Brinkman ferromagnetic convection in a porous layer: Effect of MFD viscosity and magnetic boundaries

In the present study, the effect of magnetic field dependent (MFD) viscosity and different types of magnetic boundaries on the onset of ferromagnetic convection in a horizontal layer of Brinkman porous medium is investigated numerically using the Galerkin method. The simultaneous and isolation presence of buoyancy and magnetic forces on the stability characteristics of the system are emphasized. The study reveals that the linear stability of the system depends significantly on the types of magnetic boundaries. The rigid-paramagnetic boundaries are found to be preferred to the ferromagnetic ones in suppressing ferromagnetic convection. Besides, the system is more stable when the magnetic forces alone are present. In addition, increasing MFD viscosity parameter λ and decreasing magnetic number M₁ and nonlinearity of fluid magnetization parameter M₃ is to inhibit the onset of ferromagnetic convection in a porous medium. The critical wave number is found to be independent of λ, but increasing M₁ and χ as well as decreasing M₃ is to reduce the size of convection cells. At higher values of M₃, the critical Rayleigh number and the corresponding wave number coincide for different magnetic boundaries.