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首页> 外文期刊>Applied Mathematical Modelling >A novel SPH method for the solution of Dual-Phase-Lag model with temperature-jump boundary condition in nanoscale
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A novel SPH method for the solution of Dual-Phase-Lag model with temperature-jump boundary condition in nanoscale

机译：SPH新方法求解纳米跃迁边界条件下的双相滞后模型

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摘要

This paper proposes a newly developed smoothed-particle hydrodynamics (SPH) method for the solution of one-dimensional heat conduction problem within a nanoscale thin slab for Knudsen numbers of 0.1 and 1 under the effect of Dual-Phase-Lag (DPL) model. A novel temperature-jump boundary condition is applied to the Lagrangian particle-based mesh-free SPH method in order to take into account the boundary phonon scattering phenomenon in the micro- and nano-scales. The formulation and discretization of the non-Fourier DPL heat conduction equation containing a third-order combined spatial-time derivative together with a temperature-jump boundary condition are presented and then a proper nanoscale time-stepping of the SPH method has been introduced. The dimensionless temperature and heat flux distributions have shown a good agreement with the existing numerical and analytical data for different dimensionless times, temperature to heat flux phase-lag ratios, and the Knudsen numbers. It is found that the developed SPH method have accurately simulated the complex behavior of the DPL model with relatively low computational cost.
机译：针对双相滞后（DPL）模型的影响，本文提出了一种新开发的光滑粒子流体动力学（SPH）方法，用于解决Knudsen数为0.1和1的纳米级薄板中的一维导热问题。为了在微尺度和纳米尺度上考虑边界声子散射现象，将一种新型的温度跳跃边界条件应用于基于拉格朗日粒子的无网格SPH方法。提出了包含三阶组合时空导数和温度跳跃边界条件的非傅里叶DPL导热方程的公式化和离散化，然后介绍了SPH方法的适当的纳米级时步。无量纲的温度和热通量分布与现有的数值和分析数据在不同的无量纲时间，温度与热通量的相位滞后比以及克努森数方面显示出良好的一致性。发现所开发的SPH方法以相对较低的计算成本准确地模拟了DPL模型的复杂行为。

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