Onset of Bénard-Marangoni ferroconvection with a convective surface boundary condition: The effects of cubic temperature profile and MFD viscosity

The combined effects of basic cubic temperature profiles and magnetic field dependent (MFD) viscosity on the onset of Bénard-Marangoni convection in a ferrofluid layer are studied. The lower boundary is rigid-isothermal, while the upper free boundary open to the atmosphere is flat and subject to a general thermal boundary condition. The Galerkin technique is employed to extract the critical stability parameters numerically. The results indicate that the basic cubic temperature profiles have a profound influence on the stability characteristics of the system and can be effectively used to either suppress or augment the onset of Bénard-Marangoni ferroconvection. Besides, increasing the magnetic Rayleigh number and the nonlinearity of magnetization hastens, while an increase in the Biot number and MFD viscosity parameter delays the onset of Bénard-Marangoni ferroconvection. The existing results in the literature are obtained as particular cases from the present study.