Asymptotic Solutions for Gaseous Flow in a Three-Dimensional Rectangular Microchannel

Abstract

This paper analyzes compressible gaseous flow through a three-dimensional straight uniform rectangular microchannel, and reports a set of asymptotic solutions. This work represents an extension of previous work on compressible flows through a two-dimensional microchannel. First, we choose the ratio of Dh/L as the small expansion parameter, where Dh and L are the channel’s hydrodynamic diameter and length correspondingly. Secondly, by comparing the magnitudes of different forces in the compressible gas flow, we obtain a proper criteria to estimate the Reynolds and Mach numbers at the channel exit. We select two sets of Mach and Reynolds numbers and obtain asymptotic analytical solutions of velocities and pressure distributions of compressible gas flow inside the microchannel; and a set of the slip velocity boundary conditions are examined. The analytical results of pressure and velocities are compared with numerical simulation results of the direct simulation Monte Carlo method.