Effect of Cubic Temperature Profiles on Ferro Convection in a Brinkman Porous Medium

The effect of cubic temperature profiles on the onset ferroconvection in a Brinkman porous medium in presence of a uniform vertical magnetic field is studied. The lower and upper boundaries are taken to be rigidisothermal and ferromagnetic. The Rayleigh-Ritz method with Chebyshev polynomials of the second kind as trial functions is employed to extract the critical stability parameters numerically. The results indicate that the stability of ferroconvection is significantly affected by cubic temperature profiles and the mechanism for suppressing or augmenting the same is discussed in detail. It is observed that the effect of Darcy number Da,magnetic number 1 M and nonlinearity of the fluid magnetization parameter 3 M is to hasten, while an increase in the ratio of viscosity parameter λ and Biot number Bi is to delay the onset of ferroconvection in a Brinkman porous medium. Further, increase in Bi, M1, M3 and decrease inλ, Da is to decrease the size of the convection cells.