MAGNETO-ROTATIONAL CONVECTION FOR FERROMAGNETIC FLUIDS IN THE PRESENCE OF COMPRESSIBILITY AND HEAT SOURCE THROUGH A POROUS MEDIUM

摘要

The effects of various physical parameters such as rotation, magnetic field, and heat source on thermal convection of a compressible ferromagnetic fluid are investigated theoretically through a porous medium using the linear stability theory. The normal mode method is employed for the case of free boundaries. In the case of stationary convection, compressibility and medium porosity have destabilizing effects, whereas rotation and the ratio of magnetic permeabilities delay the onset of convection. The magnetic field and medium permeability have both stabilizing and destabilizing effects under certain conditions, whereas in the absence of rotation the stabilizing effects of the magnetic field and medium permeability are obvious. It is also found that the effect of the temperature gradient due to the heating underside is to accelerate the onset of convection across the layer except at the lower boundary. The critical wave number and critical thermal Rayleigh number for the onset of instability are also determined numerically by providing various values to physical parameters, and the results are also shown graphically to depict the stability region. The sufficient conditions for the non-existence of overstability are also obtained. The validity of the principle of exchange of stabilities holds true in the absence of the magnetic field and rotation under certain conditions.