Display omitted •Oblique flows alleviate the inhibited downstream growth at low undercoolings.•The melt flow inhibits upstream primary branches of columnar dendrites.•Secondary arms are firstly more developed at left sides of primary branches.•Flows do more significant effects under lower undercooling or cooling conditions. A cellular automaton (CA) model coupled with momentum, mass and heat transport models was developed to investigate equiaxed and columnar dendritic growth of Fe–0.82wt%C alloy under four elaborately designed forced flows. During the iterative solution, the evolution of solidification interface and the solute diffusion in solid phase were explicitly tracked and solved, while other transport equations were implicitly solved in staggered grids with the block-corrected TDMA approach. The self-developed codes show a good performance in predicting dendritic growth and melt flow and temperature fields according to the comparisons with LGK analytical model and commercial software. The growth behavior of dendrites under melt flow is determined by the competition between bringing in solute enriched melt from upstream side and carrying away solute rejected at interfaces. The growth of equiaxed dendrites is promoted at the upstream side and inhibited at the downstream side, which becomes more significant with the increase of inlet velocity and the decrease of melt undercooling. Meanwhile, the oblique flow plays an important role in the growth of arms at the downstream side and alleviates the inhibited growth at the lower melt undercooling. Columnar dendrites are under inhibited growth in sequence along the flow direction, except that those near the outlet are promoted under weaker melt flow. Secondary dendrite arms firstly well formed at left sides of columnar dendrites become fatter and better developed compared with those without flow, although those near the upstream side are difficult to be developed. Under the circular flow condition, columnar dendrites at the bottom wall of the modeling domain firstly grow faster than those symmetrically in the right wall, and then become slower as the solidification proceeds under stronger melt flow. Moreover, the effect of melt flow on dendritic growth becomes more significant under the lower melt undercooling condition for equiaxed dendrites and the weaker cooling condition for columnar dendrites. In addition, compared with the effect on the temperature distribution, the effect of the melt flow on the solute distribution around columnar dendrites governs their growth.