The tip temperature of a freely growing dendrite: the influence of various modifications to the Ivantsov solution

The space shuttle dendritic growth data for high-purity succinonitrile (SCN) are reinterpreted here in terms of the model proposed earlier by the present author. Unlike other recent growth models that have been used to rationalize the SCN growth data, all of which include two adjustable parameters, the present model includes only one unknown parameter, λt. It has been shown that λt = 1/Nu, the reciprocal of the “local” value of the heat transfer Nusselt number at the dendrite tip. Thus λt may also be interpreted as a measure of the heat flux generated by the dendritic sidebranches. Estimates for λt based on the space shuttle dendritic growth data are provided. A comparison of this model with the solutions to the heat transfer problem for simple geometric shapes, such as a slowly growing sphere (λt = 1), the Fisher solution for a cylindrical body with a hemispherical tip (λt = 1/2), and the Ivantsov paraboloid, λt = (φt/2pt), suggest that λt can be bounded between the values of 1/2 ≤ λt ≤ φt/2pt.