Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore -560 056, India
UGC-Centre for Advanced Studies in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore – 560 001, India
Department of Mathematics, Sai Vidya Institute of Technology, Bangalore- 560 064, India
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 rigid-isothermal 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 magnetic number and nonlinearity of the fluid magnetization parameter is to hasten, while an increase in the ratio of viscosity parameter and Biot number is to delay the onset of ferroconvection in a Brinkman porous medium. Further, increase in and decrease in is to decrease the size of the convection cells.