Stability of a double diffusive convection in a Darcy porous layer saturated with Maxwell nanofluid under macroscopic filtration law: A realistic approach

Double diffusive convection in a Darcy Maxwell Buongiorno's nanofluid confined between two parallel plates incorporating thermophoretic and Brownian diffusion has been examined. Two important aspects of the study are: the macroscopic filtration law for Darcy Maxwell fluid and zero nanoparticle flux at the boundaries. Under normal mode analysis of linear stability theory, Galerkin-type weighted residual technique is employed and the stationary and oscillatory convections are analyzed. It is found that Horton-Rogers' Rayleigh number is reduced due to the two peers of the flow-nanoparticles and salt; stationary convection is governed indirectly by the Brownian motion and thermophoresis through the coupling between buoyancy and conservation of nanoparticles and the solutal diffusivity inhibits the convection. Further it is found that the mode of convection is changed in the presence of salt as the oscillatory convection is suppressed by stationary convection throughout the flow domain. Under non-linear stability analysis the Nusselt numbers corresponding to heat, salt and mass are derived for steady as well as unsteady state. The effect of different parameters is found on the rate of transfer of heat, salt and mass and the mode of isotherms, isonanoconcentrations and isohalines is established in the two states.