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

Unsteady and steady convection in a fluid-saturated, vertical and homo geneous 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 an d mass on the vertical walls. For the steady state, an analytical solu tion, valid for stratified flow in slender enclosures, is presented. S cale analysis is applied to the two extreme cases of heat-driven and s olute-driven natural convection. Comparisons between the fully numeric al and analytical solutions are presented for 0.1 less-than-or-equal-t o 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 num ber, inverse of buoyancy ratio and enclosure aspect ratio, respectivel y. The numerical results show that for any value of Le > 1, there exis ts a minimum A below which the concentration field in the core region is rather uniform and above which it is linearly stratified in the ver tical direction. For sufficiently high aspect ratios, the agreement be tween the numerical and analytical solutions is good. The results of t he scale analysis agree well with approximations of the analytical sol ution in the heat-driven and solute-driven limits, The numerical resul ts indicate that for Le > 1 the thermal layers at the top and the bott om of the enclosure are thinner than their solutal counterparts. In th e boundary layer regime, and for sufficiently high A, the thicknesses of the vertical boundary layers of velocity, concentration and tempera ture are shown to be equal, regardless of the value of Le.