The Effect of a Magnetic Field Dependent Viscosity on the Thermal Convection in a Ferromagnetic Fluid in a Porous Medium

The effect of the magnetic field dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of a uniform vertical magnetic field is considered for a fluid layer in a porous medium, heated from below. For a ferromagnetic fluid layer between two free boundaries an exact solution is obtained, using a linear stability analysis. For the case of stationary convection, the medium permeability has a destabilizing effect, whereas the MFD viscosity has a stabilizing effect. In the absence of MFD viscosity, the destabilizing effect of magnetization is depicted, but in its presence the magnetization may have a destabilizing or stabilizing effect. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for sufficiently large values of the magnetic parameter M1. Graphs are plotted to depict the stability characteristics. The principle of exchange of stabilities is valid for a ferromagnetic fluid heated from below and saturating a porous medium.