Transient Double-Diffusive Convection of Water Around $4°C$ in a Porous Cavity

The buoyancy-driven transient double-diffusive convection in a square cavity filled with water-saturated porous medium is studied numerically. While the right and left side wall temperatures vary linearly from $θa$ to $θo$ and $θo$ to $θb$⁠, respectively, with height, the top and bottom walls of the cavity are thermally insulated. The species concentration levels at the right and left walls are $c1$ and $c2$⁠, respectively, with $c1>c2$⁠. The Brinkman–Forchheimer extended Darcy model is considered to investigate the average heat and mass transfer rates and to study the effects of maximum density, the Grashof number, the Schmidt number, porosity, and the Darcy number on buoyancy-induced flow and heat transfer. The finite volume method with power law scheme for convection and diffusion terms is used to discretize the governing equations for momentum, energy, and concentration, which are solved by Gauss–Seidel and successive over-relaxation methods. The heat and mass transfer in the steady-state are discussed for various physical conditions. For the first time in the literature, the study of transition from stationary to steady-state shows the existence of an overshooting between the two cells and in the average Nusselt number. The results obtained in the steady-state regime are presented in the form of streamlines, isotherms, and isoconcentration lines for various values of Grashof number, Schmidt number, porosity and Darcy number, and midheight velocity profiles. It is found that the effect of maximum density is to slow down the natural convection and reduce the average heat transfer and species diffusion. The strength of convection and heat transfer rate becomes weak due to more flow restriction in the porous medium for small porosity.