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The Rayleigh–Bénard problem in intermediate bounded domains

Published online by Cambridge University Press:  26 April 2006

F. Stella ,
G. Guj  and
E. Leonardi
F. Stella
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università degli Studi di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
G. Guj
Affiliation:
Dipartimento di Meccanica e Aeronautica, Università degli Studi di Roma ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy
E. Leonardi
Affiliation:
The University of New South Wales, Kensington, NSW, Australia 2033
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Abstract

The stationary instabilities of flow patterns associated with Rayleigh–Bénard convection in a 3 × 1 × 9 rectangular container are extensively investigated by numerical simulation. Two types of spatial instabilities of the base convection rolls are predicted in the transition from steady two-dimensional flow to the unsteady oscillatory regime; these instabilities depend on the Prandtl number. For Pr = 0.71 the soft-roll instability is found at moderate Rayleigh number Ra. The results obtained confirm the importance of this flow pattern as a continuous mechanism for steady transition from one wavenumber to another. For Pr = 15, cross-roll instability is obtained, which at larger Ra leads to bimodal convection. For this value of Pr the soft-roll flow pattern is found at intermediate Ra. At higher Ra a new flow structure in which cross-rolls are superimposed on the soft roll is obtained. The effects of the various flow structures on the heat transfer are given. A quantitative comparison with previous experimental and theoretical findings is also presented and discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 375 - 400
Copyright
© 1993 Cambridge University Press

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