Asymptotic modeling of thermal binary monatomic gas flows in plane microchannels—Comparison with DSMC simulations

Abstract

Asymptotic models are constructed to investigate the basic physical phenomena of thermal flows of a mixture of two monatomic gases inside a two-dimensional microchannel. The steady flows are described by the Navier-Stokes-Fourier balance equations, with additional coupling terms in momentum and energy equations, and with first-order slip boundary conditions for the velocities and jump boundary conditions for the temperatures on the two walls. The small parameter equal to the ratio of the two longitudinal and transverse lengths is introduced, and then an asymptotic model is proposed. It corresponds to small Mach numbers and small or moderate Knudsen numbers. Attention is paid to the first-order asymptotic solutions. Results are given and discussed for different cases: the mass flow rates, the molecular weights of the gases, and the temperature gradients along the walls. Comparisons between the first-order asymptotic solutions and Direct Simulation Monte Carlo (DSMC) simulations corresponding to the same physical data show rather good agreement. It should be noted that obtaining an asymptotic solution is very fast compared to obtaining a DSMC result.