Penetrative Bénard-Marangoni Convection in a Micropolar Ferrofluid Layer via Internal Heating and Submitted to a Robin Thermal Boundary Conditions

Abstract

Penetrative Benard-Maranagoni convection in micropolar ferromagnetic fluid layer in the presence of a uniform vertical magnetic field has been investigated via internal heating model. The lower boundary is considered to be rigid at constant temperature, while the upper boundary free open to the atmosphere is flat and subject to a convective surface boundary condition. The resulting eigenvalue problem is solved numerically by Galerkin method. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, magnetic parameter M1, the non-linearity of magnetization parameter M3, coupling parameter N1, spin diffusion parameter N3 and micropolar heat conduction parameter N5. The results show that the onset of ferroconvection is delayed with an increase in N1 and N5 but hastens the onset of ferroconvection with an increase in M1, M3, N3 and Ns. The dimension of ferroconvection cells increases when there is an increase in M3, N1, N5 and Ns and decrease in M1 and N3.