The unsteady mixed convection stagnation-point flow of a nanofluid toward a vertical surface is investigated numerically. The external velocity impinges normal to the vertical surface, the surface temperature, and the surface volume fraction of nanoparticles are assumed to vary linearly with the distance from the stagnation point. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented, which depends on the Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt. The governing system of equations is first transformed into a dimensionless form, and then the resulting equations are solved numerically by using a fourth-order Runge-Kutta scheme coupled with a conventional shooting procedure. The features of the flow, heat, and mass transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The quantitative comparison of skin friction and heat transfer rates with the published results for special cases is shown.

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In this article, the magnetohydrodynamic stagnation point flow and heat transfer of an incompressible viscous nanofluid over a shrinking/stretching permeable sheet is investigated theoretically and analytically. The ambient fluid velocity, stretching/shrinking velocity of sheet and the wall temperature are assumed to vary linearly with the distance from the stagnation point. The similarity solution is used to reduce the governing system of partial differential equations to a set of highly non-linear ordinary differential equations which are then solved analytically using a very efficient technique, namely homotopy analysis method. Expressions for velocity and temperature fields are developed in series form and graphical results are presented to investigate the influence of various pertinent parameters. Here, three different types of nanoparticles, namely copper Cu, alumina Al 2 O 3 and titania TiO 2 with water as the base fluid are considered. It is observed that, for all three nanoparticles, the magnitude of the skin friction coefficient and local Nusselt number increases with the nanoparticle volume fraction È. The highest values of the skin friction coefficient and the local Nusselt number were obtained for the Cu nanoparticles compared to Al 2 O 3 and TiO 2 .