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Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

Cormack, D. E. and Leal, L. G. and Seinfeld, J. H. (1974) Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions. Journal of Fluid Mechanics, 65 (2). pp. 231-246. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120802-124203574

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Abstract

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6.983, 10 ≤ Gr ≤ 2x10^4 and 0.05 ≤ A ≤ 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A ≾ 0.1 and Gr^2A^3Pr^2 ≾ l0^5. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.


Item Type:Article
Related URLs:
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http://dx.doi.org/10.1017/S0022112074001364DOIUNSPECIFIED
http://journals.cambridge.org/abstract_S0022112074001364PublisherUNSPECIFIED
Additional Information:© 1974 Cambridge University Press. Received 23 March 1973; in revised form 15 February 1974; published Online March 29 2006. This work was supported, in part, by National Science Foundation Grant GK-35476.
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Funding AgencyGrant Number
NSFGK-35476
Record Number:CaltechAUTHORS:20120802-124203574
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120802-124203574
Official Citation:D. E. Cormack, L. G. Leal and J. H. Seinfeld (1974). Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions. Journal of Fluid Mechanics, 65 , pp 231-246 doi:10.1017/S0022112074001364
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32884
Collection:CaltechAUTHORS
Deposited By: Aucoeur Ngo
Deposited On:02 Aug 2012 20:01
Last Modified:26 Dec 2012 15:48

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