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Nonlinear convection in a porous layer 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, Illinois 61801
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Abstract

The problem of finite-amplitude thermal convection in a porous layer with finite conducting boundaries is investigated. The nonlinear problem of three-dimensional convection is solved by expanding the dependent variables in terms of powers of the amplitude of convection. The preferred mode of convection is determined by a stability analysis in which arbitrary infinitesimal disturbances are superimposed on the steady solutions. Square-flow-pattern convection is found to be preferred in a bounded region [Gcy ] in the (γb, γt)-space, where γb and γt are the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid. Two-dimensional rolls are found to be the preferred pattern outside [Gcy ]. The qualitative features of the convection problem appear to be essentially symmetric with respect to γb and γt. The dependence of the heat transported by convection on γb and γt is computed for the various solutions analysed in the paper.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 129 , April 1983 , pp. 153 - 171
Copyright
© 1983 Cambridge University Press

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