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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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References

Busse, F. H. 1967 The stability of finite amplitude cellular convection and its relation to an extremum principle J. Fluid Mech. 30, 625–649.Google Scholar
Busse, F. H. & Riahi, N. 1980 Nonlinear convection in a layer with nearly insulating boundaries J. Fluid Mech. 96, 243–256.Google Scholar
Joseph, D. D. 1976 Stability of Fluid Motions I and II. Springer.
Lapwood, E. R. 1948 Convection of a fluid in a porous medium Proc. Camb. Phil. Soc. 44, 508–521.Google Scholar
Mckenzie, D., Watts, A., Parsons, B. & Roufosse, M. 1980 Planform of mantle convection beneath the Pacific Ocean Nature 288, 442–446.Google Scholar
Palm, E., Weber, J. E. & Kvernvold, O. 1972 On steady convection in a porous medium J. Fluid Mech. 54, 153–161.Google Scholar
Schltuter, A., Lortz, D. & Busse, F. H. 1965 On the stability of finite amplitude convection J. Fluid Mech. 23, 129–144.Google Scholar
Schubert, G. & Straus, J. M. 1979 Three-dimensional and multicellular steady and unsteady convection in fluid-saturated porous media at high Rayleigh numbers J. Fluid Mech. 94, 25–38.Google Scholar
Straus, J. M. 1974 Large amplitude convection in porous media J. Fluid Mech. 64, 51–63.Google Scholar
Straus, J. M. & Schubert, G. 1978 On the existence of three-dimensional convection in a rectangular box containing fluid-saturated porous material J. Fluid Mech. 87, 385–394.Google Scholar
Straus, J. M. & Schubert, G. 1979 Three-dimensional convection in a cubic box of fluid-saturated porous material J. Fluid Mech. 91, 155–165.Google Scholar
Straus, J. M. & Schubert, G. 1981 Modes of finite-amplitude three-dimensional convection in a rectangular box of fluid-saturated porous material J. Fluid Mech. 103, 23–32.Google Scholar
Zebib, A. & Kassoy, D. R. 1978 Three-dimensional natural convection motion in a confined porous medium Phys. Fluids 21, 1–3.Google Scholar