Analytical and numerical study of double diffusive convection in a vertical enclosure (original) (raw)

1996, Heat and Mass Transfer

This paper presents an analytical and numerical study of natural convection of a double-diffusive fluid contained in a rectangular slot subject to uniform heat and mass fluxes along the vertical sides. Governing parameters of the problem under study are the thermal Rayleigh number, Ra 2 ; buoyancy ratio, N; Lewis number, Le; Prandtl number, Pr and aspect ratio of the cavity, A. In the first part of the analytical study a scale analysis is applied to the two extreme cases of heat-transfer and mass-transfer-driven flows. In the second part, an analytical solution, based on the parallel flow approximation, is reported for tall enclosures (A<1). Solutions for the flow fields, temperature and concentration distributions and Nusselt and Sherwood numbers are obtained in terms of the governing parameters of the problem. In the limits of heat-driven and solute-driven flows a good agreement is obtained between the prediction of the scale analysis and those of the analytical solution. The numerical solutions are based on the complete governing equations for two-dimensional flows, and cover the range 14Ra 2 4107, 04N4105, 10\34Le4103, 14A420 and Pr:7. A good agreement is found between the analytical predictions and the numerical simulation.

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