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

A layer of a ferromagnetic fluid permeated with dust particles heated and soluted from below saturating a porous medium is considered in the presence of a transverse uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For the case of stationary convection, medium permeability, dust particles and non-buoyancy magnetization have a destabilizing effect whereas stable solute gradient has a 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 buoyancy magnetic parameter M1 and results are depicted graphically. It is observed that the critical magnetic thermal Rayleigh number is reduced because of the specific heat of the dust particles. The principle of exchange of stabilities is found to hold true for a ferromagnetic fluid saturating a porous medium heated from below in the absence of dust particles and stable solute gradient. The oscillatory modes are introduced due to the presence of the dust particles and stable solute gradient, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study.