Study on Dendrite Shapes of Solidification in an Undercooled Melt

Dendrite needles grow from an undercooled melt and their shapes depend on the temperature distribution on the solidification front, which are specified by some parameters such as undercooling, capillary length, diffusivity, convection and kinetic effects. Neglecting the convection and kinetic effects, this study numerically computes the quasi-steady-state integral-differential equation to obtain the shape of a dendrite using solvability condition and investigates the effect of parameters changing the temperature field on the shape of a dendrite. The results reveal that the tip shape enlarges with the decreasing undercooling and increasing capillary length. On the other hand, the increase of thermal diffusivity only slightly reduces the tip radius and shape of a dendrite.