Exact Solutions for Internal and External Collisionless Gas Flows

Abstract

This paper presents some recent progress on internal and external free molecular flows. The first part of this paper concentrates on steady collisionless gas flows inside arbitrary enclosures, which are either convex or concave, two-dimensional or three-dimensional, formed by several plates maintained at different temperatures. If the molecular reflections on these plates are completely diffuse, then at the final steady flow stage for any point inside the enclosures, the velocity distribution function (VDF) is completely determined, and macroscopic properties such as density, velocities, temperature and heat flux can be exactly determined by integrating the VDF with different moments. The result from this study leads to many exact solutions for internal collisionless gas flow and thermal fields, such as those inside vacuum packaged Micro-/Nano- Electro-Mechanical System (MEMS/NEMS) devices. The second part considers collisionless flows over a flat plate with a sticking coefficient, such as a cryogenic pump. We obtain the corresponding exact solutions for the flow and thermal fields. Numerical simulation results obtained with the direct simulation Monte Carlo method validate the analytical solutions. In general, the comparisons between the exact analytical solutions and the numerical results are virtually identical.