A unified model of microsegregation and coarsening

Using a coordinate transform in a standard microsegregation model it is shown that the effect of coarsening on the dilution of the liquid phase can be accounted for by adding a dimensionless parameter alpha(c) to the back-diffusion Fourier number. Through theory, for the case of parabolic growth, and numerical experiments for the constant cooling rate, it is shown that a constant value of alpha(c) = 0.1 is a sound choice across a wide range of casting and alloy conditions. This finding allows for the development of a unified model for microsegregation and coarsening. In particular, previous approximate microsegregation models can be readily modified to account for coarsening.