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The thermosolutal convection in Walters’ (Model B') elastico-viscous rotating fluid permeated with suspended particles (fine dust) and variable gravity field in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved numerically. It is observed that the rotation, magnetic field, gravity field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B') elastico-viscous fluid behave like an ordinary Newtonian fluid and it is observed that rotation and stable solute gradient has stabilizing effects and suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions. The effect of rotation, suspended particles, magnetic field, stable solute gradient and medium permeability has also been shown graphically. AMS subject classifications are 76A10, 76E07, 76E25 and 76S05.

The thermosolutal convection in a couple-stress fluid layer heated and soluted from below in porous medium is considered to include the effects of uniform vertical magnetic field and uniform vertical rotation. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, the stable solute gradient and rotation have stabilizing effects on the system. In the presence of rotation, the medium permeability has a destabilizing (or stabilizing) effect whereas magnetic field and couple-stress parameter have stabilizing (or destabilizing) effect on the system. On the other hand, in the absence of rotation, medium permeability has a destabilizing effect whereas magnetic field and couple-stress parameter have a stabilizing effect. The dispersion relation is also analyzed numerically. The stable solute gradient, rotation and magnetic field introduce oscillatory modes in the system, which were nonexistent in their absence. A condition for the system to be stable is obtained by using Rayleigh-Ritz inequality