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Asymptotics of slow flow of very small exponent power-law shear-thinning fluids in a wedge

Published online by Cambridge University Press:  26 September 2008

M. E. Brewster
Affiliation:
Department of Mathematics, University of Colorado, Boulder, CO, USA
S. J. Chapman
Affiliation:
Mathematical Institute, 24-29 St. Giles', Oxford OX1 3LB, UK
A. D. Fitt
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO 17 1BJ, UK
C. P. Please
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO 17 1BJ, UK

Abstract

The incompressible slow viscous flow of a power-law shear-thinning fluid in a wedge-shaped region is considered in the specific instance where the stress is a very small power of the strain rate. Asymptotic analysis is used to determine the structure of similarity solutions. The flow is shown to possess an outer region with boundary layers at the walls. The boundary layers have an intricate structure consisting of a transition layer 0(ɛ) adjoining an inner layer O(ɛlnɛ), which further adjoins an inner-inner layer 0(ɛ) next to the wall. Explicit solutions are found in all the regions and the existence of ‘dead zones’ in the flow is discussed.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1995

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References

Mansutti, D. & Pontrelli, G. 1991 Jeffrey-Hamel flow of power-law fluids for exponent values close to the critical value. Int. J. Nonlinear Mechanics 26, 761767.CrossRefGoogle Scholar
Mansutti, D. & Rajagopal, K. R. 1991 Flow of a shear thinning fluid between intersecting planes. Int. J. Nonlinear Mechanics 26, 769775.CrossRefGoogle Scholar
Nayfeh, A. H. 1973 Perturbation Methods. John Wiley.Google Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Dover.Google Scholar
Pakdemiru, M. 1993 Boundary layer flow of fluids past arbitrary profiles. IMA J. Appl. Math. 50, 133148.CrossRefGoogle Scholar
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