A numerical model for the calculation of the growth velocity of nonisothermal parabolic dendrites

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Abstract
For a circular paraboloid of revolution growing in a shape preserving manner neither the surface curvature, nor the local interface velocity are constant on the freezing front. Yet within the widely quoted model [J. Lipton, W. Kurz and R. Trivedi, Acta Metall. 35, 957 (1987)] for the calculation of dendritic growth velocities the kinetic and GibbsThomson undercoolings evaluated at the dendrite tip are assumed to apply equally over the whole dendrite surface, approximating the non-isothermal dendrite as an isothermal dendrite with a reduced surface melting temperature. Reasons are discussed why this approach may seriously overestimate the growth velocity at high undercooling, where kinetic effects are important. Using a finite difference model the full, non-isothermal growth problem is solved for the solidification of pure Ni. The model shows that an undercooling of 175 K neglecting non-isothermal effects leads to a 35% error in the calculated growth velocity. Comparison with the available experimental data suggest an adequate fit to the data for Ni can be made without the need for adjustable parameters.