a b s t r a c tThe effect of magnetic field dependent viscosity on the onset of Bé nard-Marangoni ferroconvection in a horizontal layer of ferrofluid is investigated theoretically. The lower boundary is taken to be rigid with fixed temperature, while the upper free boundary at which temperature-dependent surface tension effect is considered is non-deformable and subject to a general thermal condition. 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 show that the onset of ferroconvection is delayed with an increase in the magnetic field dependent viscosity parameter (L) and Biot number (Bi) but opposite is the case with an increase in the value of magnetic Rayleigh number (R m ) and nonlinearity of magnetization (M 3 ). Further, increase in R m , M 3 , and decrease in L and Bi is to decrease the size of the convection cells.

The effect of internal heat generation on the onset of Benard-Marangoni convection in a horizontal ferrofluid layer heated from below in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid and the upper free boundary is assumed to be flat and undeformable. Both the boundaries are considered to be perfectly insulated to temperature perturbations and the resulting eigenvalue problem is solved numerically using the Galerkin technique as well as analytically by regular perturbation technique with wave number as a perturbation parameter. It is observed that the analytical results agree well with those obtained numerically. It is noted that the combined effect of magnetic Rayleigh number and dimensionless internal heat source strength is to reinforce together and to hasten the onset of BenardMarangoni ferroconvection compared to their presence in isolation. In addition, the nonlinearity of fluid magnetization is found to have no influence on the criterion for the onset of ferroconvection. Some existing results are reproduced as particular cases from the present study.

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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.