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The effect of magnetic field on double-diffusive natural convection in a square cavity filled with a fluid-saturated porous medium is studied numerically. The bottom wall is fully heated at a constant temperature, and the top wall is maintained at a constant cold temperature. The right wall is fully salted to a high concentration, while the left wall is fully salted at a lower concentration than the right one. A magnetic force is applied on the cavity along the gravity force direction. The Darcy model is used for the mathematical formulation of the fluid flow through porous media. The governing equations for heat and mass transfer are solved using the finite volume method. The governing parameters of the present study are Rayleigh number (Ra), Lewis number (Le), buoyancy ratio (N), and Hartmann number (Ha). The numerical solutions were studied in the range of −10 ≤ ≤ 10, 0 ≤ Ha ≤ 10, 50 ≤ Ra ≤ 500, and 10 −4 ≤ Le ≤ 10. The results were discussed considering the effect of these parameters on the heat and mass transfer processes. The results were presented in terms of streamlines, isotherms, isoconcentration, average Nusselt number, and average Sherwood number for different values of the governing parameters. In general, it has been found that the increase of magnetic force has an effect to retard the strength of the flow inside the cavity and reduce the heat and mass transfer processes. For high Hartmann number, the flow is almost suppressed.

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number.

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