Diffusive mushy layer similarity solution (Worster 1986): Mathematica solver

Zenodo (CERN European Organization for Nuclear Research)

Abstract

Implements a prototype iterative ODE solver to find the similarity solution for a binary mush with no advective transport, following Worster 1986, https://doi.org/10.1017/S0022112086002938. In particular, we recreate Fig. 5 of the respective paper, meaning that we solve for the (nondimensional) solid-mush and mush-liquid nterface locations given the first parameter set (Set I) from Table 1 of the reference. The similarity solutions computed by this notebook are useful as validation data for mixture solidification codes. I allows manual recreation of the solution at custom undercooling conditions and implements the resulting analytical concentration, temperature and liquid fraction profiles as functions of the similarity parameters.

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