a b s t r a c tA model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N s , magnetic number M 1 Darcy number Da and the non-linearity of magnetization parameter M 3 is to hasten, while increase in the ratio of viscosities L, Biot number Bi and magnetic susceptibility w is to delay the onset of ferroconvection.Further, increase in Bi, Da À 1 and N s and decrease in L, M 1 and M 3 is to diminish the dimension of convection cells.
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.
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