Effect of Magnetic Field Dependent Viscosity on Darcy-Brinkman Ferroconvection with Second Sound

Abstract

The problem of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law and MFD viscosity is investigated by the method of small perturbation. The fluid motion is described using the Brinkman model. It is assumed that the fluid and solid matrices are in local thermal equilibrium. For simplified boundary conditions, the eigenvalue problem is solved exactly, and closed form solutions for stationary instability are obtained. Magnetic forces and second sound were found to enhance the beginning of Brinkman ferroconvection. However, ferroconvection is hampered when the porous parameters are increased. The results show that MFD viscosity inhibits the beginning of Darcy-Brinkman ferroconvection and that MFD viscosity stabilizing effect is decreased when the magnetic Rayleigh number is significant. Furthermore, it is demonstrated that oscillatory instability arises before stationary instability, assuming that the Prandtl and Cattaneo numbers are sufficiently large.

Keywords

• ferrofluid
• mfd viscosity
• porous media
• magnetic field
• second sound