Linear stability analysis for ferromagnetic fluids in the presence of magnetic field, compressibility, internal heat source and rotation through a porous medium

The effects of magnetic field and heat source strength on thermal convection of a compressible rotating ferromagnetic fluid through a porous medium are investigated theoretically using linear stability theory. A normal mode analysis method is employed to find solutions for the fluid layer confined between parallel planes with free boundaries. The cases of stationary and oscillatory instabilities are discussed. For the stationary state, compressibility, medium porosity and temperature gradient due to heat source have destabilizing effects, whereas rotation and ratio of magnetic permeability delay the onset of convection. The magnetic field and medium permeability have both stabilizing and destabilizing effects under certain conditions. The variations in the stationary critical thermal Rayleigh number and neutral instability curves in (Ra1,x)-plane for various values of physical parameters are shown graphically to depict the stability characteristics. The sufficient conditions for the non-existence of overstability are obtained and the principle of exchange of stabilities holds true in the absence of magnetic field and rotation under certain conditions.