Penetrative ferroconvection in a porous layer

Penetrative convection in a horizontal ferrofluid-saturated porous layer in the presence of a uniform applied vertical magnetic field has been investigated via the internal heating model using the Brinkman-extended Darcy equation. The rigid-isothermal boundaries of the porous layer are considered to be either paramagnetic or ferromagnetic. The eigenvalue problem is solved numerically using the Galerkin method with either thermal or magnetic Rayleigh number as the eigenvalue. The stability of the system is significantly affected by the internal heating in the porous layer. It is noted that the paramagnetic boundaries with large magnetic susceptibility delay the onset of penetrative ferroconvection the most when compared to very low magnetic susceptibility as well as ferromagnetic boundaries. An increase in the value of magnetic Rayleigh number (R _m ), heat source strength (N _S ) and non-linearity of magnetization (M ₃) is to hasten the onset of ferroconvection. In addition, the stability of the system when heated from above and also in the absence of thermal buoyancy has been discussed in detail.