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On a linear, partly hyperbolic model of viscoelastic flow past a plate

Published online by Cambridge University Press:  14 November 2011

L. E. Fraenkel
L. E. Fraenkel
Affiliation:
School of Mathematics, University of Bath, Bath BA2 7AY, U.K.
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Synopsis

The paper presents solutions, for a class of shear relaxation functions, ofa linear problem formulated by Joseph [8] to elucidate the steady, supercritical flow of a viscoelastic fluid past a semi-infinite flat plate. The velocity (U, 0) at infinity is parallel to the plate, and‘supercritical flow ‘means that U is greater than the propagation speed C of shear waves. As a result, the vorticity satisfies a hyperbolic equation and is confined to the region downstream of a shock wave from the leading edge of the plate. The disturbance velocity fieldextends upstream of the shock and is continuous across it. In contrast to the case of a Newtonian fluid, the solutions are unique under the condition that the functions representing the vorticity on the two sides of the platebelong to a certain Banach space.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 299 - 354
Copyright
Copyright © Royal Society of Edinburgh 1990

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