Study of Convection Under Hall Current Generation in a Rivlin-Erickson Nanofluid

Abstract

The major objective of the present study is to recognize the passion of parameters to fill the gaps between the experimental solutions and theoretical solutions of a Rivlin-Erickson nanofluid confined between two horizontal infinite free-free boundaries. The physical system is portrayed by Brownian motion and thermophoresis of nanoparticles, an external uniform transverse magnetic field, and effective Hall currents. Furthermore, constant temperatures and no flux of nanoparticles at the two boundaries have also been considered. To formulate the problem normal mode technique is employed and for mathematical analysis, Galerkin-type weighted residual method is implemented. Thus, a linear dispersion equation is obtained and the stability or instability stipulations are illustrated graphically displaying the impacts of several parameters entering the problem. It is found that in the case of stationary convection, the nanofluid Lewis number, concentration Rayleigh number, modified diffusivity ratio, and Hall current are responsible for aggravating the convection while the effect of the magnetic field is stabilizing. The conditional existence of oscillatory convection has been established. Behaviour of the stationary as well as oscillatory convection have been verified for the water alumina nanofluid. Valuable comparisons with the existing studies have been given. It has been observed that the convection in a continuous medium is more stable than it is in a porous medium. Further, in comparison to the regular Rivlin Erikson fluid, the Rivlin Erickson fluid with heavier density nanoparticles supports the convection.