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New boundary conditions in the transition régime

Published online by Cambridge University Press:  13 March 2009

Carlo Cercignani  and
Gino Tironi
Carlo Cercignani
Affiliation:
Applicazioni e Ricerche Scientifiche, S.p.A.—Milano, and Istituto di Scienze Fisiche, University of Milano, Milano, Italy
Gino Tironi
Affiliation:
Applicazioni e Ricerche Scientifiche, S.p.A.—Milano, and Istituto di Scienze Fisiche, University of Milano, Milano, Italy
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Abstract

Starting from the Boltzmann equation, new boundary conditions are derived to be matched with the Navier—Stokes equations, that are supposed to hold in the main body of a gas. The idea upon which this method is based goes back to Maxwell and Langmuir. Since the distribution function is supposed to be completely determined by the Navier—Stokes equations, this new set of boundary conditions extends in some sense the validity of the macroscopic equations to the transition and free molecular régimes. In fact, it is shown that the free molecular and slip flow régimes are correctly described by this method; the latter is also supposed to give a reasonable approximation for the complete range of Knudsen numbers. The new procedure is applied to different problems such as plane Couette flow, plane and cylindrical Poiseuile flow, heat transfer between parallel plates and concentric cylinders. Results are obtained and compared with the exact numerical solutions for the above-mentioned problems.

Type
Research Article
Information
Journal of Plasma Physics , Volume 2 , Issue 3 , August 1968 , pp. 293 - 310
Copyright
Copyright © Cambridge University Press 1968

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