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 exponentially decaying temperature change on both sides is investigated by solving the hyperbolic heat conduction equation. Analytical expressions are obtained for the temperature and heat flux distributions. Numerical computations are performed in order to determine the behavior of temperature and heat flux distributions before and after the collision of the wave fronts from two sides of the film. It is disclosed that in transient heat conduction a heat pulse is transported as a wave only when the decaying frequency of wall temperature equals the reciprocal of thermal relaxation time of the medium (ω = 1\τ), which is attenuated in the film, and that non-Fourier heat conduction is extremely significant with certain range of film thickness and time. The Fouriers law used in macroscale heat conduction cannot be applied. The results also show that both temperature overshoot and temperature undershoot occur in the films with smaller values of x0\τC within a very short period of time, and that the first reverse flow of heat occurs at the same moment β = 0.79 for all films with different values of x0\τC considered in this work.