Natural convection in a vertical porous cavity filled with a non-newtonian binary fluid

Authors

  • Nabil Ben Khelifa,

    1. Laboratoire des Technologies Innovantes, Université de Picardie Jules Vernes d'Amiens rue des Facultés le Bailly, 80025 Amiens Cedex, France
    2. Laboratoire des Procédés Thermiques, Centre des Recherches et des Technologies de l'Energie, Technopole Borj Cedria B.P No 95, Hammam Lif 2050, Tunisie
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  • Zineddine Alloui,

    Corresponding author
    1. Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. “Centre Ville”, Montréal, QC H3C 3A7, Canada
    • Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. “Centre Ville”, Montréal, QC H3C 3A7, Canada

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  • Hassen Beji,

    1. Laboratoire des Technologies Innovantes, Université de Picardie Jules Vernes d'Amiens rue des Facultés le Bailly, 80025 Amiens Cedex, France
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  • Patrick Vasseur

    1. Laboratoire des Technologies Innovantes, Université de Picardie Jules Vernes d'Amiens rue des Facultés le Bailly, 80025 Amiens Cedex, France
    2. Ecole Polytechnique, Université de Montréal, C.P. 6079, Succ. “Centre Ville”, Montréal, QC H3C 3A7, Canada
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Abstract

Numerical and analytical study of natural convection in a vertical porous cavity filled with a non-Newtonian binary fluid is presented. The density variation is taken into account by the Boussinesq approximation. A power-law model is used to characterize the non-Newtonian fluid behavior. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. Both double-diffusive convection (a = 0) and Soret-induced convection (a = 1) are considered. Scale analysis is presented for the two extreme cases of heat-driven and solute-driven natural convection. For convection in a thin vertical layer (A ≫ 1), a semianalytical solution for the stream function, temperature, and solute fields, Nusselt and Sherwood numbers are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. Numerical results of the full governing equations show the effects of the governing parameters, namely the thermal Rayleigh number, RT, the Lewis number, Le, the buoyancy ratio, φ, the power-law index, n, and the integer number a. A good agreement between the analytical predictions and the numerical simulations is obtained. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1704–1716, 2012

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