Reflection and refraction of a thermal wave at an ideal interface

Thermal waves are of great significance as non-Fourier effects arise with ultrafast heating rates and small system length. This study analytically and numerically investigated the behavior of thermal waves based on the Cattaneo-Vernotte model at an ideal interface. A stable, fast algorithm based on the alternative direction implicit method is introduced to solve the two-dimensional heat conduction problem. When thermal waves meet with an ideal interface, some energy is reflected back while the rest is conveyed across the interface, which are called the reflection and refraction of thermal waves. The changes of the profile and direction and the energy distribution between the reflection and refraction of the thermal waves are studied both analytically and numerically. Regardless of the boundary conditions imposed on the interface, the reflection angle is always identical to the incident angle, and the ratio of the sine of the refraction angle of the thermal waves to that of the incident angle is equal to the ratio of the thermal wave speeds in the two material layers. A theoretical equation to describe the relationships between the energy distribution and the material thermal properties shows that the thermal wave speeds in the materials, the specific heat and the incident angle determine the thermal energy transmittance ratio. Total reflection can occur for some conditions, and the nature of the energy conveyed by thermal waves is interesting and instructive.