Abstract
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.
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