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Throughflow effects in the Rayleigh-Bénard convective instability problem

Published online by Cambridge University Press:  21 April 2006

D. A. Nield
D. A. Nield
Affiliation:
Department of Theoretical and Applied Mechanics, University of Auckland, Auckland, New Zealand
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Abstract

The effect of vertical throughflow on the onset of convection in a fluid layer, between permeable horizontal boundaries, when heated uniformly from below, is re-examined analytically. It is shown that when the Péclet number Q is large in magnitude, the critical Rayleigh number Rc is proportional to Qn, where n = 0, 1, 2, 3 or 4, with a coefficient depending on the Prandtl number P, according to the types of boundaries. When the upper and lower boundaries are of different types, the effect of a small amount of throughflow in one direction is to decrease Rc. This is so when the throughflow is away from the more restrictive boundary. Contributions arise from the curvature of the basic temperature profile, and from the vertical transport of perturbation velocity and perturbation temperature. The decrease in Rc is small if P ∼ 1 but can be of significant size if P [Lt ] 1 or P [Gt ] 1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 353 - 360
Copyright
© 1987 Cambridge University Press

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