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Two-dimensional flow past a flat plate in the presence of boundary walls

Published online by Cambridge University Press:  24 October 2008

L. Todd
L. Todd
Affiliation:
Department of Mathematics, Laurentian University, Sudbury, Ontario, Canada
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Extract

1. Introduction. Flow of viscous fluid at low Reynolds number has attracted a great deal of attention over the last hundred years or so and is still an area of active research at the present time. For a general background on this field, we refer the reader to Langois(4). The present paper is concerned with steady flow past a finite flat plate which spans a long rectangular channel, of large aspect-ratio, at the centre ‘line’ (see Fig. 1). The flow is motivated by a constant pressure difference which is applied

between the ends of the channel. We examine such flows when the Reynolds number based on the semi-channel height, a, is much less than 1. Our main task is to show that Stokes approximation, i.e. neglection of the inertia terms, is uniformly valid † over the whole flow field. (†Such a result contrasts with the non-uniformity of the approximation when the channel walls are removed and the external flow is a uniform stream.) Harper & Chang (1) who treat the corresponding problem for a circular cylinder, give a full account of recent theoretical and experimental work on this class of fluid flows. We shall therefore defer comments on related papers until the appropriate part of the text.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 189 - 199
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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