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. doi:10.1017/S0022112074001364. https://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 ≤ 2 x 10⁴ 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 Gr²A³Pr² ≾ l0⁵. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.
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| 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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| Issue or Number: | 2 | ||||||
| DOI: | 10.1017/S0022112074001364 | ||||||
| Record Number: | CaltechAUTHORS:20120802-124203574 | ||||||
| Persistent URL: | https://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: | INVALID USER | ||||||
| Deposited On: | 02 Aug 2012 20:01 | ||||||
| Last Modified: | 13 Apr 2023 18:37 |
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