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Poiseuille and thermal transpiration flows of a highly rarefied gas: over-concentration in the velocity distribution function

Published online by Cambridge University Press:  16 February 2011

SHIGERU TAKATA  and
HITOSHI FUNAGANE
SHIGERU TAKATA*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 606-8501, Japan Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Kyoto 606-8501, Japan
HITOSHI FUNAGANE
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 606-8501, Japan
*
†Email address for correspondence: takata@aero.mbox.media.kyoto-u.ac.jp
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Abstract

Poiseuille and thermal transpiration flows of a highly rarefied gas are investigated on the basis of the linearized Boltzmann equation, with a special interest in the over-concentration of molecules on velocities parallel to the walls. An iterative approximation procedure with an explicit error estimate is presented, by which the structure of the over-concentration is clarified. A numerical computation on the basis of the procedure is performed for a hard-sphere molecular gas to construct a database that promptly gives the induced net mass flow for an arbitrary value of large Knudsen numbers. An asymptotic formula of the net mass flow is also presented for molecular models belonging to Grad's hard potential. Finally, the resemblance of the profiles between the heat flow of the Poiseuille flow and the flow velocity of the thermal transpiration is pointed out. The reason is also given.

JFM classification

Rarefied Gas Flow: Kinetic theory Micro-/Nano-fluid dynamics: Non-continuum effects Rarefied Gas Flow: Rarefied Gas Flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 242 - 259
Copyright
Copyright © Cambridge University Press 2011

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References

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