Ferromagnetic Convection in a Heterogeneous Porous Medium

Abstract

The effect of vertical heterogeneity of permeability on the onset convection in a horizontal layer of magnetized ferrofluid-saturated Darcy porous medium is investigated. Four different forms of vertical heterogeneity permeability function \({\Gamma (z)}\) are considered for discussion. The eigenvalue problem is solved numerically using the Galerkin method for three types of temperature boundary conditions namely, (i) isothermal, (ii) insulated to temperature perturbations, and (iii) lower insulated to temperature perturbations and upper isothermal. The general quadratic variation in the vertical heterogeneity of permeability is to hasten the onset of ferromagnetic convection compared with other forms of \({\Gamma(z)}\). The measure of nonlinearity of magnetization and the magnetic susceptibility is found to influence the onset if the boundaries are either isothermal or lower insulated and upper isothermal. Increasing the magnetic number is to augment the onset of ferromagnetic convection. The system is more stabilizing when the boundaries are isothermal and least stable for insulated ones. Compared to the homogeneous porous medium case, the critical wave number is higher if the permeability of the porous medium is heterogeneous and the boundaries are isothermal.