Transient heat-transfer phenomenon of two-dimensional hyperbolic heat conduction problem

Abstract

This article presents a numerical analysis of the two-dimensional hyperbolic heat conduction problem in an anisotropic medium under a point heat source with different boundary conditions. A simple model has been developed to solve the anisotropic problem. In this analysis, the second-order total variation diminishing (TVD) scheme is employed to solve this problem. The effects of boundary conditions and anisotropy on the thermal wave induced by different types of heat sources in the medium are examined in detail. The results show that the transient behavior of the propagation of the two-dimensional thermal wave is much more complicated than that of the one-dimensional thermal wave due to a circular wave formed to propagate uniformly in all directions, reflections by boundaries, interaction with each other, and serious discontinuity on the wavefront.