Penetrative ferroconvection via internal heating in a ferrofluid anisotropic porous medium

C. E. Nanjundappa¹ - B Vijay Kumar²

¹ Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore-560 056, India
² Department of Mathematics, Don Bosco Institute of Technology, Bangalore-560 074, India

Abstract
A model for penetrative ferroconvection via internal heat generation in a ferrofluid anisotropic porous layer is investigated theoretically using a Brinkman extended-Darcy equation with fluid viscosity different from effective viscosity. The bounding surface of the ferrofluid layer is considered to be 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 with the wave number a as a perturbation parameter. It is observed that the analytical results agree well with those obtained numerically. It is found that increasing in dimensionless heat source strength N_s, magnetic number (M₁), Darcy number (Da) and in mechanical anisotropy parameter (ξ) is to hasten the onset of ferroconvection, while increase in ratio of viscosities (Λ ) and thermal anisotropy parameter (η) is to delay the onset of ferroconvection. In addition, the nonlinearity of fluid magnetization (M₃) is found to have no influence on the criterion for the ferroconvection onset. Some existing results are reproduced as particular cases from the present study. Figs 6, Refs 11.