Effect MFD Viscosity on Bénard–Marangoni Ferroconvection in a Rotating Ferrofluid Layer with Convective Surface Boundary Condition

Abstract

Abstract The combined effect of Coriolis force due to rotation and magnetic field dependent (MFD) viscosity on the onset of Benard–Marangoni convection in a horizontal layer of ferrofluid is investigated theoretically. The lower boundary is taken to be rigid–isothermal, while the upper free boundary open to the atmosphere is flat and subject to a convective surface boundary condition. The Galerkin technique is employed to extract the critical stability parameters numerically. It is shown that convection sets in as oscillatory motions provided that the Prandtl number ( ) is less than unity. A mechanism for suppressing or augmenting Benard–Marangoni ferroconvection by Coriolis force ( ), MFD viscosity parameter ( ), Biot number ( ), magnetic number ( ) and nonlinearity of fluid magnetization parameter ( ) is discussed in detail. It is found that the onset of Benard–Marangoni ferroconvection is delayed with an increase in , , but opposite is the case with an increase in , . Further, increase in and decrease in and is to decrease the size of the convection cells. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found. Keywords: Benard–Marangoni convection, ferrofluids, Coriolis force, MFD viscosity, heat transfer coefficient. Cite this Article Savitha B, C E Nanjundappa C E. Effect MFD Viscosity on Benard–Marangoni Ferroconvection in a Rotating Ferrofluid Layer with Convective Surface Boundary Condition. Recent Trends in Fluid Mechanics . 2020; 7(2): 12–32p.