OSCILLATION ABOUT DOUBLE-DIFFUSIVE CONVECTION IN A POROUS CAVITY DUE TO OPPOSING FLUXES OF HEAT AND MASS AT THE VERTICAL WALLS

摘要

Two-dimensional double-diffusive convection in porous media is analyzed numerically. The top and bottom walls of the enclosure are insulated and aspect ratio is 5. Constant and opposing fluxes of heat and mass are prescribed on the vertical walls. The time-dependent evolution of the velocity, concentration and temperature is calculated by using finite difference method. The discretized equations and boundary conditions are solved by the method of conjugate gradients. At each time step, the solution is converged when the error is less than 10{sup}(-5). In this calculation, oscillating convection are obtained when the Rayleigh-Darcy (R{sub}c) is over 50 and Lewis number (Le) is over 2. These oscillating convection is always temperature-dominated and such oscillations reveal the competition between the convection due to temperature and due to concentration. In a recent paper, the authors found that the oscillating solutions are calculated in the range of N{sub}(min) < N < N{sub}(max) and the agreement between the analytical and numerical solutions are satisfactory out of the range when aspect ratio is sufficiently large, where N correspond to the inverse of buoyancy ratio. N{sub}(min) and N{sub}(max) are determined numerically. The range of N (N{sub}(min) and N{sub}(max)) which is obtained oscillating solution for various values of the input parameters R{sub}c and Le. The oscillation patterns are determined by Rayleigh-Darcy number, Lewis number and buoyancy ratio. Especially, buoyancy ratio is the most important parameter. Figure A-1 shows the oscillation of Nusselt number when R{sub}c = 50, Le = 10 and N = 0.75. For this R{sub}c and Le, N{sub}(max) is 0.86. Near N{sub}(max), the oscillating convection is monotony. The oscillation pattern makes more complicated than N is smaller (see Figure A-1). It is found that oscillations from monotony to chaotic are observed as the inverse of buoyancy ratio become smaller near N{sub}(min) when R{sub}c = 50 and 100.