Effect of temperature-dependent viscosity on the onset of Bénard–Marangoni ferroconvection in a ferrofluid saturated porous layer

The criterion for the onset of Benard–Marangoni ferroconvection in an initially quiescent magnetized ferrofluid saturated horizontal Brinkman porous layer is investigated in the presence of a uniform vertical magnetic field. The viscosity is considered to be varying exponentially with temperature. The lower rigid boundary and the upper free boundary at which the surface tension effects are accounted for are assumed to be perfectly insulated to temperature perturbations. The eigenvalue problem is solved numerically using the Galerkin technique and analytically by regular perturbation technique with wave number a as a perturbation parameter. It is observed that the analytical and numerical results are very well comparable. The characteristics of stability of the system are strongly dependent on the viscosity parameter B. The effect of B on the onset of Benard–Marangoni ferroconvection in a porous layer is dual in nature depending on the choices of the physical parameters, and a sublayer starts to form at higher values of B. The nonlinearity of fluid magnetization M3 is found to have no influence on the onset of ferroconvection, whereas an increase in the value of the magnetic number M1 and the Darcy number Da is to advance the onset of Benard–Marangoni ferroconvection in a porous layer.