Asymmetrical collision of thermal waves in thin films: An analytical solution

• Thermal wave phenomena in thin films subjected to non-homogeneous boundary is studied.
• C -V model is solved using the superposition principle with solution structure theorems.
• Thermal wave front has a sharp temperature gradient due to finite speed of transport.
• Asymmetric collisions using the C -V results could be seen within the slab.
• Effect of thermal wave propagation may be critical in many engineering applications.

The purpose of this study is to examine thermal wave phenomena in a thin finite film subjected to non-homogeneous boundary conditions. The Cattaneo–Vernotte (C–V) heat conduction model is solved using the superposition principle in conjunction with the solution structure theorems. For comparison purposes, the diffusion model is also solved to demonstrate the flexibility in the technique as well as to show the differences in the results. It is recognized that the solution structure theorems are suitable for homogeneous systems only. However, by performing a functional transformation, the original non-homogeneous partial differential equation governing the physical problem can be cast into a new form with homogeneous boundary conditions such that it can be solved directly with the solution structure theorems. In this study, details of this process will be examined and explored for achieving solutions in such systems. The methodology provides a convenient technique for the solution of the diffusion and C–V heat conduction equations with non-homogeneous boundary conditions.