Effect of temperature dependent viscosity on the ferroconvection onset in a ferrofluid saturated porous medium

C. E. Nanjundappa¹ - B. Savitha²

¹ Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore -- 560 056, India
² Department of Mathematics, Rajarajeswari College of Engineering, Bangalore -- 560 074, India

Abstract
Temperature-dependent viscosity variation effect on the onset of ferroconvection in a ferrofluid horizontal layer in a Brinkman porous medium is studied in the presence of a vertical magnetic field. The variation of viscosity is expressed as an exponential function of 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 analytically by a regular perturbation technique for different types of velocity boundary conditions, namely, free-free, rigid-rigid as well as lower rigid and upper free boundaries. The effect of the viscosity parameter on the onset of ferroconvection in a porous medium is dual in nature depending on the choices of physical parameters. It is found that increasing the magnetic number \M ₁ and the Darcy number Da is to hasten the onset of ferroconvection. Moreover, the nonlinearity of fluid magnetization \M ₃ is observed to have no effect on the onset of ferroconvection in the case of fixed heat flux boundary conditions. Figs 6, Refs 15.