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The flow around a semi-infinite oscillating plate and the skin friction on arbitrarily cross-sectioned infinite cylinders oscillating parallel to their length

Published online by Cambridge University Press:  24 October 2008

Graham Wilks
Affiliation:
Department of Engineering Mechanics, The University of Michigan, Ann Arbor, Michigan

Abstract

In Part I of the work that follows solutions for the flow around a semi-infinite oscifiating plate are obtained, one by an operational method using parabolic coordinates and one in the form of a series solution. The latter is used to obtain an estimate of the skin friction distribution about the edge of the plate and hence the excess skin friction over the infinite oscilliating plate value. A valuable check on this result is provided by an equivalent consideration of the operational solution. Having demonstrated the usefulness of the series solution we proceed to extend its application to a wedge of arbitrary angle in Part II and eventually use the results to derive a general expression for the skin friction on an infinite cylinder of arbitrary cross-section oscifiating rapidly parallel to its length.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Abramowitz, M. and Stegun, I. A.Handbook of Mathematical functions.Google Scholar
(2)Batchelor, G. K.The skin friction on infinite cylinders moving parallel to their length. Quart. J. Mech. Appl. Math. 7 (1954), 179192.CrossRefGoogle Scholar
(3)Carslaw, H. S. and Jaeger, J. C.Conduction of heat in solids (Oxford University Press, 1947).Google Scholar
(4)Erdelyi, A., ed. Tables of integral transforms (McGraw-Hill Book Company, 1954).Google Scholar
(5)Drake, D. G.On the flow in a channel due to a periodic pressure gradient. Quart. J. Mech. Appl. Math. 18 (1965), 110.CrossRefGoogle Scholar
(6)Gunn, J. C.Philos. Trans. Roy. Soc. London Ser. A 240 (1947), 327373.Google Scholar
(7)Hasimoto, H. J.Phys. Soc. Japan 6 (1951), 400.CrossRefGoogle Scholar
(8)Howarth, L.Rayleigh's problem for a semi-infinite plate. Proc. Cambridge Philos. Soc. 46 (1950), 127140.CrossRefGoogle Scholar
(9)Sowerby, L.The unsteady flow of viscous incompressible fluid inside an infinite channel. Philos. Mag. 42 (1951).CrossRefGoogle Scholar
(10)Sowerby, L. and Cooke, J. C.The flow of fluid along corners and edges. Quart. J. Mech. Appl. Math. 6 (1953), 5070.CrossRefGoogle Scholar
(11)Watson, G. N.Treatise on the theory of Bessel functions, 2nd ed. (Cambridge, 1944).Google Scholar