Dual solutions for stagnation-point flow and convective heat transfer of a Williamson nanofluid past a stretching/shrinking sheet

In this paper, the problem of boundary layer stagnation-point flow and heat transfer of a Williamson nanofluid on a linear stretching/shrinking sheet with convective boundary condition is studied. The effects of Brownian motion and thermophoresis are considered in the energy equation. The governing partial differential equations are first transformed into set of ordinary differential equations, which are then solved numerically using Runge-Kutta-Felhberg fourth-fifth order method with Shooting technique. The characteristics of the flow and heat transfer as well as skin friction and Nusselt number for various prevailing parameters are presented graphically and discussed in detail. A comparison with the earlier reported results has been done and an excellent agreement is shown. It is found that dual solutions exist for the shrinking sheet case. Further, it is observed that the thermal boundary layer thickness increases with increase in Williamson parameter for both solutions.