A novel SPH method for the solution of Dual-Phase-Lag model with temperature-jump boundary condition in nanoscale

Abstract

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.