Non-Newtonian nanofluid free convection flow subject to mixed thermal boundary conditions about a vertical cone

A similarity analysis for natural convection past a vertical cone in Darcy porous medium saturated with a non-Newtonian nanofluid is considered assuming that the cone is subjected to a mixed thermal boundary condition. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Moreover, numerical solutions of the boundary layer equations are obtained for several values of the nanofluid parameters (Brownian motion number N-b, thermophoresis parameter N-t, buoyancy ratio number N-r). A comparison with previously published work on a special case of the general problem was performed and the results were found to be in excellent agreement.