The present work deals with the numerical study of two-dimensional incompressible, magnetohydrodynamic Falkner-Skan flow of Carreau nanofluid over wedge, plate and stagnation of the flat plate with convective boundary condition and chemical reaction. The influence of thermophoresis and Brownian motion are taken into account. Similarity transformations are utilized to transform the governing equations into a system of non-linear ordinary differential equations and solved numerically using Runge–Kutta Fehlberg scheme. A comparison has been made with the published results which reveals a good agreement. The influence of different physical parameters on flow, temperature and nanoparticle concentration distributions have been discussed in detail. A constitutional analysis has been made for skin friction coefficient, heat and mass transfer rates. Results elucidate that the influence of magnetic parameter on velocity is high over flat plate compared with wedge and stagnation point of the flat plate. Heat transfer performance is higher on shear thinning fluid compared with shear thickening fluid. Further, an increase in Brownian motion decreases the heat transfer rate but enhances the mass transfer rate. © 2019, EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.