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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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References

Arakawa, A. 1966 J. Comp. Phys. 1, 119.
Batchelor, G. K. 1954 Quart. Appl. Math. 12, 209.
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 J. Fluid Mech. 65, 209.
De Vahl Davis, G. 1968 Int. J. Heat Mass Transfer, 11, 1675.
Elder, J. W. 1965 J. Fluid Mech. 23, 77.
Elder, J. W. 1966 J. Fluid Mech. 24, 823.
Gill, A. E. 1966 J. Fluid Mech. 26, 515.
Newell, M. E. & Schmidt, F. W. 1970 J. Heat Transfer, 92, 159.
Peaceman, D. W. & Rachford, H. H. 1955 J. Soc. Ind. Appl. Math. 3, 28.
Quon, C. 1972 Phys. Fluids, 15, 12.
Rubel, A. & Landis, F. 1969 Phys. Fluids Suppl. II, 12, II–208.
Von Rosenberg, D. U. 1969 Methods for the Numerical Solution of Partial Differential Equations. Elsevier.
Wilkes, J. O. & Churchill, S. W. 1966 A.I.Ch.E. J. 12, 161.
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