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On the influence of longitudinal diffusion in time-dependent convective-diffusive systems

Published online by Cambridge University Press:  21 April 2006

H. K. Kuiken
H. K. Kuiken
Affiliation:
Philips Research Laboratories, P.O. Box 80000, 5600 JA Eindhoven, The Netherlands
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Abstract

A model problem is solved mathematically in order to clarify how an essential singularity, which is an integral part of the boundary-layer solution of a time-dependent convective–diffusive system, is removed by the inclusion of the effect of longitudinal diffusion. The model problem involves a uniform velocity field along a plane boundary at which boundary conditions of a mixed type are prescribed. The problem is solved by means of a method involving the Laplace transform and the Wiener–Hopf technique. An exact solution is presented.

Special attention is given to an asymptotic solution that is valid for large values of the dimensionless time. It is shown that the large-time asymptote and the naïve boundary-layer solution are close approximations of one another, except in the neighbourhood of the location where the latter is singular. Around this point the present solution provides an interlayer which matches smoothly the purely time-dependent Rayleigh-like and the stationary components of the boundary-layer approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 165 , April 1986 , pp. 147 - 162
Copyright
© 1986 Cambridge University Press

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