International Journal of Heat and Mass Transfer, Vol.42, No.15, 2991-3005, 1999
Analytical and numerical study of double-diffusive natural convection in a Brinkman porous layer
Thermosolutal natural convection in a vertical porous layer submitted to uniform fluxes of heat and mass is studied analytically and numerically. The Brinkman model is used in the particular situation where the solutal and thermal volumetric forces are opposite and equal. The analytical solution, based on the parallel flow approximation, is developed for sufficiently high values of the aspect ratio A of the porous matrix. The critical Rayleigh numbers above which convective flows are possible are predicted analytically as function of the Lewis Le and Darcy Da numbers. The results presented here cover the following ranges: 0 < R-T < 10(3), 0 < Le < 10(3) and 0 < Da < 10. The limiting results of the Darcy model and those of the fluid medium (Pr greater than or equal to 0.5) are correctly predicted by the Brinkman model respectively for weak and high values of Da. Only monocellular solutions have been obtained numerically despite the multiplicity of solutions demonstrated analytically.
Keywords:RECTANGULAR CAVITY;HEAT-TRANSFER;MASS;ENCLOSURE;ONSET;MODEL;FORMULATION;FLUXES;REGIME;WALLS