A semi-analytical model of microsegregation in a binary alloy

At small Fourier diffusion numbers semi-analytical microsegregation models, of the form suggested by Brody and Flemings, are known to perform poorly in the analysis of solidifications controlled by a parabolic solid growth. The basic inconsistency in the development of this class of models is highlighted. It is shown that an alternative, consistent development, for solidifications controlled by a constant cooling rate, results in the same microsegregation model. Comparison with predictions - maximum concentration and eutectic fractions - obtained with a numerical, constant cooling rate solution show a significant improvement in model performance. Further modification - based on curve fitting in the low Fourier number range - leads to a constant cooling rate microsegregation model that provides accurate predictions of microsegregation levels across a wide, practical range of parameters.