The onset of Brinkman ferroconvection in an anisotropic porous medium

Abstract

Onset of ferroconvection in an anisotropic porous layer heated from below is investigated theoretically using modified Brinkman extended-Darcy equation with fluid viscosity different from effective viscosity. The isothermal bounding surfaces of a porous layer are considered to be either free or rigid-paramagnetic/ferromagnetic. The eigenvalue problem is solved exactly for free boundaries, while for realistic rigid-paramagnetic or rigid-ferromagnetic boundaries the critical stability parameters are obtained numerically using the Galerkin method. It is seen that the stability of the system depends on the nature of boundaries and rigid-paramagnetic boundaries are found to be preferred to the ferromagnetic ones as well as free boundaries in controlling ferroconvection in an anisotropic porous layer. It is observed that increase in the value of thermal anisotropy parameter and viscosity ratio is to delay the onset of ferroconvection, while increase in the value of mechanical anisotropy parameter and magnetic number is to hasten the onset of ferroconvection. Moreover, increasing the value of thermal anisotropy parameter and decreasing the value of mechanical anisotropy parameter is to narrow the convection cells.