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Effect of boundary phonon scattering on dual-phase-lag model to simulate micro- and nano-scale heat conduction. (English) Zbl 1167.80328

Summary: One-dimensional heat conduction within a thin slab for Knudsen numbers more than 0.1 is implemented using the 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 the 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). It is also shown that the temperature distribution is closer to the results of Boltzmann equation relative to the heat flux distribution. 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.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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