Hostname: page-component-f554764f5-nt87m Total loading time: 0 Render date: 2025-04-11T03:43:24.204Z Has data issue: false hasContentIssue false
  • English
  • Français

Complementary variational principles for free molecular channel flow*

Published online by Cambridge University Press:  14 November 2011

R. J. Cole
R. J. Cole
Affiliation:
Department of Mathematics, University of Strathclyde
Get access Rights & Permissions [Opens in a new window]

Synopsis

A collisionless gas flows through a finite rectangular duct which reflects molecules diffusely. The transmission probability Q of the duct involves the solution of a pair of coupled integral equations. Complementary variational principles have been employed which supply upper and lower bounds to Q. Numerical calculations have been made for a variety of duct shapes and compared, where appropriate, to those of other authors.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 3-4 , 1979 , pp. 211 - 223
Copyright
Copyright © Royal Society of Edinburgh 1979

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.)

Article purchase

Temporarily unavailable

References

1Porodnov, B. T., Suetin, P. E., Borisov, S. F. and Akinshin, V. D.. Experimental investigation of rarefied gas flows in different channels. J. Fluid Mech. 64 (1974), 417–437.CrossRefGoogle Scholar
2Peggs, G. N.. The dynamic flow technique for tHe calibration of vacuum gauges. Rep. Natn. Phys. Lab. MOM 6 (1973).Google Scholar
3Cole, R. J. and Pack, D. C.. Some complementary bivariational principles for linear integral equations of Fredholm type. Proc. Roy. Soc. Lond. Ser. A 347 (1975), 239–252.Google Scholar
4Cole, R. J.. Complementary variational principles for Knudsen Flow rates. J. Inst. Math. Appl. 20 (1977), 107–115.CrossRefGoogle Scholar
5Neudachin, I. G., Porodnov, B. T. and Suetin, P. E.. Knudsen flow in a rectangular duct of finite length. Soviet Phys. Tech. Phys. 17 (1972), 1036–1038.Google Scholar
6Cole, R. J. and Pack, D. C.. Drag and conductance of free molecular flow through a rectangular duct. Proc. 9th International Symposium on Rarefied Gas Dynamics, II, ed. Becker, M. and Fiebig, M., D.19, 1–9 (Porz-Wahn, Germany.: DFVLR Press, 1974).Google Scholar
7Courant, R. and Hilbert., D.Methods of Mathematical Physics I, p. 205 (New York: Interscience, 1953).Google Scholar
8Hegna, H. A. and Berman., A. S.Rarefied gas flow through a slit. Phys. Fluids 15 (1972), 1850–1852.CrossRefGoogle Scholar
9Robinson, P. D. and Arthurs., A. M.Some variational principles for integral equations. J. Mathematical Phys. 9 (1968), 1364–1368.CrossRefGoogle Scholar