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Entry flow in a channel. Part 2

Published online by Cambridge University Press:  29 March 2006

S. D. R. Wilson
S. D. R. Wilson
Affiliation:
Department of Mathematics, University of Manchester
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Abstract

This paper complements an earlier paper by Van Dyke which has appeared under the same title. The problem of channel entry flow is re-examined and the early work is found to be formally incorrect. The techniques of modern boundary-layer theory are used to examine the region near the entrance. Various inlet conditions are considered and it is found that the usual condition of uniform entry velocity causes the intrusion of fractional powers of the Reynolds number into the expansions. The most satisfactory model is that of uniform flow into an infinite cascade of parallel plates.

The non-uniformity of the expansions at large downstream distances was studied in Van Dyke's paper and is not dealt with here, except to show that it may be treated separately.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 46 , Issue 4 , 27 April 1971 , pp. 787 - 799
Copyright
© 1971 Cambridge University Press

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References

Gel'’and, I. M. & Shilov, G. E. 1964 Generalised Functions, Vol. 1. Academic.
Goldstein, S. 1960 Lectures on Fluid Mechanics. Wiley (Interscience).
Libby, P. A. & Fox, H. 1963 J. Fluid Mech. 17, 433.
Schlichting, H. 1960 Boundary-Layer Theory. McGraw-Hill.
Stewartson, K. 1957 J. Math. Phys. 36, 173.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Van Dyke, M. 1970 J. Fluid Mech. 44, 813.
Wilson, S. 1969 J. Fluid Mech. 38, 793.