Non-similar solution of free convective flow of power law nanofluids in porous medium along a vertical cone and plate with thermal and mass convective boundary conditions

Abstract

This paper investigates non-similar solution of free convective boundary layer flow of a viscous incompressible fluid along a vertical cone and plate embedded in a Darcian porous medium filled with power law non-Newtonian nanofluids. The effects of the thermal and mass convective boundary conditions are taken into account, which makes the present analysis practically applicable. The governing boundary layer equations are converted into a system of non-similar differential equations by using suitable transformations before being solved numerically. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, and the local Nusselt and Sherwood numbers are reported. It is found that the velocity, temperature, and concentration increase with mass transfer velocity for both the vertical plate and cone. Further, the velocity reduces whilst the temperature and concentration increase with increasing buoyancy ratio parameter for all three types of nanofluids in the case of both geometries. The local Nusselt and the local Sherwood numbers are found to be higher for dilatant nanofluids than pseudoplastic nanofluids and Newtonian fluids in each case. The numerical results for special cases are compared with the published data and an excellent agreement has been found.