Analytical and numerical study of double-diffusive natural convection in aBrinkman porous layer

Thermosolutal natural convection in a vertical porous layer submitted to un iform fluxes of heat and mass is studied analytically and numerically. The Brinkman model is used in the particular situation where the solutal and th ermal volumetric forces are opposite and equal. The analytical solution, ba sed on the parallel flow approximation, is developed for sufficiently high values of the aspect ratio A of the porous matrix. The critical Rayleigh nu mbers above which convective flows are possible are predicted analytically as function of the Lewis Le and Darcy Da numbers. The results presented her e 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 mo del respectively for weak and high values of Da. Only monocellular solution s have been obtained numerically despite the multiplicity of solutions demo nstrated analytically. (C) 1999 Elsevier Science Ltd. All rights reserved.