A numerical solution of two-dimensional hyperbolic heat conduction with non-linear boundary conditions

Abstract. An explicit TVD scheme is used for two-dimensional non-Fourier heat conduction problems in the general coordinate system with both convection and radiation boundary conditions. The hyperbolic heat flux model is used to simulate the non-Fourier heat conduction. Because of the wave nature of hyperbolic equations, characteristics are used to find the unknown value (either heat flux or temperature) on the boundaries. For convective boundary the unknown temperature is calculated explicitly; for radiation boundary Newton's iteration method is applied to find the boundary temperature. Results of numerical examples agree with the physical expectations indicating that the present approach can be used for modeling non-Fourier heat conduction with complex boundary conditions.

[1]  Stanislaw Sieniutycz,et al.  The variational principles of classical type for non-coupled non-stationary irreversible transport processes with convective motion and relaxation , 1977 .

[2]  R. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer. By D. A ANDERSON, J. C. TANNEHILL and R. H. PLETCHER. Hemisphere, 1984. 599 pp. $39.95. , 1986, Journal of Fluid Mechanics.

[3]  A. Majumdar.  Microscale Heat Conduction in Dielectric Thin Films , 1993 .

[4]  C. L. Tien,et al.  Heat transfer mechanisms during short-pulse laser heating of metals , 1993 .

[5]  D. Tzou.  A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales , 1995 .

[6]  C. Grigoropoulos,et al.  Transient Temperature During Pulsed Excimer Laser Heating of Thin Polysilicon Films Obtained by Optical Reflectivity Measurement , 1995 .

[7]  M. N. Özişik,et al.  Hyperbolic heat conduction with surface radiation , 1985 .

[8]  H. Q. Yang.  Characteristics-based, high-order accurate and nonoscillatory numerical method for hyperbolic heat conduction , 1990 .

[9]  Han-Taw Chen,et al.  NUMERICAL SOLUTION OF TWO-DIMENSIONAL NONLINEAR HYPERBOLIC HEAT CONDUCTION PROBLEMS , 1994 .

[10]  T. Lam,et al.  A NUMERICAL SCHEME FOR NON-FOURIER HEAT CONDUCTION, PART I: ONE-DIMENSIONAL PROBLEM FORMULATION AND APPLICATIONS , 1998 .

[11]  K. J. Baumeister,et al.  Hyperbolic Heat-Conduction Equation—A Solution for the Semi-Infinite Body Problem , 1969 .

[12]  Richard H. Pletcher,et al.  Computational Fluid Mechanics and Heat Transfer , 1984 .

[13]  A. V. Luikov,et al.  Application of irreversible thermodynamics methods to investigation of heat and mass transfer , 1966 .

[14]  Solution of two-dimensional hyperbolic heat conduction by high-resolution numerical methods , 1992 .

[15]  Kenneth E. Goodson,et al.  Electron and Phonon Thermal Conduction in Epitaxial High-Tc Superconducting Films , 1993 .

[16]  M. K. Moallemi,et al.  Experimental evidence of hyperbolic heat conduction in processed meat , 1995 .