ON NATURAL-CONVECTION IN VERTICAL POROUS ENCLOSURES DUE TO PRESCRIBED FLUXES OF HEAT AND MASS AT THE VERTICAL BOUNDARIES

Unsteady and steady convection in a fluid-saturated, vertical and homogeneous porous enclosure has been studied numerically on the basis of a two-dimensional mathematical model. The buoyancy forces that induce the fluid motion are due to cooperative and constant fluxes of heat and mass on the vertical walls. For the steady state, an analytical solution, valid for stratified flow in slender enclosures, is presented. Scale analysis is applied to the two extreme cases of heat-driven and solute-driven natural convection. Comparisons between the fully numerical and analytical solutions are presented for 0.1 less-than-or-equal-to R(c) less-than-or-equal-to 500, 2 less-than-or-equal-to Le less-than-or-equal-to 10(2), 10(-2) less-than-or-equal-to N less-than-or-equal-to 10(4) and 1 less-than-or-equal-to A less-than-or-equal-to 10, where R(c), Le, N and A denote the solutal Rayleigh-Darcy number, Lewis number, inverse of buoyancy ratio and enclosure aspect ratio, respectively. The numerical results show that for any value of Le > 1, there exists a minimum A below which the concentration field in the core region is rather uniform and above which it is linearly stratified in the vertical direction. For sufficiently high aspect ratios, the agreement between the numerical and analytical solutions is good. The results of the scale analysis agree well with approximations of the analytical solution in the heat-driven and solute-driven limits, The numerical results indicate that for Le > 1 the thermal layers at the top and the bottom of the enclosure are thinner than their solutal counterparts. In the boundary layer regime, and for sufficiently high A, the thicknesses of the vertical boundary layers of velocity, concentration and temperature are shown to be equal, regardless of the value of Le.