One–Dimensional Analysis of Relativistic Heat Conduction and Thermoelastic Stress Wave

Abstract

Heat transfer in media is generally characterized by the empirical heat conduction law which had been proposed by Fourier. However, the application of this empirical law to the problem of fast transient heat transfer such as a pulsed laser heat is not available, because Fourier's law leads to an infinite velocity of heat propagation since the resulting diffusion equation is parabolic form. It has to be imposed that the heat propagates with a finite velocity from the restriction of relativistic concept. A lot of models have been suggested to overcome this difficulty. In this study, one dimensional thermal wave analysis was conducted based upon coupling with relativistic heat conduction equation formulated by Load and Shulamn and dynamic theory of thermo-elasticity. In some reports related with this problem, the relativistic heat conduction equation was linearized by eliminating a higher order term. In this study, influence of nonlinear term in the relativistic equation on thermal wave propagation was discussed strictly.