Modification of Ohnaka back diffusion equation

Abstract

The first and simplest analytical model for a binary alloy came from Gulliver-Scheil, considering a constant partition coefficient at the interface during solidification without back diffusion in solid. Later, Brody-Flemings proposed an approximate analytical model, taking into account one dimensional diffusion of solute in solid during solidification in plate-like dendrite arms for parabolic growth. However, this model does not work well at high back diffusion values. Ohnaka modified this back diffusion parameter. The Ohnaka model works well at the low and high back diffusion values but it underestimates between them. In this paper, Voller-Ohnaka back diffusion model is modified further to predict concentration profiles more accurately than all others analytical models for the parabolic growth rate.