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The thermosolutal instability problem in a horizontal layer of an elasticoviscous nanofluid in porous medium is considered. Walters' (model B') fluid model is employed to describe the rheological behavior of the nanofluid and for the porous medium, the Darcy model is employed. From the linear stability analysis based upon normal modes analysis method, the dispersion relation accounting for the effect of various parameters is derived. The onset criterion for stationary convection is analytically derived and it is observed that the Walters' (model B') elastico-viscous nanofluid fluid behaves like an ordinary Newtonian nanofluid. The effects of solutal Rayleigh Number, thermo-nanofluid Lewis number, thermosolutal Lewis number, Soret and Dufour parameter on the stability of stationary convection are investigated.

In this paper, the thermosolutal convection in compressible Walters' (model B′) elastico-viscous fluid permeated with suspended particles in a porous medium is considered. For the porous medium, the Brinkman model is employed. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the medium permeability, suspended particles, gravity field and viscoelasticity introduce oscillatory modes. For stationary convection, it is observed that the Darcy number and stable solute gradient have stabilizing effects whereas the suspended particles and medium permeability has destabilizing effects on the system. The effects of Darcy number, stable solute gradient, suspended particles and medium permeability has also been shown graphically.

In this paper, we investigate the effect of a vertical magnetic field on thermal instability of an Oldroydian visco-elastic rotating fluid in a porous medium. By applying the normal mode analysis method, the dispersion relation governing the effects of rotation, magnetic field and medium permeability is derived and solved analytically and numerically. For the case of stationary convection, the Oldroydian viscoelastic fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has a stabilizing effect while the magnetic field and medium permeability have a stabilizing/destabilizing effect under certain conditions on thermal instability of the Oldroydian viscoelastic fluid in a porous medium. The oscillatory modes are introduced due to the presence of rotation, the magnetic field and gravity field. It is also observed that the 'principle of exchange of stability' is invalid in the presence of rotation and the magnetic field.

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