ANALYTICAL AND NUMERICAL STUDY OF DOUBLE-DIFFUSIVE CONVECTION IN A VERTICAL ENCLOSURE

This paper presents an analytical and numerical study of natural conve ction of a double-diffusive fluid contained in a rectangular slot subj ect to uniform heat and mass fluxes along the vertical sides. Governin g parameters of the problem under study are the thermal Rayleigh numbe r, Ra-T; buoyancy ratio, N; Lewis number, Le; Prandtl number, Pr and a spect ratio of the cavity, A. In the first part of the analytical stud y a scale analysis is applied to the two extreme cases of heat-transfe r and mass-transfer-driven flows. In the second part, an analytical so lution, based on the parallel flow approximation, is reported for tall enclosures (A much greater than 1). Solutions for the flow fields, te mperature and concentration distributions and Nusselt and Sherwood num bers 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 com plete governing equations for two-dimensional flows, and cover the ran ge 1 less than or equal to Ra-T less than or equal to 10(7), 0 less th an or equal to N less than or equal to 10(5), 10(-3) less than or equa l to Le less than or equal to 10(3), 1 less than or equal to A less th an or equal to 20 and Pr = 7. A good agreement is found between the an alytical predictions and the numerical simulation.