Numerical Simulation of Thermal and Concentration Natural Convection in a Porous Cavity in the Presence of an Opposing Flow

Two-dimensional steady-state thermal concentration convection in a rectangular porous cavity is simulated numerically. The temperature and concentration gradients are horizontal and the buoyancy forces act either in the same or in opposite directions. The flow through the porous medium is described by the Darcy-Brinkman or Forchheimer equations. The SIMPLER numerical algorithm based on the finite volume approach is used for solving the problem in the velocity-pressure variables.Numerous series of calculations were carried out over the range Ra _t =3·10⁶ and 3·10⁷, 10^-6 < Da < 1, 1 < N < 20, Le=10 and 100, where Ra, Da, Le, and N are the Rayleigh, Darcy, and Lewis numbers and the buoyancy ratio, respectively. It is shown that the main effect of the presence of the porous medium is to reduce the heat and mass transfer and attenuate the flow field with decrease in permeability. For a certain combination of the Ra, Le, and N numbers the flow has a multicellular structure. The mean Nusselt and Sherwood numbers are presented as functions of the governing parameters.