This study is concerned with the question of what is the shape of a dendritic tip grown from an undercooled melt in the presence of external impacts? To answer this question we extend the recent theory (Alexandrov and Galenko in Philos Trans R Soc A 378:20190243, 2020) to the case of external processes influencing the crystal growth phenomenon. The tip shape function is derived and tested against experimental data and numerical simulations when forced convection and dissolved impurities play a decisive role. It is shown that the tip shape function taking external impacts into account is in good agreement with the theory, experiments and computations. Using our well tested formula for the dendrite tip shape we show that the mechanisms of heat and mass transfer in inclined fluid currents can be essentially different. Namely, heat and mass fluxes at the crystal surface can be described by Fick's or Newton's laws or even by a more general mixed-type heat and mass transfer formula.