Non-Fourier Heat Conduction in a Semi-infinite Solid Subjected to Oscillatory Surface Thermal Disturbances

Abstract

Many investigators have explored the effect of non-Fourier conduction in transient processes in recent years. Based on a relaxation model for heat conduction in solids and liquids, the traditional heat diffusion equation is replaced with a hyperbolic equation that accounts for the finite thermal propagation speed. The use of the hyperbolic equation removes the nonphysical phenomenon of the diffusion equation analysis that predicts instantaneous temperature disturbances at all points in the medium for a step heat flux at the boundary. It further removes the peculiarity of an infinite temperature gradient at the boundary as time goes to zero. The objective of this work is to show that the non-Fourier conduction effect can be important even at a long-time after the initial transient if the thermal disturbance is oscillatory with the period of oscillation of the same order of the magnitude as the thermal relaxation time. In particular, the thermal response of a semi-infinite solid subjected to a sinusoidal boundary heat flux condition is generated. The present solution illustrates readily that, in many practical situations such as the repeated irradiation of a solid by a laser with very short pulse width, heat transfer analyses using the traditional Fourier heat diffusion equationmore » can result in significant errors. The current results also suggest that the thermal relaxation time of a solid can be determined by measuring the thermal response of the solid can be determined by measuring the thermal response of the solid irradiated by a high-frequency heat flux.« less