Ferroconvection in a porous medium with vertical throughflow

The problem of thermal convection in a horizontal layer of ferrofluid-saturated porous medium is investigated theoretically in the presence of a uniform vertical magnetic field and throughflow. The flow in the porous medium is described by the modified Brinkman equation with fluid viscosity different from effective viscosity. The rigid, however permeable ferromagnetic boundaries are considered to be insulated to temperature perturbations. The resulting eigenvalue problem is solved both numerically using the Galerkin technique and analytically using regular perturbation technique with wave number a as a perturbation parameter and observed that the results complement with each other. The direction of throughflow has no influence on the stability characteristics of the system, and the effect of throughflow-dependent Peclet number Q is to delay the onset of ferroconvection. The Prandtl number Pr(>1) has insignificant while the nonlinearity of fluid magnetization parameter M₃ has no influence on the onset of ferroconvection. Besides, an increase in the value of the Darcy number Da and the magnetic number M₁ is to hasten, while an increase in the ratio of viscosity parameter λ is to delay the onset of ferroconvection.