This paper analyzes the combined effects of buoyancy force, convective heating, Brownian motion, thermophoresis and magnetic field on stagnation point flow and heat transfer due to nanofluid flow towards a stretching sheet. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for dimensionless velocity, temperature, nanoparticle volume fraction, as well as the skin friction, local Nusselt and Sherwood numbers. The results indicate that dual solutions exist for shrinking case. The effects of various controlling parameters on these quantities are investigated. It is found that both the skin friction coefficient and the local Sherwood number decrease while the local Nusselt number increases with increasing intensity of buoyancy force.