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Jeffery-Hamel boundary-layer flows over curved beds

Published online by Cambridge University Press:  21 April 2006

P. M. Eagles
P. M. Eagles
Affiliation:
Department of Mathematics, The City University, Northampton Square, London EC1V 0HB, UK
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Abstract

We find certain exact solutions of Jeffery-Hamel type for the boundary-layer equations for film flow over certain beds. If β is the angle of the bed with the horizontal and S is the arclength these beds have equation sin β = (const.)S−3, and allow a description of flows on concave and convex beds. The velocity profiles are markedly different from the semi-Poiseuille flow on a plane bed.

We also find a class of beds in which the Jeffery-Hamel flows appear as a first approximation throughout the flow field, which is infinite in streamwise extent. Since the parameter γ specifying the Jeffery-Hamel flow varies in the streamwise direction this allows a description of flows over curved beds which are slowly varying, as described in the theory, in such a way that the local approximation is that Jeffery-Hamel flow with the local value of γ. This allows the description of flows with separation and reattachment of the main stream in some cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 186 , January 1988 , pp. 583 - 597
Copyright
© 1988 Cambridge University Press

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References

Bertscnhy, J. R., Chin, R. W. & Abernathy, F. H. 1983 High-strain-rate free surface boundary-layer flows. J. Fluid Mech. 126, 443.Google Scholar
Eagles, P. M. 1966 The stability of a family of Jeffery-Hamel solutions for divergent channel flow. J. Fluid Mech. 24, 191.Google Scholar
Eagles, P. M. & Daniels, P. G. 1986 Free surface boundary-layer flow on a curved bed. IMA J. Appl. Maths 36, 101.Google Scholar
Eagles, P. M. & Smith, F. T. 1980 The influence of non-parallelism in channel flow stability. J. Engng Maths 14, 219.Google Scholar
Fraenkel, L. E. 1962 Laminar flow in symmetric channels with slightly curved walls. Part I. On the Jeffery-Hamel solutions for flow between plane walls. Proc. R. Soc. Lond. A 267, 119.Google Scholar
Fraenkel, L. E. 1963 Laminar flow in symmetric channels with slightly curved walls. Part II. An asymptotic series for the stream function. Proc. R. Soc. Lond. A 272, 406.Google Scholar
Fulford, G. D. 1964 Advances in Chemical Engineering. Academic.
Gajjar, J. 1983 On some viscous interaction problems in incompressible fluid flow. Ph.D. Thesis. Dept. of Mathematics, Imperial College, London.
Lin, S. P. 1983 Waves on Fluid Interfaces. Academic.
Merkin, J. H. 1973 The flow of a viscous liquid down a variable incline. J. Engng Maths 7, 319.Google Scholar
Wang, C. Y. 1984 Thin film flowing down a curved surface. Z. Angew. Math. Phys. 35, 532.Google Scholar
Yih, C. S. 1963 Stability of liquid film down an inclined plane. Phys. Fluids 6, 321.Google Scholar