A Lattice Boltzmann Simulation for Thermal Energy Diffusion Through a Micro/Nanoscale Thin Film

Abstract

Thermal energy diffusion through two directions of a micro/nanoscale thin film is modeled by a dimensionless form of Boltzmann transport equations of phonon density distribution functions. With the model named a lattice Boltzmann method (LBM), the discrete Boltzmann transport equations are able to be solved directly. The present model applied is based on physic expression of the dimensionless phonon density distribution functions together with both physic based dimensionless relaxation time models and the physic based dimensionless form of boundary conditions. Effects due to the variations of film thickness, distribution of temperature, and phonon transport frequency are all included in the physic based model. Phonon energy and effective thermal conductivity distributions are shown in the two-dimensional (2D) space. The spatial distributions of temperatures and thermal conductivities are validated by comparing with previous studies. Effects of the longitude and transvers direction heat transfer patterns and their effective thermal conductivities under different size and geometry ratios are compared.