Abstract
This work studies the depth of thermal penetration in the fast-transient process of heat transport, with emphasis on the rapid evolution of heat affected zone that reflects the combined behavior of thermalization and relaxation during the short-time transient. Employing the dual-phase-lag model, the heat balance integral is derived that contains both the phase lag of the heat flux vector (reflecting the relaxation behavior) and the phase lag of the temperature gradient (reflecting the thermalization behavior). The early-time responses where both phase lags are strong functions of temperature are modeled in detail, which emphasize the ways in which the classical diffusion behavior is retrieved as the thermalization and relaxation behaviors gradually diminish in the time-history. It shows that the classical diffusion model assuming Fourier’s law does not provide a conservative estimate for the response of temperature in the thermal process zone, which may result in unexpected early-time failure of conductors if not properly controlled. From a microscopic point of view, these unexpected factors are interpreted in terms of the microscopic parameters, including the coupling factor in phonon-electron interactions (for metallic structure) and the umklapp and normal relaxation times in phonon scattering (for semiconductors and insulators.
