Analysis for Microscopic Hyperbolic Two-Step Heat Transfer Problems

This work analyzes the heat transfer problems in thin metal films using the microscopic hyperbolic two-step model. It is necessary in dealing with such problems to solve a set of the coupled energy equations or an equation containing higher-order mixed derivatives in both time and space. This present numerical scheme eliminates the coupling between energy equations with the Laplace transform technique and leads to a second-order governing differential equation in the transform domain. Afterward, the transformed second- order governing differential equation is discretized by the control volume scheme. To demonstrate the efficiency and accuracy of the present numerical scheme, a comparison between the present numerical results and the analytical solution is made. Theoretical insight into the hyperbolic two-step heat conduction is provided. Results show that the thermal propagation velocity is finite and is independent of the coupling factor and the volumetric heat capacity ratio between electrons and the lattice.