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The effect of a sudden change in the crossing section on the microstructural evolution as well as solute and heat diffusions during solidification of the Ni-40.8%Cu alloy was investigated by implementing a non-isothermal phase-field model. Simulations with lateral constraints of different sizes were carried out to study the changes of the dendritic growth manner. Significant changes in microstructures had been observed as the interface encountered a sharply reduced crossing section; a cellular-dendrite transition could be achieved with lateral constraints, and the tip velocity significantly changed during the development of dendrite microstructures, and also, lateral constraints of different sizes had different effects on changes of the tip positions as well as tip velocities during the dendritic growing through constraints, which agreed well with experimental results.