The Onset of Ferromagnetic Convection in a Micropolar Ferromagnetic Fluid Layer Heated from Below

C. E. Nanjundappa, I. S. Shivakumara, K. Srikumar

Department of Mathematics, Ambedkar Institute of Technology, Bangalore, India;.
Department of Mathematics, East Point College of Engineering for Women, Bangalore, India..
UGC-CAS in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore, India.

DOI: 10.4236/jemaa.2013.53020                

Abstract

The onset of ferromagnetic convection in a micropolar ferromagnetic fluid layer heated from below in the presence of a uniform applied vertical magnetic field has been investigated. The rigid-isothermal boundaries of the fluid layer are considered to be either paramagnetic or ferromagnetic and the eigenvalue problem is solved numerically using the Galerkin method. It is noted that the paramagnetic boundaries with large magnetic susceptibility χ delays the onset of ferromagnetic convection the most when compared to very low magnetic susceptibility as well as ferromagnetic boundaries. Increase in the value of magnetic parameter M₁ and spin diffusion (couple stress) parameter N₃ is to hasten, while increase in the value of coupling parameter N₁ and micropolar heat conduction parameter N₅ is to delay the onset of ferromagnetic convection. Further, increase in the value of M₁, N₁, N₅ and χ as well as decrease in N₃ is to diminish the size of convection cells.

Keywords

Micropolar Ferrofluid; Ferromagnetic Convection; Paramagnetic Boundaries; Rigid Boundaries; Magnetic Susceptibility

Conflicts of Interest

The authors declare no conflicts of interest.

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