Reply to “Comment on ‘Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method”’

In this reply to the Comment by Li-Shi Luo, we discuss the results of the lattice Bhatnagar-Gross-Krook (LBGK) model for high-Knudsen-number (Kn) flow and heat transfer, in the range of $\mathrm{Kn}⩽1$. We present various studies employing the LBGK model for high-Kn flow and heat transfer simulations. It is concluded that, with the use of the LBGK model in the thermal lattice Boltzmann method for $\mathrm{Kn}⩾0.8$, some approximations appear in the negative pressure deviation from the linear distribution along the channel. But for $\mathrm{Kn}<0.8$, the velocity and temperature profiles, compressibility effects, Knudsen layer capturing, and Knudsen paradox phenomenon can be predicted by the LBGK model. We also reject Li-Shi Luo’s claim about the nonconvergence of our numerical scheme by presenting a velocity profile across the channel corresponding to three different high-resolution meshes.

Figure 1

Comparison of the dimensionless velocity profiles obtained from the LBGK model for $\mathrm{Kn}=0.6$ and $N_H=51$, 101, and 151.