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Journal of Statistical Physics

, Volume 136, Issue 4, pp 751–784 | Cite as

Symmetry of the Linearized Boltzmann Equation and Its Application

  • Shigeru Takata
Article

Abstract

A symmetric relation of macroscopic quantities between two different steady problems of the linearized Boltzmann equation is derived. A few applications to half-space problems are presented first. Then, for the gas in bounded or unbounded domains such that solid bodies or condensed phases are confined in a finite region, general representations of the mass, momentum, and heat fluxes through the boundary (possibly at a point on or on a part of it) are derived from the symmetric relation linked to the separability of boundary data. This result implies a reduction of the original problem to a single elemental problem in the same domain, as far as the fluxes are concerned. Many applications are also presented.

Keywords

Boltzmann equation Reciprocity Green function Knudsen layer 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Science, (also Advanced Research Institute of Fluid Engineering and Science), Graduate School of EngineeringKyoto UniversityKyotoJapan

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