Highly Dilute Gas Flows Through A Non-Isothermal Planar Micro-Channel

Abstract

This paper reports theoretical and numerical investigations on free molecular gas flows through micro-channels. Both diffusely and specularly reflective channel surfaces are considered. Gaskinetic methods are adopted to develop the analytical solutions for surface and flowfield properties. The crucial steps include constructing the velocity distribution functions (VDFs) for points at the plate surfaces and inside flowfield, and then completing the integration over the related velocity phases. For diffusely reflective surfaces, the VDFs are related to the densities and temperatures at the two exits and the plate temperatures. For surfaces with specular reflections, the VDFs at the plate surface and inside the flowfield are identical, and independent of the surface temperature ratio and the geometric aspect ratio. Based on the VDFs and velocity phases, surface property coefficients (e.g., C_p, C_f, and C_q) and flowfield properties (e.g., density, velocity components, and temperature) are obtained. For the diffusely reflective surface scenario, the mass flow rate can be approximated and the results include four non-dimensional parameters: the aspect ratio, the density ratio, and two temperature ratios. For specularly reflective surface scenario, the surface and flowfield properties are uniform everywhere, the channel aspect ratio and plate temperatures do not have any influence. Particle simulations with the direct simulation Monte Carlo (DSMC) method are performed, and essentially identical results validate the theoretical work. This work is heuristic and can be used to investigate less rarefied micro-channel gaseous flows, for example, aid experimental measurement design for thermal transpiration flows.