Thermal Convection of Rivlin-Ericksen Fluid Governed by the Brownian Motion and Thermophoresis of Nanoparticles with Passive Behaviour of Nanoparticles at the Parallel Boundaries

Stability of Rivlin-Ericksen category of nanofluid saturated in a continuous medium bounded by infinite horizontal plates has been studied. Energy equation has been supplemented with the variables belonging to the Brownian motion and thermophoresis of nanoparticles. For the linear and the non-linear stability analyses, other than the specific boundary conditions appraised with the physical situation, the boundary conditions for the flux of nanoparticle mass, in analogy with the passive behaviour of temperature at the boundaries have been explored. The novelty of the paper is that the stationary convection exists for both positive as well as negative Rn (concentration Rayleigh number) and the convection sets in earlier in comparison to a porous medium. It is also shown that the non-existence of the oscillatory convection in a Newtonian nanofluid has been ruled out for Rivlin-Ericksen nanofluid, though it exists only for negative Rn, the situation when the density of the fluid is greater than the density of nanoparticle. The viscoelastic parameter of Rivlin-Ericksen nanofluid annihilates the instability of oscillatory convection. Under non-linear stability analysis, the truncated representation of Fourier series approach has been used and the parameters belonging to the heat and mass transfer have been evaluated. It is shown that corresponding to certain parameters, the rate of heat and mass transfer rises rapidly. The valuable results are shown graphically and verified numerically.