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The boundary correction for the Rayleigh-Darcy problem: limitations of the Brinkman equation

Published online by Cambridge University Press:  20 April 2006

D. A. Nield
D. A. Nield
Affiliation:
Department of Mathematics, University of Auckland, New Zealand
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Abstract

The no-slip condition on rigid boundaries necessitates a correction to the critical value of the Rayleigh–Darcy number for the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below. It is shown that the use of the Brinkman equation to obtain this correction is not justified, because of the limitations of that equation. These limitations are discussed in detail. An alternative procedure, based on a model in which the porous medium is sandwiched between two fluid layers, and the Beavers–Joseph boundary condition is applied at the interfaces, is described, and an expression for the correction is obtained. It is found that the correction can be of either sign, depending on the relative magnitudes of the parameters involved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 128 , March 1983 , pp. 37 - 46
Copyright
© 1983 Cambridge University Press

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