A Hybrid FE-FD Scheme for Solving Parabolic Two-Step Micro Heat Transport Equations in an Irregularly Shaped Three-Dimensional Double-Layered Thin Film

Abstract

Heat transport at the microscale is important in microtechnology applications. The heat transport equations are parabolic two-step equations, which differ from the traditional heat diffusion equation. In this study, a hybrid finite-element–finite-difference (FE-FD) method for solving the parabolic two-step heat transport equations in a three-dimensional, irregular geometry, double-layered thin film exposed to ultrashort-pulsed lasers is developed. It is shown that the scheme is unconditionally stable with respect to the heat source. The method is illustrated by three numerical examples in which the temperature rise in a gold layer on a chromium padding layer is investigated.