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Slow rotation of a circular cylinder in a viscous fluid bounded by parallel walls

Published online by Cambridge University Press:  24 October 2008

R. C. J. Howland  and
R. C. Knight
R. C. J. Howland
Affiliation:
Professor of Mathematics, Emmanuel College, University College, Southampton
R. C. Knight
Affiliation:
Assistant Lecturer in Mathematics, University College, Southampton.
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Extract

Solutions of the bi-harmonic equation valid in the region bounded externally by parallel lines and internally by a circle midway between the lines have been given by one of the Authors in a recent paper [2]. These solutions were adapted to the requirements of certain problems in the theory of elasticity, but modified solutions satisfying the boundary conditions characteristic of viscous fluid motion are easily derived. These modified solutions will here be given and will be used to find the stream function corresponding to the slow rotation of a cylinder placed symmetrically between parallel walls.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 29 , Issue 2 , May 1933 , pp. 277 - 287
Copyright
Copyright © Cambridge Philosophical Society 1933

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References

REFERENCES

1.Howland, R. C. J.; Proc. Roy. Soc., A, 124 (1929), 89–119.Google Scholar
2.Howland, R. C. J.; Phil. Trans., A, 229 (1930), 49–86.Google Scholar
3.Howland, R. C. J.; Proc. Intern. Congr. Appl. Mech., Stockholm (1930), 2, 74–79.Google Scholar
4.Howland, R. C. J. and Stevenson, A. C.; Phil. Trans., A. In the Press.Google Scholar