In this paper, a mathematical model is analyzed in order to study the natural convection boundary layer flow along an inverted cone. The shape of nanosize particles on entropy generation with based fluid is considered. Simultaneous effects of porous medium, magnetohydrodynamics, radiation and power law index effects are also taken into account. Hamilton-Crosser model is used for the effective thermal conductivity. The nonlinear coupled equations under the assumption of Boussinesq approximation are solved analytically. The calculations are performed for different governing parameters such as Prandtl number, Rayleigh number, power law index, porosity parameter, radiation parameter and magnetic parameter. The physical interpretations of obtained results are illustrated by graphs and tables. In addition, correlation of Nusselt number and skin friction corresponding to active parameters are also analyzed in this investigation. (C) 2014 Elsevier Ltd. All rights reserved.