The present paper deals with the two-dimensional numerical simulation of gaseous flow and heat transfer in planar microchannel and nanochannel with different wall temperatures in transitional regime $0.1\le \text{Kn}\le 1$. An atomistic molecular simulation method is used known as thermal lattice-Boltzmann method. The results of simulation are presented in four cases corresponding to the Fourier flow, shear-driven flow (Couette flow), pressure-driven flow (Poiseuille flow), and mixed shear–pressure-driven flow in the developing and fully developed regions. The mixed shear–pressure-driven flow is divided into two subcases with shear stress and pressure gradient acting in the same and the opposite directions. Normalized temperature and velocity profiles across the channel, distribution of local wall Nusselt number, and friction coefficient are illustrated. Using this method, nonlinear pressure distribution in the streamwise direction, reduction in mass flow rate, $C_f\text{Re}$, and Nu by increasing the Knudsen number are studied. It is seen that for Couette flow, Nu over the hotter plate is greater than the cooler plate, but for the pressure-driven flow with stationary wall temperature dependency of viscosity and thermal conductivity causes this trend to be reversed. The reversed flow appearance in the velocity profile is captured in the case of opposite shear–pressure-driven flow.

• Received 6 June 2010

DOI:https://doi.org/10.1103/PhysRevE.82.026307