Non-Fourier Heat Conduction of Nano-Films under Ultra-Fast Laser

Abstract

The ultra-fast laser heating process of nano-films is characterized by an ultra-short duration and ultra-small space size, in which the classical Fourier law based on the hypothesis of local equilibrium is no longer applicable. Based on the Cattaneo–Vernotte (CV) model and the dual-phase-lag (DPL) model, the two-dimensional analytical solutions of heat conduction in nano-films under ultra-fast laser are obtained using the integral transformation method. The results show that there is a thermal wave phenomenon inside the film, which becomes increasingly evident as the elapse of the lag time of the temperature gradient. Moreover, the wave amplitude in the vertical direction is much larger than that in the horizontal direction of the nano-film. By comparing the numerical result of the two models, it is found that the temperature distribution inside the nano-film based on the DPL model is gentler than that of the CV model. Additionally, the temperature distribution in the two-dimensional solution is lower than that in the one-dimensional solution under the same Knudsen number. In the comparison results of the CV model, the maximum peak difference in the thermal wave reaches 75.08 K when the Knudsen number is 1.0. This demonstrates that the horizontal energy carried by the laser source significantly impacts the temperature distribution within the film.

Keywords

• non-Fourier heat conduction
• ultra-fast laser
• nano-films
• Cattaneo–Vernotte model
• dual-phase-lag model