K. Aoki and S. Takata

Fluid models and simulations of internal rarefied gas flows

Pages: 1-69
Received: 13 November 2008
Accepted: 9 February 2009
Mathematics Subject Classification (2000): 76P05 - 82B40 - 82C40 - 82D05

Keywords: Rarefied gas, Boltzmann equation, slip flow, thermal transpiration, thermal edge flow, Poiseuille flow, Knudsen compressor.

This research was partially supported by KAKENHI (Nos. 20360046 and 19560066) from JSPS

Abstract: Fluid flows in small systems become increasingly important in various applications such as micromechanical systems. The present article focuses its attention on internal rarefied gas flows, in particular, flows induced by temperature fields, and summarizes some of the results that seem to be useful or interesting for applications to micromechanical systems. In the first half, after a brief description of the Boltzmann equation, its boundary-value problems for small Knudsen numbers are considered, and the results of the asymptotic theory that gives the recipe to obtain correct solutions via fluid-dynamic systems are summarized. Numerical analyses of flows induced by temperature fields at intermediate Knudsen numbers are also presented. In the latter half, potential applications of the flows caused by temperature fields are surveyed, with special emphasis on the Knudsen compressor and its variants. Convenient convection-diffusion systems for the Knudsen compressor are proposed, and the methods of numerical analysis of fundamental problems, such as Poiseuille flow and thermal transpiration, are reviewed in the connection to the convection-diffusion systems.