Theoretical investigation of transport and reflection of thermal waves

Scope and method of study. The purpose of this study is to investigate the behavior of thermal waves which are important in microscale heat conduction. The propagation and reflection of thermal waves are studied based on the hyperbolic heat conduction model and phonon transport theory. Numerical methods such as the TVD (Total Variational Diminishing) method and the characteristic method are used to solve the hyperbolic heat conduction equations and phonon transport equations.; Findings and conclusions. Through this research, the propagation and reflection of thermal waves in homogeneous and non-homogeneous materials are investigated, and the relationships for the reflectivity are developed for one-dimensional and two-dimensional hyperbolic thermal waves. The study of the phonon transport process has shown that both the parabolic heat conduction model and the hyperbolic heat conduction model are not accurate when the time scale and dimension scale are small. For large dimension scale and time scale the three models are very close. Therefore, the phonon transport model should be used to study small scale heat conduction problems. The hyperbolic waves are found to be the basic wave form of thermal waves. The intensity waves are hyperbolic waves, and the reflection theory for hyperbolic waves can be used to solve for the interface reflection of phonon transport processes.