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Similarity solutions for the two-phase Rubinstein binary-alloy solidificationproblem in a semi-infinite material are developed. These new explicit solutionsare obtained by considering two cases: a heat flux or a convective boundaryconditions at the fixed face, and the necessary and sufficient conditions ondata are also given in order to have an instantaneous solidification process.We also show that all solutions for the binary-alloy solidification problem areequivalent under some restrictions for data. Moreover, this implies that thecoefficient which characterizes the solidification front for the Rubinsteinsolution must verify an inequality as a function of all thermal and boundaryconditions.

Explicit solutions related to the Rubinstein binary-alloy solidification problem with a heat flux or a convective condition at the fixed face