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This article deals with the study of the steady axisymmetric mixed convective   boundary layer flow of a nanofluid over a vertical circular cylinder with   prescribed external flow and surface temperature. By means of similarity   transformation, the governing partial differential equations are reduced   into highly non-linear ordinary differential equations. The resulting   non-linear system has been solved analytically using an efficient technique   namely homotopy analysis method (HAM). Expressions for velocity and   temperature fields are developed in series form. In this study, three   different types of nanoparticles are considered, namely alumina (), titania   (), and copper () with water as the base fluid. For copper-water nanofluid,   graphical results are presented to describe the influence of the   nanoparticle volume fraction on the velocity and temperature fields for the   forced and mixed convection flows. Moreover, the features of the flow and   heat transfer characteristics are analyzed and discussed for foregoing   nanofluids. It is found that the skin friction coefficient and the heat   transfer rate at the surface are highest for copper-water nanofluid compared   to the alumina-water and titania-water nanofluids

Homotopy analysis method for mixed convective boundary layer flow of a nanofluid over a vertical circular cylinder