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Laminar Flow in a Uniformly Porous Channel with Large Injection

Published online by Cambridge University Press:  07 June 2016

R. M. Terrill
R. M. Terrill*
Affiliation:
Department of Applied Mathematics, The University of Liverpool
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Summary

The author has previously discussed the flow in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. Yuan has given a solution for high injection in which certain derivatives of the axial velocity become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and that Yuan’s solution is ignoring the shear layer. In this paper the complete solution for large injection is obtained by the method of inner and outer expansions and therefore includes the viscous layer. The resulting series solutions are confirmed by numerical results.

Type
Research Article
Information
Aeronautical Quarterly , Volume 16 , Issue 4 , November 1965 , pp. 323 - 332
Copyright
Copyright © Royal Aeronautical Society. 1965

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References

1. Terrill, R. M. Laminar Flow in a Uniformly Porous Channel. Aeronautical Quarterly, Vol. XV, p. 299, August 1964.CrossRefGoogle Scholar
2. Berman, A. S. Laminar Flow in Channels with Porous Walls. Journal of Applied Physics, Vol. 24, p. 1232, December 1953.CrossRefGoogle Scholar
3. Yuan, S. W. Further Investigations of Laminar Flow in Channels with Porous Walls. Journal of Applied Physics, Vol. 27, p. 267, March 1956.Google Scholar
4. Erdeyli, A. Higher Transcendental Functions, Vol. II, p. 147. McGraw-Hill, 1953.Google Scholar
5. Rosser, J. B. Theory and Application of Office of Scientific Research and Development, OSRD 5861, p. 158, 1945.Google Scholar