Parabolic two-step model and accurate numerical scheme for nanoscale heat conduction induced by ultrashort-pulsed laser heating

Abstract

Simulation of nanoscale heat transfer phenomena has attracted great attention, particularly the nano-scale heat conduction induced by ultrashort-pulsed laser heating. In this article, we propose a nanoscale parabolic two-step model and an accurate numerical scheme for thermal analysis of the nanoscale heat conduction induced by ultrashort-pulsed laser heating. To this end, we first introduce the Knudsen number (Kn) into the original parabolic two-step heat conduction equations and couple them with the Kn-dependent and temperature-jump boundary condition. We then develop a fourth-order accurate compact finite difference method for solving the nanoscale model. Stability and convergence of the obtained numerical scheme are analyzed theoretically. We finally test the accuracy and applicability of the nanoscale model and the obtained numerical scheme in three examples. By choosing various values of the Kn and the parameter α in the boundary condition, the simulation could be a tool for analyzing the nanoscale heat conduction induced by ultrashort-pulsed laser heating.