Transient Micro-Nano Heat Conduction Analysis Using a Combination of the Finite Difference Method, the Collocation Meshfree Method and the Discrete Ordinate Method

Abstract

For studying transient heat conduction problems in the micro-nano scale, the standard heat diffusion equation is no longer applicable, and the time-dependent Boltzmann transport equation (BTE) needs to be solved. Although mesh-based numerical methods such as the finite element method (FEM) and the finite volume method (FVM) are often employed to solve the BTE, the collocation meshfree method has special advantages since it does not require numerical integration. In this work, the collocation meshfree method and the discrete ordinate method (DOM) are implemented to discretize the spatial and angular domains, respectively, while the explicit finite difference method (FDM) is used for advancing in time. Such a method is used to solve the transient BTE for a square domain with prescribed temperature and adiabatic boundary conditions. Our results are consistent with transient heat transfer problems solved by FVM approach.