Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory
- Creators
- Cormack, D. E.
- Leal, L. G.
- Imberger, J.
Abstract
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.Attached Files
Published - CORjfm74a.pdf
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Additional details
- Eprint ID
- 32885
- Resolver ID
- CaltechAUTHORS:20120802-125446317
- NSF
- GK-35774X
- Created
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2012-08-02Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field