Effect of Exponentially Temperature-Dependent Viscosity on the Onset of Penetrative Ferro-Thermal-Convection in a Saturated Porous Layer via Internal Heating

Abstract

The effect of viscosity depending exponentially on temperature on the onset of penetrative ferro-thermal-convection (FTC) in a saturated horizontal porous layer in the presence of vertical magnetic field is investigated. The bounding surface of the ferrofluid layer is considered to be rigid-rigid and insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also analytically by a regular perturbation technique with wave number as a perturbation parameter. The analytical and numerical results are found to be concurrence. The characteristics of stability of the system are strongly dependent on the viscosity parameter B. The effect of B on the onset of ferroconvection in a porous layer is dual in nature depending on the choices of physical parameters and a sublayer starts to form at higher values of B. Whereas, increase in magnetic number M1 and the Darcy number Da is to advance the onset of ferroconvection in a porous layer. The nonlinearity of fluid magnetization M3 is found to have no influence on the onset of ferroconvection.