Hostname: page-component-5c6d5d7d68-ckgrl Total loading time: 0 Render date: 2024-08-31T11:09:40.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Rarefied gas flow between parallel plates

Published online by Cambridge University Press:  24 October 2008

M. M. R. Williams
M. M. R. Williams
Affiliation:
Nuclear Engineering Department, Queen Mary College, University of London
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow of a rarefied gas between parallel plates has been studied via the linearized Boltzmann transport equation. Using a general boundary condition, which includes an arbitrary ratio of specular to diffuse reflection from the wall, we have derived an integral equation for the mass flow velocity. The integral equation is solved by using a replication property of the kernel and application of the method of Muskelishvili.

The total volumetric flow rate is obtained and a slip boundary condition is deduced for use with the hydrodynamic equations.

Certain aspects of the eigenvalue spectrum associated with the Boltzmann equation are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 1 , July 1969 , pp. 189 - 196
Copyright
Copyright © Cambridge Philosophical Society 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Knudsen, M.Kinetic theory of gases (Methuen, 1950).Google Scholar
(2)Maxwell, J. C.Collected Papers (New York, 1953).Google Scholar
(3)Von Smoluchowski, M.Ann. Physik 33 (1910), 1559.Google Scholar
(4)Clausing, P.Physica 9 (1929), 65.Google Scholar
(5)Takao, K.Trans. Japan Soc. Aero. Space Sci. 3 (1960), 30.Google Scholar
(6)Cercignani, C.Rarefied gas dynamics, vol. 2, p. 92 (Academic Press, 1963).Google Scholar
(7)Cercignani, C. and Daneri, A.J. Appl. Phys. 34 (1963), 3509.CrossRefGoogle Scholar
(8)Simons, S.Proc. Roy. Soc. Ser. A 301 (1967), 387.Google Scholar
(9)Simons, S.Proc. Roy. Soc. Ser. A 301 (1967), 401.Google Scholar
(10)Cercignani, C. J.Math. Anal. Appl. 12 (1965), 254.CrossRefGoogle Scholar
(11)Bhatnagar, P. L. et al. Phys. Rev. 94 (1954), 511.CrossRefGoogle Scholar
(12)Cercignani, C.Ann. Physics 20 (1962), 219.Google Scholar
(13)Case, K.Developments in transport theory (Edited by Inönu, E. and Zweifel, P.) (Academic Press, 1967).Google Scholar
(14)Febziger, J. H.Phys. Fluids 10 (1967), 1448.CrossRefGoogle Scholar
(15)Williams, M. M. R.J. Mathematical Phys. 9 (1968), 1873CrossRefGoogle Scholar
Williams, M. M. R.J. Mathematical Phys. 9 (1968), 1885.Google Scholar
(16)Williams, M. M. R. (unpublished, 1967).Google Scholar
(17)Muskelishvili, N. I.Singular integral equations (Noordhoff, 1960).Google Scholar