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Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory

Published online by Cambridge University Press:  29 March 2006

D. E. Cormack
Chemical Engineering, California Institute of Technology, Pasadena
L. G. Leal
Chemical Engineering, California Institute of Technology, Pasadena
J. Imberger
Department of Mathematics and Mechanical Engineering, University of Western Australia, Nedlands


The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A → 0, are derived.

Research Article
© 1974 Cambridge University Press

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