Analytical solution of hyperbolic heat conduction equation in a thin film layer with space-dependent thermal conductivity

Abstract

In this paper, the non-Fourier heat conduction problem in a finite slab is analyzed. Dependence of thermal conductivity on space which is mostly encountered in nonhomogeneous materials has been considered. HHC equation has been solved by employing trial solution method and collocation optimization criterion. A temperature peak on the insulated wall of the slab has been observed due to linear variation of thermal conductivity, so the main feature of this article is to find the amount of temperature peak and the time at which it occurs. It has been shown that the magnitude of the temperature peak increases with increasing the dimensionless relaxation time. In order to validate the approach, the results have been compared with the analytical solution obtained for a special case which shows a good agreement.