Bénard–Marangoni ferroconvection with magnetic field dependent viscosity

The effect of magnetic field dependent viscosity on the onset of Bénard–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 (Λ) and Biot number (Bi) but opposite is the case with an increase in the value of magnetic Rayleigh number (Rm) and nonlinearity of magnetization (M3). Further, increase in Rm, M3, and decrease in Λ and Bi is to decrease the size of the convection cells.