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A unified kinetic theory approach to external rarefied gas flows. Part 1. Derivation of hydrodynamic equations

Published online by Cambridge University Press:  29 March 2006

H. Atassi  and
S. F. Shen
H. Atassi
Affiliation:
University of Notre Dame
S. F. Shen
Affiliation:
Cornell University
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Abstract

A set of partial differential equations of the Navier-Stokes type is derived for external rarefied gas flows at all Knudsen numbers. Only the expressions of the stress tensor and heat flux vector are different from the customary Navier-Stokes relations and Fourier law. The new expressions are calculated from an approximate distribution function constructed through analysis of the BGK model of the Boltzmann equation so that it retains the qualitative property of the collision term and reproduces accurately the two extreme continuum and free-molecule regimes. Explicit forms of the stress tensor and heat flux components are given for low-speed two-dimensional flows. Solutions for vanishing Mach number and compressibility effects are then discussed. For a nearly isothermal cylinder, the present formulation leads to only one governing equation of the Navier-Stokes type for all flow regimes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 53 , Issue 3 , 13 June 1972 , pp. 417 - 431
Copyright
© 1972 Cambridge University Press

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