Onset of Thermogravitational Convection in a Ferrofluid Layer With Temperature Dependent Viscosity

The onset of thermogravitational convection in a horizontal ferrofluid layer is investigated with viscosity depending exponentially on temperature. The bounding surfaces of the ferrofluid layer are considered to be either stress free or rigid-ferromagnetic and insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also by a regular perturbation technique for different types of velocity boundary conditions, namely free-free, rigid-rigid, and lower rigid- upper free. It is observed that increasing the viscosity parameter, $Λ$⁠, and the magnetic number, $M1$⁠, is to hasten the onset of ferroconvection, while the nonlinearity of fluid magnetization, $M3$⁠, is found to have no influence on the stability of the system. The critical stability parameters are found to be the same in the limiting cases of either no magnetic forces or no buoyancy forces.