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A slow motion of viscous liquid caused by the rotation of a solid sphere

Published online by Cambridge University Press:  26 February 2010

W. R. Dean  and
M. E. O'Neill
W. R. Dean
Affiliation:
University College, London, W.C.I.
M. E. O'Neill
Affiliation:
University College, London, W.C.I.
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Extract

A steady motion of incompressible viscous liquid caused by the slow rotation of a rigid sphere of radius a is considered. The medium is bounded by an infinite rigid plane and the axis of rotation is parallel to, and at a distance d from, this plane. To complete the analysis the solution by successive approximation of an infinite set of linear equations is required. Satisfactory solutions have been found numerically for four values of d/a, of which 1·13 is the smallest; we gratefully acknowledge valuable help from Miss S. M. Burrough in this part of the work.

Type
Research Article
Information
Mathematika , Volume 10 , Issue 1 , June 1963 , pp. 13 - 24
Copyright
Copyright © University College London 1963

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References

Jeffery, G. B., Proc. London Math. Soc. (2), 14 (1915), 327–338.CrossRefGoogle Scholar
Jeffery, G. B., Proc. Roy. Soc. (A), 87 (1912), 109–120.Google Scholar
MacRobert, T. M., Spherical Harmonics, Ch. 5 (London, 1947).Google Scholar