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Thermal transpiration for the linearized Boltzmann equation
Author(s) -
Chen ChiunChuan,
Chen IKun,
Liu TaiPing,
Sone Yoshio
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20167
Subject(s) - boltzmann equation , knudsen number , pointwise , lattice boltzmann methods , mathematics , flow (mathematics) , direct simulation monte carlo , temperature gradient , mechanics , boundary value problem , mathematical analysis , physics , thermodynamics , quantum mechanics , statistics , dynamic monte carlo method , monte carlo method
The phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hard‐sphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number κ, the flow velocity between two plates is of the order of log κ, and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation. © 2006 Wiley Periodicals, Inc.