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Convection in a porous cavity

Published online by Cambridge University Press:  12 April 2006

Ken L. Walker  and
George M. Homsy
Ken L. Walker
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
George M. Homsy
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
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Abstract

Convection in a porous cavity driven by heating in the horizontal is analysed by a number of different techniques which yield a fairly complete description of the two-dimensional solutions. The solutions are governed by two dimensionless parameters: the Darcy-Rayleigh number R and the cavity aspect ratio A. We first find solutions valid for shallow cavities, A → 0, by using matched asymptotic expansions. These solutions are given up to O(A6R4). For A fixed, we find regular expansions in R by semi-numerical techniques, up to O(R30) in some cases. Series-improvement techniques then enable us to cover the range 0 ≤ R ≤ ∞. A limited result regarding bifurcations is noted. Finally, for R → ∞ with A fixed, we propose a self-consistent boundary-layer theory which extends previous approximate work. The results obtained by these different methods of solution are in good agreement with each other and with experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 3 , 15 August 1978 , pp. 449 - 474
Copyright
© 1978 Cambridge University Press

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