Heat transfer characteristics of thermo-diffusion (Soret) and diffusion-thermo (Dufour) effects in a square cavity containing a non-Darcy porous medium

The impact of the double-diffusive natural convection of water in a square enclosure with diffusion-thermo and thermo-diffusion around the non-Darcy porous medium is studied numerically. The top and bottom side walls of the cavity are maintained at constant temperatures, while the vertical left and right walls are considered to be cold. Water is considered the working fluid. The resulting nondimensional partial differential equation is solved by the Marker and Cell (MAC) method by using a staggered grid system. The Dufour and Soret effects processes will be a significantly essential role in the double-diffusive velocity flow processes. For different values of the relevant parameters, the fluid flow velocity, temperature, and concentration are presented for various Rayleigh numbers, Prandtl numbers, non-Darcy, thermo-diffusion, and diffusion-thermo. The streamlines, isotherms, and iso-concentration contours are obtained using the MATLAB software. Finally, it is observed that the Nusselt numbers increased with non-Darcy, thermo-diffusion, and Rayleigh numbers and decreased with diffusion-thermo effects.