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The unsteady boundary layer on a rotating disk in a counter-rotating fluid. Part 2

Published online by Cambridge University Press:  20 April 2006

K. Stewartson ,
C. J. Simpson  and
R. J. Bodonyi
K. Stewartson
Affiliation:
Department of Mathematics, University College London
C. J. Simpson
Affiliation:
Department of Mathematics, University College London
R. J. Bodonyi
Affiliation:
Department of Mathematical Sciences, Indiana–Purdue University at Indianapolis
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Abstract

An unsteady boundary layer on a rotating disk in a counter-rotating fluid was shown in Bodonyi & Stewartson (1977) to develop a singularity at the axis of rotation after a finite time. The structure proposed to describe the singularity is, however, incomplete, even after an additional term was added by Banks & Zaturska (1981). A description is given here in which the boundary layer is divided into three regions; this description seems to be free of the weaknesses of the earlier studies, and is in good agreement with data from the numerical solution of the governing equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 507 - 515
Copyright
© 1982 Cambridge University Press

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References

Banks, W. H. H. & Zaturska, M. B. 1981 The unsteady boundary-layer development on a rotating disc in counter-rotating flow. Acta Mechanica 38, 143–145.Google Scholar
Bodonyi, R. J. & Stewrartson, K. 1977 The unsteady boundary layer on a rotating disk in a counter-rotating fluid. J. Fluid Mech. 79, 669–688.Google Scholar
Cebeci, T. & Bradshaw, P. 1977 Momentum Transfer in Boundary Layers. Hemisphere/McGraw-Hill.
Ockendon, H. 1972 An asymptotic solution for steady flow above an infinite rotating disc with suction. Q. J. Mech. Appl. Math. 25, 291–301.Google Scholar
Simpson, C. J. & Stewartson, K. 1982 A singularity in an unsteady free-convection boundary layer. Q. J. Mech. Appl. Math. (To be published.)Google Scholar
Simpson, C. J. 1982 Ph.D. thesis, London University.