Effect of temperature dependent viscosity on the onset of Bénard–Marangoni ferroconvection

Abstract

The onset of coupled Bénard–Marangoni convection in a horizontal layer of ferrofluid with viscosity depending exponentially on temperature is investigated. The lower rigid and the upper free boundaries are assumed to be insulated to temperature perturbations and the free boundary at which the surface tension effects are accounted for is assumed to be non-deformable. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also analytically by a regular perturbation technique with a wave number as a perturbation parameter. The analytical and numerically computed results are found to be in concurrence. The combined effect of magnetic number M1 and the viscosity parameter B is to reinforce together and to hasten the onset of Bénard–Marangoni ferroconvection compared to their presence in isolation. Nonetheless, the effect of increasing B also shows initially some stabilizing effect on the system depending on the strength of magnetic and buoyancy forces. In addition, the nonlinearity of fluid magnetization M3 is found to have no influence on the criterion for the onset of Bénard–Marangoni ferroconvection.