A numerical study of the effect of an external mean flow on dendritic growth has been performed. All simulations are 2D phase-field computations using an adaptive finite element method. The dendritic growth starts from a small nucleus that is attached to a solid insulated wall. A flow of melt past the wall is maintained by prescribing a shear stress far from the wall. The orientation of the preferred growth directions of the nucleus is varied. In the simulations, a non-dimensional undercooling of 0.1 is used. The Prandtl number of the melt is taken to be 23, which corresponds approximately to that of SCN. Different initial orientations of the preferred growth directions of the nucleus gives different vertical growth velocities. The results depend also on the flow strength (the flow Peclet number) and the degree of anisotropy. The maximal vertical growth velocity tends to be achieved for crystals with a preferred growth direction that is moderately inclined in the upstream direction.