Study of Hyperbolic Heat Conduction Problem in the Film and Substrate Composite with the Interface Resistance

Abstract

The hybrid application of the Laplace transform technique and the control-volume method in conjunction with the hyperbolic shape functions is employed to analyze the hyperbolic heat conduction problem in the film and substrate composite under a pulsed volumetric source adjacent to the exterior film surface. The model of the convective boundary condition is applied to specify the interface thermal resistance. The major difficulty encountered in the present problem is the numerical oscillations in the vicinity of the jump discontinuity. In order to evidence the accuracy of the present numerical method, a comparison between the present numerical results and the analytical solution is made. The results show that the present numerical method can suppress the numerical oscillations and the present numerical results agree well with the analytical solution. The propagation behavior of the thermal wave in the film and substrate composite depends on the thermal property ratios of two dissimilar materials and the interface thermal resistance. The interface thermal resistance restricts the energy transmission across the interface of the film and substrate composite and alters the strength of the reflected and transmitted waves.