Cormack, D. E. and Leal, L. G. and Imberger, J. (1974) Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory. Journal of Fluid Mechanics, 65 (2). pp. 209-229. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120802-125446317
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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.
|Additional Information:||© 1974 Cambridge University Press. Published Online March 29 2006; Received March 23 1973; Revised February 15 1974. This work was done, in part, while J. Imberger was a visitor to the Keck Laboratory of Environmental Engineering at the California Institute of Technology, with the support of a National Science Foundation Grant GK-35774X.|
|Official Citation:||D. E. Cormack, L. G. Leal and J. Imberger (1974). Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory. Journal of Fluid Mechanics, 65 , pp 209-229 doi:10.1017/S0022112074001352|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Aucoeur Ngo|
|Deposited On:||02 Aug 2012 20:09|
|Last Modified:||26 Dec 2012 15:48|
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