Effect of dust particles on a rotating ferromagnetic fluid heated from below saturating a porous medium

This paper deals with the theoretical investigation of the effect of dust particles on a layer of a rotating ferromagnetic fluid heated from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linearized stability theory and normal mode analysis. For the case of stationary convection, dust particles and nonbuoyancy magnetization always have a destabilizing effect, whereas rotation has a stabilizing effect on the onset of instability. In the absence of rotation, a destabilizing effect of medium permeability is depicted, but in the presence of rotation, medium permeability may have a destabilizing or stabilizing effect on the onset of instability. The critical wave number and critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of the buoyancy magnetization parameter M1 and results are depicted graphically. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of dust particles and rotation. The oscillatory modes are introduced due to the presence of the dust particles and rotation, which were nonexistent in their absence. The sufficient conditions for the nonexistence of overstability are also obtained.