Analytical Study of Heat Diffusion and Propagation in Solids Induced by Exponentially-Decaying Heat Source

Abstract

The classical parabolic heat conduction equation based on Fourier’s law of heat conduction and the hyperbolic heat conduction equation based on the Cattaneo-Vernotte (C-V) constitutive relation are compared in this study. The present investigation considers the effect of thermal diffusion and wave propagation in solids subjected to a timevarying and spatially-decaying laser irradiation. The incoming energy is simulated as internal heat generation inside the medium. Temperature profiles are presented as closed-form series solutions for both models by using the method of superposition and the solution structure theorem. Results demonstrate that temperatures, based on the classical diffusion theory, are under-predicted at small and moderate times as compared to the wave model under high heat flux and rapid change in temperature situations. The C-V model predicts a higher peak temperature inside the medium and forms a small wave beneath the incident surface due to the lagging behavior in energy transport when compared to the diffusion model at extremely short time periods. The diffusion model may show an overall smaller temperature in the beginning; however, it over-predicts the peak temperature as compared to the results with the wave model at large times.