Modeling Finite Amplitude Propagation in Waveguides.

DTIC Science & Technology

1991-08-01

performed entirely in the time domain, solves the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wdve equation for pulsed, axisymmetric...finite amplitude sound beams. The KZK equation accounts for the combined effects of nonlinearity, diffraction and thermoviscous absorption on the...those used by Naze Tjotta, Tjotta, and Vefring to produce Fig. 7 of Ref. 4 with a frequency domain numerical solution of the KZK equation. However

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Classical heat transport in anharmonic molecular junctions: exact solutions.

PubMed

Liu, Sha; Agarwalla, Bijay Kumar; Wang, Jian-Sheng; Li, Baowen

2013-02-01

We study full counting statistics for classical heat transport through anharmonic or nonlinear molecular junctions formed by interacting oscillators. An analytical result of the steady-state heat flux for an overdamped anharmonic junction with arbitrary temperature bias is obtained. It is found that the thermal conductance can be expressed in terms of a temperature-dependent effective force constant. The role of anharmonicity is identified. We also give the general formula for the second cumulant of heat in steady state, as well as the average geometric heat flux when two system parameters are modulated adiabatically. We present an anharmonic example for which all cumulants for heat can be obtained exactly. For a bounded single oscillator model with mass we found that the cumulants are independent of the nonlinear potential.

Comparative study of Eyring and Carreau fluids in a suspension of dust and nickel nanoparticles with variable conductivity

NASA Astrophysics Data System (ADS)

Mamatha Upadhya, S.; Mahesha; Raju, C. S. K.

2018-04-01

A theoretical analysis is carried out to investigate the magnetohydrodynamic unsteady flow of Eyring-Powell and Carreau non-Newtonian fluids in a suspension of dust and nickel nanoparticles by considering variable thermal conductivity and thermal radiation. Dispersion of nickel nanoparticles in dusty fluids finds applications in heat exchanger systems, rechargeable batteries, chemical catalysts, metallurgy, conducting paints, magnetic recording media, drug delivery, nanofibers, textiles, etc. The initially arising set of physical governing partial differential equations is transformed to ordinary differential equations (ODEs) with the aid of similarity transformations. Consequentially, the nonlinear ODEs are solved numerically through the Runge-Kutta Fehlberg scheme (RKFS). The computational results for non-dimensional temperature and velocity profiles are presented through graphs. Furthermore, the numerical values of friction factor and heat transfer rate are tabulated numerically for the unsteady and steady cases of the Eyring and Carreau fluid cases and of the dusty non-Newtonian (φ=0) and the dusty non-Newtonian nanofluid (φ≠ 0) cases of the unsteady flow. We also validated the present results with previous published studies and found them to be highly satisfactory. The formulated model reveals that the rate of heat transfer is higher in the mixture of the nickel + Eyring-Powell case compared to the nickel + Carreau case. From this we can highlight that, depending on the industrial appliances, we can use heating or cooling processes for Eyring and Carreau fluids, respectively.

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

Evaluation of laser radiation regimes at thermal tissue destruction

NASA Astrophysics Data System (ADS)

Ivanov, Anatoly; Kazaryan, Mishik A.; Molodykh, E. I.; Shchetinkina, T. A.

1996-01-01

The existing methods of laser destruction of biotissues, widely spread in surgery and coagulation action, are based on local heat emission in the tissues after light absorption. Here we present the results of the simulation of tissues heat destruction, taking into account the influence of blood and lymph circulation on the processes of heat transfer. The problem is adapted to the case of liver tissue with tumor. A liver is considered as a capillary-porous body with internal blood circulation. Heatconductivity and tissue-blood heat transfer are considered. Heat action is assumed to be implemented with contact laser scalpel. The mathematical model consists of two inhomogeneous nonlinear equations of heatconductivity with spherical symmetry. Nonstationary temperature fields of tissue and blood are determined and the main parameters are: (1) coefficients of heatconductivity and capacitance of blood and tissue, (2) blood and tissue density, (3) total metabolic energy, (4) volume coefficient accounting for heat-exchange between tissue and blood, and (5) blood circulation velocity. The power of laser radiation was taken into account in boundary conditions set for the center of coagulated tissue volume. We also took into account the process connected with changing of substance phase (vaporization). The original computer programs allow one to solve the problem varying in a wide range of the main parameters. Reasonable agreement was found between the calculation results and the experimental data for operations on microsamples and on test animals. It was demonstrated, in particular, that liver tissue coagulation regime is achieved at 10 W laser power during 25 s. The coagulation radius of 0.7 cm with the given tumor radius of 0.5 cm corresponds to the real clinical situation in case of metastasis liver affection.

Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

PubMed

Xie, Xue-Jun; Zhang, Xing-Hui

2014-03-01

In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

Real-time trajectory optimization on parallel processors

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1993-01-01

A parallel algorithm has been developed for rapidly solving trajectory optimization problems. The goal of the work has been to develop an algorithm that is suitable to do real-time, on-line optimal guidance through repeated solution of a trajectory optimization problem. The algorithm has been developed on an INTEL iPSC/860 message passing parallel processor. It uses a zero-order-hold discretization of a continuous-time problem and solves the resulting nonlinear programming problem using a custom-designed augmented Lagrangian nonlinear programming algorithm. The algorithm achieves parallelism of function, derivative, and search direction calculations through the principle of domain decomposition applied along the time axis. It has been encoded and tested on 3 example problems, the Goddard problem, the acceleration-limited, planar minimum-time to the origin problem, and a National Aerospace Plane minimum-fuel ascent guidance problem. Execution times as fast as 118 sec of wall clock time have been achieved for a 128-stage Goddard problem solved on 32 processors. A 32-stage minimum-time problem has been solved in 151 sec on 32 processors. A 32-stage National Aerospace Plane problem required 2 hours when solved on 32 processors. A speed-up factor of 7.2 has been achieved by using 32-nodes instead of 1-node to solve a 64-stage Goddard problem.

Nonlinear Fourier algorithm applied to solving equations of gravitational gas dynamics

NASA Technical Reports Server (NTRS)

Kolosov, B. I.

1979-01-01

Two dimensional gas flow problems were reduced to an approximating system of common differential equations, which were solved by a standard procedure of the Runge-Kutta type. A theorem of the existence of stationary conical shock waves with the cone vertex in the gravitating center was proved.

Comparison of penalty functions on a penalty approach to mixed-integer optimization

NASA Astrophysics Data System (ADS)

Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.

2016-06-01

In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.

Application of Least-Squares Adjustment Technique to Geometric Camera Calibration and Photogrammetric Flow Visualization

NASA Technical Reports Server (NTRS)

Chen, Fang-Jenq

1997-01-01

Flow visualization produces data in the form of two-dimensional images. If the optical components of a camera system are perfect, the transformation equations between the two-dimensional image and the three-dimensional object space are linear and easy to solve. However, real camera lenses introduce nonlinear distortions that affect the accuracy of transformation unless proper corrections are applied. An iterative least-squares adjustment algorithm is developed to solve the nonlinear transformation equations incorporated with distortion corrections. Experimental applications demonstrate that a relative precision on the order of 40,000 is achievable without tedious laboratory calibrations of the camera.

Off-policy reinforcement learning for H∞ control design.

PubMed

Luo, Biao; Wu, Huai-Ning; Huang, Tingwen

2015-01-01

The H∞ control design problem is considered for nonlinear systems with unknown internal system model. It is known that the nonlinear H∞ control problem can be transformed into solving the so-called Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that is generally impossible to be solved analytically. Even worse, model-based approaches cannot be used for approximately solving HJI equation, when the accurate system model is unavailable or costly to obtain in practice. To overcome these difficulties, an off-policy reinforcement leaning (RL) method is introduced to learn the solution of HJI equation from real system data instead of mathematical system model, and its convergence is proved. In the off-policy RL method, the system data can be generated with arbitrary policies rather than the evaluating policy, which is extremely important and promising for practical systems. For implementation purpose, a neural network (NN)-based actor-critic structure is employed and a least-square NN weight update algorithm is derived based on the method of weighted residuals. Finally, the developed NN-based off-policy RL method is tested on a linear F16 aircraft plant, and further applied to a rotational/translational actuator system.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

PubMed

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

A Program for Solving the Brain Ischemia Problem

PubMed Central

DeGracia, Donald J.

2013-01-01

Our recently described nonlinear dynamical model of cell injury is here applied to the problems of brain ischemia and neuroprotection. We discuss measurement of global brain ischemia injury dynamics by time course analysis. Solutions to proposed experiments are simulated using hypothetical values for the model parameters. The solutions solve the global brain ischemia problem in terms of “master bifurcation diagrams” that show all possible outcomes for arbitrary durations of all lethal cerebral blood flow (CBF) decrements. The global ischemia master bifurcation diagrams: (1) can map to a single focal ischemia insult, and (2) reveal all CBF decrements susceptible to neuroprotection. We simulate measuring a neuroprotectant by time course analysis, which revealed emergent nonlinear effects that set dynamical limits on neuroprotection. Using over-simplified stroke geometry, we calculate a theoretical maximum protection of approximately 50% recovery. We also calculate what is likely to be obtained in practice and obtain 38% recovery; a number close to that often reported in the literature. The hypothetical examples studied here illustrate the use of the nonlinear cell injury model as a fresh avenue of approach that has the potential, not only to solve the brain ischemia problem, but also to advance the technology of neuroprotection. PMID:24961411

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

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

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

Computational inverse methods of heat source in fatigue damage problems

NASA Astrophysics Data System (ADS)

Chen, Aizhou; Li, Yuan; Yan, Bo

2018-04-01

Fatigue dissipation energy is the research focus in field of fatigue damage at present. It is a new idea to solve the problem of calculating fatigue dissipation energy by introducing inverse method of heat source into parameter identification of fatigue dissipation energy model. This paper introduces the research advances on computational inverse method of heat source and regularization technique to solve inverse problem, as well as the existing heat source solution method in fatigue process, prospects inverse method of heat source applying in fatigue damage field, lays the foundation for further improving the effectiveness of fatigue dissipation energy rapid prediction.

Nonlinear convective flows in a two-layer system under the action of spatial temperature modulation of heat release/consumption at the interface

NASA Astrophysics Data System (ADS)

Simanovskii, Ilya B.; Viviani, Antonio; Dubois, Frank

2018-06-01

An influence of a spatial temperature modulation of the interfacial heat release/consumption on nonlinear convective flows in the 47v2 silicone oil - water system, is studied. Rigid heat-insulated lateral walls, corresponding to the case of closed cavities, have been considered. Transitions between the flows with different spatial structures, have been investigated. It is shown that the spatial modulation can change the sequence of bifurcations and lead to the appearance of specific steady and oscillatory flows in the system.

Application of genetic algorithms in nonlinear heat conduction problems.

PubMed

Kadri, Muhammad Bilal; Khan, Waqar A

2014-01-01

Genetic algorithms are employed to optimize dimensionless temperature in nonlinear heat conduction problems. Three common geometries are selected for the analysis and the concept of minimum entropy generation is used to determine the optimum temperatures under the same constraints. The thermal conductivity is assumed to vary linearly with temperature while internal heat generation is assumed to be uniform. The dimensionless governing equations are obtained for each selected geometry and the dimensionless temperature distributions are obtained using MATLAB. It is observed that GA gives the minimum dimensionless temperature in each selected geometry.

Off-Policy Integral Reinforcement Learning Method to Solve Nonlinear Continuous-Time Multiplayer Nonzero-Sum Games.

PubMed

Song, Ruizhuo; Lewis, Frank L; Wei, Qinglai

2017-03-01

This paper establishes an off-policy integral reinforcement learning (IRL) method to solve nonlinear continuous-time (CT) nonzero-sum (NZS) games with unknown system dynamics. The IRL algorithm is presented to obtain the iterative control and off-policy learning is used to allow the dynamics to be completely unknown. Off-policy IRL is designed to do policy evaluation and policy improvement in the policy iteration algorithm. Critic and action networks are used to obtain the performance index and control for each player. The gradient descent algorithm makes the update of critic and action weights simultaneously. The convergence analysis of the weights is given. The asymptotic stability of the closed-loop system and the existence of Nash equilibrium are proved. The simulation study demonstrates the effectiveness of the developed method for nonlinear CT NZS games with unknown system dynamics.

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

PubMed

Neilson, Peter D; Neilson, Megan D

2005-09-01

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

One-dimensional nonlinear theory for rectangular helix traveling-wave tube

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

Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong

A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numericallymore » using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.« less

Modeling of Inverted Annular Film Boiling using an integral method

NASA Astrophysics Data System (ADS)

Sridharan, Arunkumar

In modeling Inverted Annular Film Boiling (IAFB), several important phenomena such as interaction between the liquid and the vapor phases and irregular nature of the interface, which greatly influence the momentum and heat transfer at the interface, need to be accounted for. However, due to the complexity of these phenomena, they were not modeled in previous studies. Since two-phase heat transfer equations and relationships rely heavily on experimental data, many closure relationships that were used in previous studies to solve the problem are empirical in nature. Also, in deriving the relationships, the experimental data were often extrapolated beyond the intended range of conditions, causing errors in predictions. In some cases, empirical correlations that were derived from situations other than IAFB, and whose applicability to IAFB was questionable, were used. Moreover, arbitrary constants were introduced in the model developed in previous studies to provide good fit to the experimental data. These constants have no physical basis, thereby leading to questionable accuracy in the model predictions. In the present work, modeling of Inverted Annular Film Boiling (IAFB) is done using Integral Method. Two-dimensional formulation of IAFB is presented. Separate equations for the conservation of mass, momentum and energy are derived from first principles, for the vapor film and the liquid core. Turbulence is incorporated in the formulation. The system of second-order partial differential equations is integrated over the radial direction to obtain a system of integral differential equations. In order to solve the system of equations, second order polynomial profiles are used to describe the nondimensional velocity and temperatures. The unknown coefficients in the profiles are functions of the axial direction alone. Using the boundary conditions that govern the physical problem, equations for the unknown coefficients are derived in terms of the primary dependent variables: wall shear stress, interfacial shear stress, film thickness, pressure, wall temperature and the mass transfer rate due to evaporation. A system of non-linear first order coupled ordinary differential equations is obtained. Due to the inherent mathematical complexity of the system of equations, simplifying assumptions are made to obtain a numerical solution. The system of equations is solved numerically to obtain values of the unknown quantities at each subsequent axial location. Derived quantities like void fraction and heat transfer coefficient are calculated at each axial location. The calculation is terminated when the void fraction reaches a value of 0.6, the upper limit of IAFB. The results obtained agree with the experimental trends observed. Void fraction increases along the heated length, while the heat transfer coefficient drops due to the increased resistance of the vapor film as expected.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

NASA Astrophysics Data System (ADS)

Bower, Dan J.; Sanan, Patrick; Wolf, Aaron S.

2018-01-01

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, ∂S / ∂r , as well as entropy itself. First we present a simplified model with semi-analytical solutions that highlights the large dynamic range of ∂S / ∂r -around 12 orders of magnitude-for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple yet stable numerical scheme able to capture the large dynamic range of ∂S / ∂r and hence provide a flexible and robust method for time-integrating the energy equation. Using insight gained from the simplified model, we consider a full model, which includes energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using ∂S / ∂r as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. The computational framework we devise is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations that arise in other science and engineering disciplines, particularly for non-linear functional forms of the diffusion coefficient.

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).

Variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states and its bridge function study

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Bao, Lin; Tong, Binggang

2009-12-01

This paper is a research on the variation character of stagnation point heat flux for hypersonic pointed bodies from continuum to rarefied flow states by using theoretical analysis and numerical simulation methods. The newly developed near space hypersonic cruise vehicles have sharp noses and wingtips, which desires exact and relatively simple methods to estimate the stagnation point heat flux. With the decrease of the curvature radius of the leading edge, the flow becomes rarefied gradually, and viscous interaction effects and rarefied gas effects come forth successively, which results in that the classical Fay-Riddell equation under continuum hypothesis will become invalid and the variation of stagnation point heat flux is characterized by a new trend. The heat flux approaches the free molecular flow limit instead of an infinite value when the curvature radius of the leading edge tends to 0. The physical mechanism behind this phenomenon remains in need of theoretical study. Firstly, due to the fact that the whole flow regime can be described by Boltzmann equation, the continuum and rarefied flow are analyzed under a uniform framework. A relationship is established between the molecular collision insufficiency in rarefied flow and the failure of Fourier’s heat conduction law along with the increasing significance of the nonlinear heat flux. Then based on an inspiration drew from Burnett approximation, control factors are grasped and a specific heat flux expression containing the nonlinear term is designed in the stagnation region of hypersonic leading edge. Together with flow pattern analysis, the ratio of nonlinear to linear heat flux W r is theoretically obtained as a parameter which reflects the influence of nonlinear factors, i.e. a criterion to classify the hypersonic rarefied flows. Ultimately, based on the characteristic parameter W r , a bridge function with physical background is constructed, which predicts comparative reasonable results in coincidence well with DSMC and experimental data in the whole flow regime.

Nonlinear Upshift of Trapped Electron Mode Critical Density Gradient: Simulation and Experiment

NASA Astrophysics Data System (ADS)

Ernst, D. R.

2012-10-01

A new nonlinear critical density gradient for pure trapped electron mode (TEM) turbulence increases strongly with collisionality, saturating at several times the linear threshold. The nonlinear TEM threshold appears to limit the density gradient in new experiments subjecting Alcator C-Mod internal transport barriers to modulated radio-frequency heating. Gyrokinetic simulations show the nonlinear upshift of the TEM critical density gradient is associated with long-lived zonal flow dominated states [1]. This introduces a strong temperature dependence that allows external RF heating to control TEM turbulent transport. During pulsed on-axis heating of ITB discharges, core electron temperature modulations of 50% were produced. Bursts of line-integrated density fluctuations, observed on phase contrast imaging, closely follow modulations of core electron temperature inside the ITB foot. Multiple edge fluctuation measurements show the edge response to modulated heating is out of phase with the core response. A new limit cycle stability diagram shows the density gradient appears to be clamped during on-axis heating by the nonlinear TEM critical density gradient, rather than by the much lower linear threshold. Fluctuation wavelength spectra will be quantitatively compared with nonlinear TRINITY/GS2 gyrokinetic transport simulations, using an improved synthetic diagnostic. In related work, we are implementing the first gyrokinetic exact linearized Fokker Planck collision operator [2]. Initial results show short wavelength TEMs are fully stabilized by finite-gyroradius collisional effects for realistic collisionalities. The nonlinear TEM threshold and its collisionality dependence may impact predictions of density peaking based on quasilinear theory, which excludes zonal flows.[4pt] In collaboration with M. Churchill, A. Dominguez, C. L. Fiore, Y. Podpaly, M. L. Reinke, J. Rice, J. L. Terry, N. Tsujii, M. A. Barnes, I. Bespamyatnov, R. Granetz, M. Greenwald, A. Hubbard, J. W. Hughes, M. Landreman, B. Li, Y. Ma, P. Phillips, M. Porkolab, W. Rowan, S. Wolfe, and S. Wukitch.[4pt] [1] D. R. Ernst et al., Proc. 21st IAEA Fusion Energy Conference, Chengdu, China, paper IAEA-CN-149/TH/1-3 (2006). http://www-pub.iaea.org/MTCD/Meetings/FEC200/th1-3.pdf[0pt] [2] B. Li and D.R. Ernst, Phys. Rev. Lett. 106, 195002 (2011).

Nonlinear Acoustical Assessment of Precipitate Nucleation

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Yost, William T.

2004-01-01

The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.

Comment on “Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems”

NASA Astrophysics Data System (ADS)

Pan, Yongping; Huang, Daoping

2011-03-01

In this comment, we point out the inappropriateness of Theorem 1 in the article [Tsung-Chih Lin, Mehdi Roopaei. Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems. Commun Nonlinear Sci Numer Simulat 2010;15:4065-75]. For solving this problem, some formular mistakes are corrected and novel parameter adaptive laws of interval type-2 fuzzy neural network system are given.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems

NASA Astrophysics Data System (ADS)

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

Arbitrarily high-order time-stepping schemes based on the operator spectrum theory for high-dimensional nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Wu, Xinyuan

2017-07-01

In this paper we explore arbitrarily high-order Lagrange collocation-type time-stepping schemes for effectively solving high-dimensional nonlinear Klein-Gordon equations with different boundary conditions. We begin with one-dimensional periodic boundary problems and first formulate an abstract ordinary differential equation (ODE) on a suitable infinity-dimensional function space based on the operator spectrum theory. We then introduce an operator-variation-of-constants formula which is essential for the derivation of our arbitrarily high-order Lagrange collocation-type time-stepping schemes for the nonlinear abstract ODE. The nonlinear stability and convergence are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix under some suitable smoothness assumptions. With regard to the two dimensional Dirichlet or Neumann boundary problems, our new time-stepping schemes coupled with discrete Fast Sine / Cosine Transformation can be applied to simulate the two-dimensional nonlinear Klein-Gordon equations effectively. All essential features of the methodology are present in one-dimensional and two-dimensional cases, although the schemes to be analysed lend themselves with equal to higher-dimensional case. The numerical simulation is implemented and the numerical results clearly demonstrate the advantage and effectiveness of our new schemes in comparison with the existing numerical methods for solving nonlinear Klein-Gordon equations in the literature.

Wave-induced response of a floating two-dimensional body with a moonpool

PubMed Central

Fredriksen, Arnt G.; Kristiansen, Trygve; Faltinsen, Odd M.

2015-01-01

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. PMID:25512594

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.

A globally convergent LCL method for nonlinear optimization.

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

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm

PubMed Central

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness. PMID:26819583

A Generalized National Planning Approach for Admission Capacity in Higher Education: A Nonlinear Integer Goal Programming Model with a Novel Differential Evolution Algorithm.

PubMed

El-Qulity, Said Ali; Mohamed, Ali Wagdy

2016-01-01

This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.

A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2016-01-01

This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful tool to solve these DDEs. This method reduces the DDEs to ordinary differential equations that are then solved by the DTM. Furthermore, we show that the solutions can be improved by Laplace-Padé resummation method. Two examples are presented to show the efficiency of the proposed technique. The main advantage of this technique is that it possesses a simple procedure based on a few straight forward steps and can be combined with any analytical method, other than the DTM, like the homotopy perturbation method.

Numerical study of heterogeneous mean temperature and shock wave in a resonator

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

Yano, Takeru

2015-10-28

When a frequency of gas oscillation in an acoustic resonator is sufficiently close to one of resonant frequencies of the resonator, the amplitude of gas oscillation becomes large and hence the nonlinear effect manifests itself. Then, if the dissipation effects due to viscosity and thermal conductivity of the gas are sufficiently small, the gas oscillation may evolve into the acoustic shock wave, in the so-called consonant resonators. At the shock front, the kinetic energy of gas oscillation is converted into heat by the dissipation process inside the shock layer, and therefore the temperature of the gas in the resonator rises.more » Since the acoustic shock wave travels in the resonator repeatedly over and over again, the temperature rise becomes noticeable in due course of time even if the shock wave is weak. We numerically study the gas oscillation with shock wave in a resonator of square cross section by solving the initial and boundary value problem of the system of three-dimensional Navier-Stokes equations with a finite difference method. In this case, the heat conduction across the boundary layer on the wall of resonator causes a spatially heterogeneous distribution of mean (time-averaged) gas temperature.« less

Theoretical Issues for Plasma Regimes to be Explored by the Ignitor Experiment

NASA Astrophysics Data System (ADS)

Cardinali, A.; Coppi, B.; Sonnino, G.

2014-10-01

At present, the Ignitor experiment is the only one designed and planned to approach and explore ignition regimes under controlled DT burning conditions. The machine parameters have been established on the basis of existing knowledge of the confinement properties of high density plasmas. A variety of improved confinement regimes are expected to be accessible by means of the available ICRH heating power in addition to the prevalent programmable Ohmic heating power and relying on the injection of high velocity pellets for density profile control. The relevance of the various known confinement regimes to the objectives of Ignitor is discussed. Among other theoretical efforts, a non-linear thermal energy balance equation is investigated to study the onset of thermonuclear instability in the plasmas expected to be produced in Ignitor. The equation for the temperature profile in the equilibrium state is solved with the resulting profiles in agreement with those obtained by a full transport code and commonly adopted scalings for them. The evolution of the thermonuclear instability that relies on the solution of the time dependent energy balance equation is obtained. Sponsored in part by the U.S. DOE.

Three-dimensional rotating flow of MHD single wall carbon nanotubes over a stretching sheet in presence of thermal radiation

NASA Astrophysics Data System (ADS)

Nasir, Saleem; Islam, Saeed; Gul, Taza; Shah, Zahir; Khan, Muhammad Altaf; Khan, Waris; Khan, Aurang Zeb; Khan, Saima

2018-05-01

In this article the modeling and computations are exposed to introduce the new idea of MHD three-dimensional rotating flow of nanofluid through a stretching sheet. Single wall carbon nanotubes (SWCNTs) are utilized as a nano-sized materials while water is used as a base liquid. Single-wall carbon nanotubes (SWNTs) parade sole assets due to their rare structure. Such structure has significant optical and electronics features, wonderful strength and elasticity, and high thermal and chemical permanence. The heat exchange phenomena are deliberated subject to thermal radiation and moreover the impact of nanoparticles Brownian motion and thermophoresis are involved in the present investigation. For the nanofluid transport mechanism, we implemented the Xue model (Xue, Phys B Condens Matter 368:302-307, 2005). The governing nonlinear formulation based upon the law of conservation of mass, quantity of motion, thermal field and nanoparticles concentrations is first modeled and then solved by homotopy analysis method (HAM). Moreover, the graphical result has been exposed to investigate that in what manner the velocities, heat and nanomaterial concentration distributions effected through influential parameters. The mathematical facts of skin friction, Nusselt number and Sherwood number are presented through numerical data for SWCNTs.

The ALI-ARMS Code for Modeling Atmospheric non-LTE Molecular Band Emissions: Current Status and Applications

NASA Technical Reports Server (NTRS)

Kutepov, A. A.; Feofilov, A. G.; Manuilova, R. O.; Yankovsky, V. A.; Rezac, L.; Pesnell, W. D.; Goldberg, R. A.

2008-01-01

The Accelerated Lambda Iteration (ALI) technique was developed in stellar astrophysics at the beginning of 1990s for solving the non-LTE radiative transfer problem in atomic lines and multiplets in stellar atmospheres. It was later successfully applied to modeling the non-LTE emissions and radiative cooling/heating in the vibrational-rotational bands of molecules in planetary atmospheres. Similar to the standard lambda iterations ALI operates with the matrices of minimal dimension. However, it provides higher convergence rate and stability due to removing from the iterating process the photons trapped in the optically thick line cores. In the current ALI-ARMS (ALI for Atmospheric Radiation and Molecular Spectra) code version additional acceleration of calculations is provided by utilizing the opacity distribution function (ODF) approach and "decoupling". The former allows replacing the band branches by single lines of special shape, whereas the latter treats non-linearity caused by strong near-resonant vibration-vibrational level coupling without additional linearizing the statistical equilibrium equations. Latest code application for the non-LTE diagnostics of the molecular band emissions of Earth's and Martian atmospheres as well as for the non-LTE IR cooling/heating calculations are discussed.

Heat transfer flow of Cu-water and Al2O3-water micropolar nanofluids about a solid sphere in the presence of natural convection using Keller-box method

NASA Astrophysics Data System (ADS)

Swalmeh, Mohammed Z.; Alkasasbeh, Hamzeh T.; Hussanan, Abid; Mamat, Mustafa

2018-06-01

Natural convection boundary layer flow over a solid sphere in micropolar nanofluid with prescribed wall temperature is studied. Copper (Cu) and alumina (Al2O3) in water-based micropolar nanofluid has been considered. Tiwari and Das's nanofluid model with realistic empirical correlations are considered to analyze the nanoparticles effects on natural convective flow. The nonlinear partial differential equations of the boundary layer are first transformed into a non-dimensional form and then solved numerically using an implicit finite difference scheme known as Keller-box method. The effects of nanoparticles volume fraction, Prandtl number, micro-rotation parameter on temperature, velocity and angular velocity are plotted and discussed. Further, numerical results for the local Nusselt number and the local skin friction coefficient are obtained. It is found that Cu has a low heat transfer rate as compare to Al2O3 water-based micropolar nanofluid with increasing micro-rotation parameter. The present results of local Nusselt number and the local skin friction for viscous fluid are found to be in good agreement with the literature.

Simplifications for hydronic system models in modelica

DOE PAGES

Jorissen, F.; Wetter, M.; Helsen, L.

2018-01-12

Building systems and their heating, ventilation and air conditioning flow networks, are becoming increasingly complex. Some building energy simulation tools simulate these flow networks using pressure drop equations. These flow network models typically generate coupled algebraic nonlinear systems of equations, which become increasingly more difficult to solve as their sizes increase. This leads to longer computation times and can cause the solver to fail. These problems also arise when using the equation-based modelling language Modelica and Annex 60-based libraries. This may limit the applicability of the library to relatively small problems unless problems are restructured. This paper discusses two algebraicmore » loop types and presents an approach that decouples algebraic loops into smaller parts, or removes them completely. The approach is applied to a case study model where an algebraic loop of 86 iteration variables is decoupled into smaller parts with a maximum of five iteration variables.« less

The Transport of Mass, Energy, and Entropy in Cryogenic Support Struts for Engineering Design

NASA Technical Reports Server (NTRS)

Elchert, J. P.

2012-01-01

Engineers working to understand and reduce cryogenic boil-off must solve a variety of transport problems. An important class of nonlinear problems involves the thermal and mechanical design of cryogenic struts. These classic problems are scattered about the literature and typically require too many resources to obtain. So, to save time for practicing engineers, the author presents this essay. Herein, a variety of new, old, and revisited analytical and finite difference solutions of the thermal problem are covered in this essay, along with commentary on approach and assumptions. This includes a few thermal radiation and conduction combined mode solutions with a discussion on insulation, optimum emissivity, and geometrical phenomenon. Solutions to cooling and heat interception problems are also presented, including a discussion of the entropy generation. The literature on the combined mechanical and thermal design of cryogenic support struts is reviewed with an introduction to the associated numerical methods.

The Transport of Mass, Energy, and Entropy in Cryogenic Support Struts for Engineering Design

NASA Technical Reports Server (NTRS)

Elchert, J. P.

2012-01-01

Engineers working to understand and reduce cryogenic boil-off must solve a. variety of transport problems. An important class of nonlinear problems involves the thermal and mechanical design of cryogenic struts. These classic problems are scattered about the literature and typically require too many resources to obtain. So, to save time for practicing engineers, the author presents this essay. Herein, a variety of new, old, and revisited analytical and finite difference solutions of the thermal problem are covered in this essay, along with commentary on approach and assumptions, This includes a few thermal radiation and conduction combined mode solution with a discussion on insulation, optimum emissivity, and geometrical phenomenon. Solutions to cooling and heat interception problems are also presented, including a discussion of the entropy generation. And the literature on the combined mechanical and thermal design of cryogenic support struts is reviewed with an introduction to the associated numerical methods.

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

Thermal Pollution Mathematical Model. Volume 3: User's Manual for One-Dimensional Numerical Model for the Seasonal Thermocline. [environment impact of thermal discharges from power plants

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.; Nwadike, E. V.

1980-01-01

A user's manual for a one dimensional thermal model to predict the temperature profiles of a deep body of water for any number of annual cycles is presented. The model is essentially a set of partial differential equations which are solved by finite difference methods using a high speed digital computer. The model features the effects of area change with depth, nonlinear interaction of wind generated turbulence and buoyancy, adsorption of radiative heat flux below the surface, thermal discharges, and the effects of vertical convection caused by discharge. The main assumption in the formulation is horizontal homogeneity. The environmental impact of thermal discharges from power plants is emphasized. Although the model is applicable to most lakes, a specific site (Lake Keowee, S.C.) application is described in detail. The programs are written in FORTRAN 5.

Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime

NASA Astrophysics Data System (ADS)

Kumar, Rakesh; Sood, Shilpa; Shehzad, Sabir Ali; Sheikholeslami, Mohsen

A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM). The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number) on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables.

An Introduction to System-Level, Steady-State and Transient Modeling and Optimization of High-Power-Density Thermoelectric Generator Devices Made of Segmented Thermoelectric Elements

NASA Astrophysics Data System (ADS)

Crane, D. T.

2011-05-01

High-power-density, segmented, thermoelectric (TE) elements have been intimately integrated into heat exchangers, eliminating many of the loss mechanisms of conventional TE assemblies, including the ceramic electrical isolation layer. Numerical models comprising simultaneously solved, nonlinear, energy balance equations have been created to simulate these novel architectures. Both steady-state and transient models have been created in a MATLAB/Simulink environment. The models predict data from experiments in various configurations and applications over a broad range of temperature, flow, and current conditions for power produced, efficiency, and a variety of other important outputs. Using the validated models, devices and systems are optimized using advanced multiparameter optimization techniques. Devices optimized for particular steady-state operating conditions can then be dynamically simulated in a transient operating model. The transient model can simulate a variety of operating conditions including automotive and truck drive cycles.

Multi-gene genetic programming based predictive models for municipal solid waste gasification in a fluidized bed gasifier.

PubMed

Pandey, Daya Shankar; Pan, Indranil; Das, Saptarshi; Leahy, James J; Kwapinski, Witold

2015-03-01

A multi-gene genetic programming technique is proposed as a new method to predict syngas yield production and the lower heating value for municipal solid waste gasification in a fluidized bed gasifier. The study shows that the predicted outputs of the municipal solid waste gasification process are in good agreement with the experimental dataset and also generalise well to validation (untrained) data. Published experimental datasets are used for model training and validation purposes. The results show the effectiveness of the genetic programming technique for solving complex nonlinear regression problems. The multi-gene genetic programming are also compared with a single-gene genetic programming model to show the relative merits and demerits of the technique. This study demonstrates that the genetic programming based data-driven modelling strategy can be a good candidate for developing models for other types of fuels as well. Copyright © 2014 Elsevier Ltd. All rights reserved.

Mixed Convection Opposing Flow in a Vertical Porous Annulus-Two Temperature Model

NASA Astrophysics Data System (ADS)

Al-Rashed, Abdullah A. AA; J, Salman Ahmed N.; Khaleed, H. M. T.; Yunus Khan, T. M.; NazimAhamed, K. S.

2016-09-01

The opposing flow in a porous medium refers to a condition when the forcing velocity flows in opposite direction to thermal buoyancy obstructing the buoyant force. The present research refers to the effect of opposing flow in a vertical porous annulus embedded with fluid saturated porous medium. The thermal non-equilibrium approach with Darcy modal is considered. The boundary conditions are such that the inner radius is heated with constant temperature Tw the outer radius is maintained at constant temperature Tc. The coupled nonlinear partial differential equations such as momentum equation, energy equation for fluid and energy equation for solid are solved using the finite element method. The opposing flow variation of average Nusselt number with respect to radius ratio Rr, Aspect ratioAr and Radiation parameter Rd for different values of Peclet number Pe are investigated. It is found that the flow behavior is quite different from that of aiding flow.

Laser beam propagation through bulk nonlinear media: Numerical simulation and experiment

NASA Astrophysics Data System (ADS)

Kovsh, Dmitriy I.

This dissertation describes our efforts in modeling the propagation of high intensity laser pulses through optical systems consisting of one or multiple nonlinear elements. These nonlinear elements can be up to 103 times thicker than the depth of focus of the laser beam, so that the beam size changes drastically within the medium. The set of computer codes developed are organized in a software package (NLO_BPM). The ultrafast nonlinearities of the bound-electronic n2 and two-photon absorption as well as time dependent excited-state, free-carrier and thermal nonlinearities are included in the codes for modeling propagation of picosecond to nanosecond pulses and pulse trains. Various cylindrically symmetric spatial distributions of the input beam are modeled. We use the cylindrical symmetry typical of laser outputs to reduce the CPU and memory requirements making modeling a real- time task on PC's. The hydrodynamic equations describing the rarefaction of the medium due to heating and electrostriction are solved in the transient regime to determine refractive index changes on a nanosecond time scale. This effect can be simplified in some cases by an approximation that assumes an instantaneous expansion. We also find that the index change obtained from the photo-acoustic equation overshoots its steady-state value once the ratio between the pulse width and the acoustic transit time is greater than unity. We numerically study the sensitivity of the closed- aperture Z-scan experiment to nonlinear refraction for various input beam profiles. If the beam has a ring structure with a minimum (or zero) on axis in the far field, the sensitivity of Z-scan measurements can be increased by up to one order of magnitude. The linear propagation module integrated with the nonlinear beam propagation codes allows the simulation of typical experiments such as Z-scan and optical limiting experiments. We have used these codes to model the performance of optical limiters. We study two of the most promising limiter designs: the monolithic self-protective semiconductor limiter (MONOPOL) and a multi-cell tandem limiter based on a liquid solution of reverse saturable absorbing organic dye. The numerical outputs show good agreement with experimental results up to input energies where nonlinear scattering becomes significant.

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.

Shock-induced heating and millisecond boiling in gels and tissue due to high intensity focused ultrasound

PubMed Central

Canney, Michael S.; Khokhlova, Vera A.; Bessonova, Olga V.; Bailey, Michael R.; Crum, Lawrence A.

2009-01-01

Nonlinear propagation causes high intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency. Although such nonlinear effects have previously been investigated and found not to significantly alter high intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm. One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue. The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves. In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm2 was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples. Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector, and fluctuation of the drive voltage at the HIFU source. The time to boil obtained experimentally was used to quantify heating rates and was compared to calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and from measurements with a fiber optic hydrophone. As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output. Nonlinear heating due to shock waves is therefore important to HIFU and clinicians should be aware of the potential for very rapid boiling since it alters treatments. PMID:20018433

Enhanced energy transport owing to nonlinear interface interaction

PubMed Central

Su, Ruixia; Yuan, Zongqiang; Wang, Jun; Zheng, Zhigang

2016-01-01

It is generally expected that the interface coupling leads to the suppression of thermal transport through coupled nanostructures due to the additional interface phonon-phonon scattering. However, recent experiments demonstrated that the interface van der Waals interactions can significantly enhance the thermal transfer of bonding boron nanoribbons compared to a single freestanding nanoribbon. To obtain a more in-depth understanding on the important role of the nonlinear interface coupling in the heat transports, in the present paper, we explore the effect of nonlinearity in the interface interaction on the phonon transport by studying the coupled one-dimensional (1D) Frenkel-Kontorova lattices. It is found that the thermal conductivity increases with increasing interface nonlinear intensity for weak inter-chain nonlinearity. By developing the effective phonon theory of coupled systems, we calculate the dependence of heat conductivity on interfacial nonlinearity in weak inter-chain couplings regime which is qualitatively in good agreement with the result obtained from molecular dynamics simulations. Moreover, we demonstrate that, with increasing interface nonlinear intensity, the system dimensionless nonlinearity strength is reduced, which in turn gives rise to the enhancement of thermal conductivity. Our results pave the way for manipulating the energy transport through coupled nanostructures for future emerging applications. PMID:26787363

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

NASA Astrophysics Data System (ADS)

Farhadi, L.; Abdolghafoorian, A.

2015-12-01

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

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

Nonlinearization and waves in bounded media: old wine in a new bottle

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; Seymour, Brian R.

2017-02-01

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

Nonlinear single-spin spectrum analyzer.

PubMed

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2013-03-15

Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

A Novel Approach to Anharmonicity for a Wealth of Applications in Nonlinear Science Technologies

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

Hanusse, Patrick

2011-04-19

We present a new theory of the anharmonicity of nonlinear oscillations that are exhibited by many physical systems. New physical quantities are introduced that describe the departure from linear or harmonic behavior and as far as extremely anharmonic situations. In order to solve the nonlinear phase equation, the key notion of our theory, which controls the anharmonic behavior, a new and fascinating nonlinear trigonometry is designed. These results provide a general and accurate yet compact description of such signals, by far better than the Fourier description, both quantitatively and qualitatively and will benefit many application fields.

Nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting

NASA Astrophysics Data System (ADS)

Abed, I.; Kacem, N.; Bouhaddi, N.; Bouazizi, M. L.

2016-04-01

We investigate the nonlinear dynamics of magnetically coupled beams for multi-modal vibration energy harvesting. A multi-physics model for the proposed device is developed taking into account geometric and magnetic nonlinearities. The coupled nonlinear equations of motion are solved using the Galerkin discretization coupled with the harmonic balance method and the asymptotic numerical method. Several numerical simulations have been performed showing that the expected performances of the proposed vibration energy harvester are significantly promising with up to 130 % in term of bandwidth and up to 60 μWcm-3g-2 in term of normalized harvested power.

Heat current through an artificial Kondo impurity beyond linear response

NASA Astrophysics Data System (ADS)

Sierra, Miguel A.; Sánchez, David

2018-03-01

We investigate the heat current of a strongly interacting quantum dot in the presence of a voltage bias in the Kondo regime. Using the slave-boson mean-field theory, we discuss the behavior of the energy flow and the Joule heating. We find that both contributions to the heat current display interesting symmetry properties under reversal of the applied dc bias. We show that the symmetries arise from the behavior of the dot transmission function. Importantly, the transmission probability is a function of both energy and voltage. This allows us to analyze the heat current in the nonlinear regime of transport. We observe that nonlinearities appear already for voltages smaller than the Kondo temperature. Finally, we suggest to use the contact and electric symmetry coefficients as a way to measure pure energy currents.

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.

Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-09-01

The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

Documentation of computer program VS2D to solve the equations of fluid flow in variably saturated porous media

USGS Publications Warehouse

Lappala, E.G.; Healy, R.W.; Weeks, E.P.

1987-01-01

This report documents FORTRAN computer code for solving problems involving variably saturated single-phase flow in porous media. The flow equation is written with total hydraulic potential as the dependent variable, which allows straightforward treatment of both saturated and unsaturated conditions. The spatial derivatives in the flow equation are approximated by central differences, and time derivatives are approximated either by a fully implicit backward or by a centered-difference scheme. Nonlinear conductance and storage terms may be linearized using either an explicit method or an implicit Newton-Raphson method. Relative hydraulic conductivity is evaluated at cell boundaries by using either full upstream weighting, the arithmetic mean, or the geometric mean of values from adjacent cells. Nonlinear boundary conditions treated by the code include infiltration, evaporation, and seepage faces. Extraction by plant roots that is caused by atmospheric demand is included as a nonlinear sink term. These nonlinear boundary and sink terms are linearized implicitly. The code has been verified for several one-dimensional linear problems for which analytical solutions exist and against two nonlinear problems that have been simulated with other numerical models. A complete listing of data-entry requirements and data entry and results for three example problems are provided. (USGS)

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.

PubMed

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

PubMed Central

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

An efficient direct solver for rarefied gas flows with arbitrary statistics

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

Diaz, Manuel A., E-mail: f99543083@ntu.edu.tw; Yang, Jaw-Yen, E-mail: yangjy@iam.ntu.edu.tw; Center of Advanced Study in Theoretical Science, National Taiwan University, Taipei 10167, Taiwan

2016-01-15

A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes themore » limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology.« less

Thermophysical analysis for three-dimensional MHD stagnation-point flow of nano-material influenced by an exponential stretching surface

NASA Astrophysics Data System (ADS)

Ur Rehman, Fiaz; Nadeem, Sohail; Ur Rehman, Hafeez; Ul Haq, Rizwan

2018-03-01

In the present paper a theoretical investigation is performed to analyze heat and mass transport enhancement of water-based nanofluid for three dimensional (3D) MHD stagnation-point flow caused by an exponentially stretched surface. Water is considered as a base fluid. There are three (3) types of nanoparticles considered in this study namely, CuO (Copper oxide), Fe3O4 (Magnetite), and Al2O3 (Alumina) are considered along with water. In this problem we invoked the boundary layer phenomena and suitable similarity transformation, as a result our three dimensional non-linear equations of describing current problem are transmuted into nonlinear and non-homogeneous differential equations involving ordinary derivatives. We solved the final equations by applying homotopy analysis technique. Influential outcomes of aggressing parameters involved in this study, effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. It is worth mentioning that Skin-friction along x and y-direction is maximum for Copper oxide-water nanofluid and minimum for Alumina-water nanofluid. Result for local Nusselt number is maximum for Copper oxide-water nanofluid and is minimum for magnetite-water nanofluid.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1986-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Nonlinear vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1987-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Plasticity - Theory and finite element applications.

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H. S.

1972-01-01

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

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

Modulation of localized solutions in a system of two coupled nonlinear Schrödinger equations.

PubMed

Cardoso, W B; Avelar, A T; Bazeia, D

2012-08-01

In this work we study localized solutions of a system of two coupled nonlinear Schrödinger equations, with the linear (potential) and nonlinear coefficients engendering spatial and temporal dependencies. Similarity transformations are used to convert the nonautonomous coupled equations into autonomous ones and we use the trial orbit method to help us solving them, presenting solutions in a general way. Numerical experiments are then used to verify the stability of the localized solutions.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites

NASA Technical Reports Server (NTRS)

Arenz, R. J.; Landel, R. F.

1989-01-01

Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.

Fast Neural Solution Of A Nonlinear Wave Equation

NASA Technical Reports Server (NTRS)

Barhen, Jacob; Toomarian, Nikzad

1996-01-01

Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).

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

Sharma, Arvind, E-mail: arvindsharma230771@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com

We investigate the interaction of optical vector soliton with a symmetric thin-film gallium-silica waveguide structure using the equivalent particle theory. The relevant nonlinear Schrodinger equation has been solved by the method of phase plane analysis. The analysis shows beam break up into transmitted, reflected and nonlinear surface waves at the interface. The stability properties of the solitons so formed have been discussed.

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

NASA Astrophysics Data System (ADS)

Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

2015-12-01

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

Solving multi-leader-common-follower games.

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

Leyffer, S.; Munson, T.; Mathematics and Computer Science

Multi-leader-common-follower games arise when modelling two or more competitive firms, the leaders, that commit to their decisions prior to another group of competitive firms, the followers, that react to the decisions made by the leaders. These problems lead in a natural way to equilibrium problems with equilibrium constraints (EPECs). We develop a characterization of the solution sets for these problems and examine a variety of nonlinear optimization and nonlinear complementarity formulations of EPECs. We distinguish two broad cases: problems where the leaders can cost-differentiate and problems with price-consistent followers. We demonstrate the practical viability of our approach by solving amore » range of medium-sized test problems.« less

Numerical solution of Euler's equation by perturbed functionals

NASA Technical Reports Server (NTRS)

Dey, S. K.

1985-01-01

A perturbed functional iteration has been developed to solve nonlinear systems. It adds at each iteration level, unique perturbation parameters to nonlinear Gauss-Seidel iterates which enhances its convergence properties. As convergence is approached these parameters are damped out. Local linearization along the diagonal has been used to compute these parameters. The method requires no computation of Jacobian or factorization of matrices. Analysis of convergence depends on properties of certain contraction-type mappings, known as D-mappings. In this article, application of this method to solve an implicit finite difference approximation of Euler's equation is studied. Some representative results for the well known shock tube problem and compressible flows in a nozzle are given.