Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

Abstract

A model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman–Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid- paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength Ns, magnetic number M1 Darcy number Da and the non-linearity of magnetization parameter M3 is to hasten, while increase in the ratio of viscosities Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of ferroconvection. Further, increase in Bi, Da−1 and Ns and decrease in Λ, M1 and M3 is to diminish the dimension of convection cells.