The slip flow or Kramers problem for rarefied gas flow is studied by the use of a number of models. The models employed include the Bhatnagar‐Gross‐Krook model, Maxwell molecules, the Gross‐Jackson model, Cercignani's variable‐collision‐frequency model, and a new model which allows variable collision frequency, the correct Chapman‐Enskog solution and the correct Prandtl number. The Kramers problem is solved by means of an approximation scheme based on the method of elementary solutions for the constant‐collision‐frequency models and by a variational method for the variable‐collision‐frequency model. Numerical results show that the slip coefficient is only slightly model‐dependent.
REFERENCES
1.
P. L.
Bhatnagar
, E. P.
Gross
, and M.
Krook
, Phys. Rev.
94
, 511
(1954
).2.
3.
L. Sirovich and K. Thurber, in Rarefied Gas Dynamics, J. H. deLeeuw, Ed. (Academic Press, Inc., New York, 1965), Vol. I, p. 21.
4.
5.
J. K.
Buckner
and J. H.
Ferziger
, Phys. Fluids
9
, 2309
, 2315
(1966
).6.
7.
8.
9.
H. Grad, in Rarefied Gas Dynamics, J. A. Laurmann, Ed. (Academic Press Inc., New York, 1963). Vol. I, p. 26.
10.
C. S. Wang Chang and G. E. Uhlenbeck, University of Michigan, Engineering Research Institute Report 2457‐1‐T (1956).
11.
12.
13.
C. S. Wang Chang and G. E. Uhlenbeck, University of Michigan Engineering Research Institute Project M999 (1952).
14.
H. S. Mott‐Smith, Massachusetts Institute of Technology Lincoln Laboratory Report V‐2 (1954).
15.
S. Chapman and T. G. Cowling, The Mathematical Theory of Non‐Uniform Gases (Cambridge University Press, London, 1952), 2nd ed.
16.
17.
C. L.
Pekeris
and Z.
Alterman
, Proc. Natl. Acad. Sci.
43
, 998
(1957
).18.
19.
K. M. Case, F. DeHoffman, and G. Placzek, Introduction to the Theory of Neutron Diffusion (U.S. Government Printing Office, Washington, D.C. 1953).
20.
21.
R.
Kladnik
and I.
Kus̆ĕer
, Nucl. Sci. and Eng.
11
, 116
(1961
). Further references are given in this paper.22.
23.
This content is only available via PDF.
© 1967 The American Institute of Physics.
1967
The American Institute of Physics
You do not currently have access to this content.