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The boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective boundary condition is studied. Numerical solutions to the governing equations are obtained using a shooting method. The results are found for the local Nusselt number and the local Sherwood number as well as the temperature and concentration profiles for some values of the convective parameter, stretching/shrinking parameter, Brownian motion parameter, and thermophoresis parameter. The results indicate that the local Nusselt number is consistently higher for higher values of the convective parameter. However, the local Nusselt number decreases with increasing values of the Brownian motion parameter as well as the thermophoresis parameter. In addition, the local Sherwood number increases with increasing Brownian motion parameter and decreases with increasing convective parameter and thermophoresis parameter.