Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-15T18:14:25.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary-value problems in the kinetic theory of gases Part I. Slip flow

Published online by Cambridge University Press:  29 March 2006

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

A new method for treating boundary-value problems in gas-kinetic theory has been developed. The new method has the advantage of reproducing the bulk or asymptotic flow properties accurately whilst giving a realistic description of the behaviour of the molecular distribution function in the neighbourhood of a wall. As an example, the Kramers, or slip-flow, problem is solved for a general specular-diffuse boundary condition and some new expressions for the slip coefficient, flow speed and molecular distribution function at the surface are derived.

A brief discussion of the eigenvalue spectrum of the associated Boltzmann equation is given and its physical significance pointed out.

Certain analogies between this problem and the Milne problem in neutron transport theory are demonstrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 1 , 27 March 1969 , pp. 145 - 159
Copyright
© 1969 Cambridge University Press

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

Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 Phys. Rev. 94, 5.
Cercignani, C. 1962 Ann. Phys. 20, 219.
Cercignani, C. 1966 Ann. Phys. 40, 469.
Cercignani, C. & Tironi, G. 1966 II Nuovo Cim. 43, 64.
Chandrasekhar, S. 1960 Radiative Transfer. New York: Dover.
Chapman, S. & Cowling, T. G. 1960 The Mathematical Theory of Non-Uniform Gases. Cambridge University Press.
Davison, B. 1957 Neutron Transport Theory. Oxford University Press.
Gross, E. P. & Jackson, E. A. 1959 Phys. Fluids, 2, 432.
Keller, J. B. 1948 Comm. Appl. Math. 1, 275.
Kramers, H. A. 1949 Nuovo Cim. 6 Suppl., 887.
Loyalka, S. K. & Ferziger, J. H. 1967 Phys. Fluids, 10, 1833.
Noble, B. 1957 The Wiener-Hopf Technique. Oxford: Pergamon.
Pekeris, C. L. & Alterman, Z. 1957 Proc. Nat. Acad. Sci., U.S.A. 43, 998.
Shen, S. F. 1965 5th International Symposium on Rarefied Gas Dynamics, p. 623. Edited by C. L. Brundin Academic Press.
Simons, S. 1967a Proc. Roy. Soc. A, 301, 387.
Simons, S. 1967b Proc. Roy. Soc. A, 301, 401.
Wang Chang, C. S. & Uhlenbeck, G. E. 1956 Engng. Res. Inst. University of Michigan Report Non r-122, 4-(15).
Williams, M. M. R. 1964 Nucl. Sci. Engng. 18, 260.
Williams, M. M. R. 1966 The Slowing Down and Thermalization of Neutrons. Amsterdam: North-Holland.
Williams, M. M. R. 1968 J. Nucl. Energy, 22, 535.