Simulation of Nano-scale Heat Conduction Using Dual-Phase-Lag Model and Introducing aGeneral Time Dependent 1-D Model

In this paper, one dimensional heat conduction within a thin slab for Knudsen numbers more than 0.1 is simulated using Dual-Phase-Lag (DPL) model including phonon scattering boundary condition. The Dual-phase-lag equation is solved with a stable and convergent finite difference scheme. Also the Laplace transformation technique is employed to solve DPL equation analytically. The results show that in the smaller values of Knudsen number, the results of the DPL model lay very close to the solution of the Boltzmann equation. Also, it is shown that moving towards the steady state, the DPL model reduces to the Cattaneo and Vernotte (CV) model and has results more accurate than the Ballistic-Diffusive Equations (BDE). Due to the simplicity of derivation of the DPL model formulation and its possibility for developing to higher dimensions, using the DPL model with new boundary condition is recommended to simulate nano- and micro-scale heat conduction. To investigate the accuracy of the DPL model, its results are compared with the results obtained from BDE model, and Boltzmann equation

کلیدواژه ها:

Micro- and nano-scale ، Heat conduction ، DPL model ، Electronic cooling