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Nearly free-molecular slit flow at finite pressure and temperature ratios

Published online by Cambridge University Press:  29 March 2006

P. Y. Wang  and
E. Y. Yu
P. Y. Wang
Affiliation:
Department of Mechanical Engineering and Astronautical Science, Northwestern University Permanent address: Chung-Shan Institute of Science and Technology, Taipei, Taiwan, The Republic of China.
E. Y. Yu
Affiliation:
Department of Mechanical Engineering and Astronautical Science, Northwestern University
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Abstract

An analytical study is made of nearly free-molecular flow of a noble gas from one reservoir to another through a two-dimensional slit, with finite pressure and temperature ratios across the slit. The fundamental solution of the linear Boltzmann equation is employed in the study. The total mass flow is calculated to the first-order correction terms, of the order of α ln α and α, where α is the inverse Knudsen number. The coefficients of these terms are in general multiple integrals, but they become explicit functions of the pressure and temperature ratios after the multiple integrations are carried out by using Krook collision model. When the general result is simplified to the isothermal case the first-order correction has a negative value, indicating the reduction of the total mass flow due to intermolecular collisions in the counter flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 3 , 14 December 1971 , pp. 565 - 577
Copyright
© 1971 Cambridge University Press

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