Fig. 1. Distributions of n/n_0, T/T_0 and u on the centerline along the x axis obtained by the DSMC simulation (black), the GKUA simulation based on the Shakhov equation (blue), and the DSBGK simulation of using τ=τ(μ) (red) and τ=τ(ζ) (green), respectively; the minimum and maximum wall temperatures are 280 K and 340 K, respectively.
Fig. 2. Thermal transpiration gas flows driven by temperature variation on the wall surface of a micro-channel, p_in ≡ p_out ≡ p_0. Flow field distributions by the simulation at Kn = 0.3 (top) and the comparison of the computed mass flow rates with the experimental data (bottom). The DSBGK simulation of argon gas flow at p_0 = 294 Pa requires 3200×400×50 cells and takes about one day to converge after 2000 time steps when using 40 CPU cores.
Quote: The BGK equation is usually deemed inaccurate in modeling thermal transpiration flows, which is because most of its ordinary applications adopted τ = τ(μ) to match the viscosity. Such application significantly underestimates the speed of thermal transpiration flow, which is consistent with our observation. However, beyond confirming the reported error of the BGK equation, we also proposed remedy of using τ = τ(ζ) to match the thermal conductivity coefficient. ... Since the Shakhov equation is not error-free, it becomes a matter of choice to use the Shakhov equation or the improved BGK equation proposed here.