سال انتشار: ۱۳۸۸

محل انتشار: سومین کنفرانس نانوساختارها

تعداد صفحات: ۴

نویسنده(ها):

J Ghazanfarian – Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
A Abbassi – Mechanical Engineering, Amirkabir University of Technology, Tehran, 15875-4413, Tehran, Iran

چکیده:

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