Penetrative Brinkman ferroconvection via internal heating in high porosity anisotropic porous layer: influence of boundaries

Abstract The penetrative ferrothermal convection (FTC) in a ferrofluid (FF) saturated high porosity anisotropic porous layer via uniform internal heating is investigated. The Brinkman-extended Darcy equation is applied to describe the flow in the porous medium. The permeability in the vertical direction is taken to be twice that of the permeability in the horizontal direction while the ratio of horizontal to vertical effective thermal diffusivity is allowed to vary. The Galerkin method is applied to solve numerically the stability eigenvalue problem for different boundary combinations namely, (i) rigid-paramagnetic (R–P) with large and low magnetic susceptibility, (ii) rigid-ferromagnetic (R–F), and (iii) free-ferromagnetic (F–F). The R–P boundaries with large magnetic susceptibility offer most, while F–F boundaries offer least stabilizing effect against FTC. Besides, the effect of increasing the magnetic number, non-linearity of fluid magnetization parameter, Darcy number and internal heat source strength is to speed up FTC, while the thermal anisotropy and magnetic susceptibility parameter indict a contradictory effect on FTC.