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.