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

Published online by Cambridge University Press:  29 March 2006

D. E. Cormack ,
L. G. Leal  and
J. H. Seinfeld
D. E. Cormack
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
L. G. Leal
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
J. H. Seinfeld
Affiliation:
Chemical Engineering, California Institute of Technology, Pasadena
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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 × 104 and 0·05 [les ] A [les ] 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A [lsim ] 0·1 and Gr2A3Pr2 [lsim ] 105. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 2 , 28 August 1974 , pp. 231 - 246
Copyright
© 1974 Cambridge University Press

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