The Onset of Brinkman-Benard Ferroconvection in a Saturated Porous Layer With Internal Heat Generation

Abstract

The effect of internal heat generation on the criterion for the onset of thermomagnetic convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman-Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid – insulating and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The effect of increase in the value of dimensionless internal heat source strength Ns, magnetic number M1 and the non-linearity of fluid magnetization parameter M3 is to hasten, while increase in the value of inverse of Darcy number Da−1, viscosity ratio Λ, Biot number Bi and magnetic susceptibility χ is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da−1 and Ns as well as decrease in Λ M1> and M3 is to diminish the dimension of convection cells.