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多孔介质期刊
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ISSN 打印: 1091-028X
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多孔介质期刊

DOI: 10.1615/JPorMedia.v7.i1.50
18 pages

Soret and Double Diffusive Convection in a Porous Cavity

N. Boutana
Ecole Polytechnique, C.P. 6079, Succ "Centre Ville," Montreal, Quebec, H3C 3A7, Canada
Ali Bahloul
Départment de Génie Mécanique École Polytechnique de Montréal C.P. 6079, Succ. Centre-ville, Montréal, Québec H3C 3A7 Canada
Patrick Vasseur
Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. "Centre ville", Montréal, Québec H3C 3A7, Canada
F. Joly
Ecole Polytechnique, C.P. 6079, Succ "Centre Ville," Montreal, Quebec, H3C 3A7, Canada; and Universite Paris-Sud, Orsay, France

ABSTRACT

Natural convection in a rectangular porous medium filled with a binary fluid is studied analytically and numerically. The two vertical walls of the cavity are subject to constant gradients of temperature while the two horizontal ones are adiabatic and impermeable. Solutal gradients are assumed to be induced either by the imposition of constant gradients of concentration on the vertical walls (double-diffusive convection, a = 0) or by the Soret effect (a = 1). Governing parameters of the problem under study are the thermal Rayleigh number RT, buoyancy ratio φ, Lewis number Le, and aspect ratio of the cavity, A. An analytical solution, based on the parallel flow approximation, is reported for tall enclosures. The analysis reveals that there is a range of buoyancy ratios φ which yields up to three analytical solutions for a given set of governing parameters. The range of buoyancy ratios for the existence of multiple solutions is found to depend on the type of convection induced by the solutal gradients, i.e., on the constant a. In the range of the governing parameters considered in this study, good agreement is observed between the analytical predictions and a numerical solution of the full governing equations.


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