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Effect of variable gravity on the onset of thermal convection in a horizontal

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.

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The Triple-Diffusive convection in Walters' (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.