Propagation of thermal waves in transient heat conduction in a thin film

Wave nature of heat propagation in a very thin film subjected to an exponen tially decaying temperature change on both sides is investigated by solving the hyperbolic heat conduction equation. Analytical expressions are obtain ed for the temperature and heat flux distributions. Numerical computations are performed in order to determine the behavior of temperature and heat fl ux distributions before and after the collision of the wave fronts from two sides of the him. It is disclosed that in transient heat conduction a heat pulse is transported as a wave only when the decaying frequency of wall te mperature equals the reciprocal of thermal relaxation time of the medium (o mega = 1/tau), which is attenuated in the film, and that non-Fourier heat c onduction is extremely significant with certain range of him thickness and time. The Fourier's law used in macroscale heat conduction cannot be applie d. The results also show that both temperature overshoot and temperature un dershoot occur in the films with smaller values of chi(0)/tau(C) within a v ery short period of time, and that the first reverse flow of heat occurs at the same moment beta = 0.79 for all films with different values of chi(0)/ tau(C) considered in this work. (C) 1998 The Franklin Institute. Published by Elsevier Science Ltd.