Stationary convection in a binary mixture of ferrofluids in a porous medium

The Brinkman model is used to study the criterion of appearance of stationary convection in a porous horizontal layer saturated by a binary mixture of ferrofluids and heated from below. The analytical expression of the Rayleigh number is determined by dimensionless numbers for the combined effects of buoyancy and magnetic force on the one hand and magnetic force alone on the other. The effect of Darcy's number, ratio of viscosities, each of the magnetic parameters and the binary parameter is illustrated on the appearance and size of the convection cells. The increasing of the number of Darcy D-a, each of the magnetic parameters M-1, M-3, psi(m) and the separation ratio psi accelerates the appearance of stationary convection. On the other hand, when the ratio of the viscosity perpendicular to or the magnetic parameter M-2 is increased, the beginning of the convection is delayed and the system is stable. We have also noticed that the size of the convection structures is contracted with each of the parameters M-1, M-2, psi, psi(m) and for low values of the parameter M-3. But by increasing the number of Darcy, the ratio of viscosities or for very high values of M-3 the size of the convection cells is enlarged. Finally, it should be noted that convection sets in with great delay when the magnetic mechanisms alone are highlighted.