The modeling of nanoscale heat conduction by Boltzmann transport equation

The discrete Boltzmann transport equation is firstly formulated by accounting for the impact of particle collisions on the distribution function in the discrete Liouville equation. Based on this equation, we re-derive the improved dual-phase-lagging heat conduction model with lagging effect in time and nonlocal effect in space. By taking into account the contribution of the higher order moments of the distribution function to the heat flux, we show that the discrete Boltzmann transport equation can give rise to the well-known Guyer–Krumhansl heat conduction model.