Through considering both the relaxation effect of local nonequilibrium solute diffusion in bulk liquid and the effect of nonisothermal and nonisosolutal nature of the solid-liquid interface, a further improved version of free dendritic growth model was proposed, for binary alloys. Comparative analysis indicates that the effect of the nonisothermal nature of the interface is significant and this effect should be taken into account in modeling the free dendritic growth. It is also concluded that the effect of the nonisosolutal nature of interface is very slight and really negligible. Thus, the simplified version of free dendritic growth model taking into account the nonisothermal nature of the interface and with an isosolutal interface assumption is reasonable. Furthermore, experimental comparison demonstrates that it is necessary to introduce the diffusion relaxation effect for achieving a good agreement between the model predictions with the available experiment data, especially at high undercoolings, for the Cu70Ni30, alloy. (C) 2019 Elsevier Ltd. All rights reserved.