Effect of Boundary Conditions on the Onset of Thermomagnetic Convection in a Ferrofluid Saturated Porous Medium

Abstract

The onset of thermomagnetic convection in a ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated for a variety of velocity and temperature boundary conditions. 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-ferromagnetic, while the upper boundary is considered to be either rigid-ferromagnetic or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective-radiative exchange at the upper boundary, which encompasses fixed temperature and heat flux as particular cases. The resulting eigenvalue problem is solved using the Galerkin technique and also by using regular perturbation technique when both boundaries are insulated to temperature perturbations. It is found that the increase in the Biot number and the viscosity ratio, and the decrease in the magnetic as well as in the Darcy number is to delay the onset of ferroconvection. Besides, the nonlinearity of fluid magnetization has no effect on the onset of convection in the case of fixed heat flux boundary conditions.