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Convection in a vertical slot

Published online by Cambridge University Press:  21 April 2006

P. G. Daniels
P. G. Daniels
Affiliation:
Department of Mathematics, The City University, Northampton Square, London EC1V 0HB, UK
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Abstract

A boundary-layer approximation is used to describe the convective regime in a laterally heated vertical slot at large Prandtl numbers. The determination of the core flow requires the solution of the vertical boundary-layer equations in a rectangle, subject to appropriate boundary conditions on each of the four walls. Solutions based on a spectral decomposition in the vertical direction allow a comparison with experimental and numerical results, and an appraisal of an approximate solution frequently used as a basis for stability studies. Both the numerical results and an approximate stability argument lead to a simple criterion for the appearance of multiple rolls in the slot which appears to be in good agreement with experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 419 - 441
Copyright
© 1987 Cambridge University Press

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