Non-isothermal gas flow in microchannel with equal wall temperatures

Abstract

A non-isothermal pressure-driven compressible subsonic slip gas flow in microchannels with variable cross section (convergent, divergent and constant high channel) is analyzed in this paper analytically. Since the flows correspond to microspaces, the rarefaction effect must be taken into account. Solutions are obtained for gas flow with equal temperatures of the walls. The slip gas flow is defined by macroscopic approach, using the continuity, Navier-Stokes and energy continuum equations, along with the velocity slip and temperature jump Maxwell-Smoluchowski first order boundary conditions. The Knudsen number is supposed for the slip gas flow, and Mach number for the subsonic flow. Fully developed flow is considered, which assumes a slow variation of all physical quantities in the streamwise direction. These assumptions, along with the known relationship between the Mach, Reynolds and Knudsen numbers, are used to derive a precise estimation of each term's contribution in the non-dimensional governing equations, as well as in the boundary conditions. This evaluation also makes a distinction between low and moderately high Reynolds numbers flows, which are solved separately. The solutions correspond to the slip and continuum flows. Finally, the analytical solutions for the pressure, velocity , and temperature are obtained. The results are in a good agreement with those obtained by some experiments found in the open literature.