Similarity and analytical solutions of free convective flow of dilatant nanofluid in a Darcian porous medium with multiple convective boundary conditions

This paper deals with an analytical solution of free convective flow of dilatant nanofluid past a vertical cone/plate. A two-phase mixture model is used for nanofluid in which the Brownian motion and thermophoretic diffusivities are the important slip mechanisms between solid and liquid phases. The governing transport equations along with physically realistic thermal and mass convective boundary conditions are reduced to similarity equations using relevant similarity transformations before being solved by homotopy analysis method. The effects of the governing parameters (Brownian motion, thermophoresis, convection-conduction, convection-diffusion, Lewis number, buoyancy ratio, and power-law) on the dimensionless velocity, temperature and nanoparticle volume fraction, friction and heat transfer rates are plotted and discussed. It is found that friction factor decreases with the increase in Le and Nr for both vertical plate and cone. The local Nusselt number decreases with the increase in the thermophoresis and Brownian motion parameters for both the plate and cone. The local Sherwood number increases with the Brownian motion parameter and decreases for thermophoresis parameter. The results have been compared with the published ones and an excellent agreement has been noticed.