Natural convection heat and mass transfer from a sphere in non-Newtonian nanofluids

Abstract

A boundary layer analysis has been presented for the natural convection flow of a non-Newtonian nanofluid past a sphere. Solutions of the set of nonsimilarity equations are obtained by employing the implicit finite difference method together with Keller box elimination method. Numerical results for friction factor, surface heat transfer rate and mass transfer rate have been presented for parametric variations of the material parameters, buoyancy ratio parameter ${\lambda }_T$ , Brownian motion parameter N_B, thermophoresis parameter N_T and Schmidt number Sc. The dependency of the surface heat transfer rate (Nusselt number) and mass transfer rate on these parameters has been discussed. It was found that the heat transfer rate decreases and mass transfer rates increase as Schmidt number increases. The friction factor and heat transfer rates decrease as the cross viscosity parameter $R$ increases. The heat transfer rates increase and mass transfer rates decrease as the buoyancy ratio parameter N increases. As the thermophoresis parameter N_T increases, the heat and mass transfer rates increase. As the Brownian parameter N_B increases, the heat and mass transfer rates decrease. Brownian motion decelerates the flow in the nanofluid boundary layer. Brownian diffusion promotes heat conduction. The Brownian motion and thermophoresis of nanoparticles increase the effective thermal conductivity of the nanofluid. Both Brownian diffusion and thermophoresis give rise to cross diffusion terms that are similar to the familiar Soret and Dufour cross diffusion terms that arise with a binary fluid.