Effect of vertical heterogeneity on the onset of ferroconvection in a Brinkman porous medium

Abstract

The onset of ferroconvection in a Brinkman porous medium is studied for different forms of vertical heterogeneity permeability function Γ(z). The eigenvalue problem is solved numerically using the Galerkin method for isothermal/insulated rigid-ferromagnetic boundary conditions. It is observed that the onset of ferromagnetic convection can be either hastened or delayed depending on the type of heterogeneity of the porous medium as well as thermal boundary conditions. The effect of increasing magnetic number is to hasten the onset of ferroconvection for all choices of Γ(z). Although the measure of nonlinearity of magnetization is to hasten the onset of ferroconvection in the case of isothermal boundaries, it shows no influence on the onset criterion when the boundaries are insulated. Further, the deviation in critical Darcy–Rayleigh number between different forms of Γ(z) is found to be not so significant with an increase in the Darcy number.