Brinkman-Benard-Marangoni convection in a magnetized ferrofluid saturated porous layer

A classical linear stability theory is used to study the onset of Brinkman-Benard-Marangoni (BBM) convection in an initially quiescent magnetized ferrofluid saturated horizontal layer of a very coarse porous medium in the presence of a uniform vertical magnetic field. The lower rigid boundary is subject to a fixed heat flux, while the upper boundary is free and open to the ambient air on which a general thermal condition which encompasses fixed temperature and fixed heat flux as particular cases is invoked. The resulting eigenvalue problem is solved using the Galerkin technique and also by a regular perturbation technique when both boundaries are insulated to temperature perturbations. The differences as well as similarities with the corresponding problem in ordinary viscous fluids and also the influence of different forces when they are acting in isolation are particularly highlighted. It is found that increase in the Biot number, porous parameter and decrease in the magnetic number as well as nonlinearity of fluid magnetization has a stabilizing effect on the onset of BBM ferroconvection. Moreover, the nonlinearity of fluid magnetization is observed to have no consequence on the onset of convection in the case of fixed heat flux boundary conditions. The present study reproduces already established results in the literature as particular cases.