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Nonlinear thermal convection with finite conducting boundaries

Published online by Cambridge University Press:  20 April 2006

N. Riahi
N. Riahi
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
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Abstract

Finite-amplitude thermal convection in a horizontal layer with finite conducting boundaries is investigated. The nonlinear steady problem is solved by a perturbation technique, and the preferred mode of convection is determined by a stability analysis. Square cells are found to be the preferred form of convection in a semi-infinite three-dimensional region Ω in the (γb,γt, P)-space (γb and γt are the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid and P is the Prandtl number). Two-dimensional rolls are found to be the preferred convection pattern outside Ω. The dependence on γb, γt and P of the heat transported by convection is computed for the various solutions analysed in the paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 152 , March 1985 , pp. 113 - 123
Copyright
© 1985 Cambridge University Press

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References

Busse, F. H. & Riahi, N. 1980 Nonlinear convection in a layer with nearly insulating boundaries. J. Fluid Mech. 96, 243–256.Google Scholar
Jenkins, D. R. & Proctor, M. R. E. 1984 The transition from roll to square-cell solutions in Rayleigh-Bénard convection. J. Fluid Mech. 139, 461–471.Google Scholar
Riahi, N. 1980 On convection with nearly insulating boundaries in a low Prandtl number fluid. Z. angew. Math. Phys. 31, 261–266.Google Scholar
Riahi, N. 1983 Nonlinear convection in a porous layer with finite conducting boundaries. J. Fluid Mech. 129, 153–171.Google Scholar
SchlÜter, A., Lortz, D. & Busse, F. H. 1965 On the stability of finite amplitude convection. J. Fluid Mech. 23, 129–144.Google Scholar