ON SOLIDIFICATION OF A BINARY ALLOY
L. N. TAO · The Quarterly Journal of Mechanics and Applied Mathematics · 1980
The solidification of a binary alloy in a semi-infinite region with arbitrarily prescribed initial temperature and composition and an arbitrarily prescribed temperature at its surface is investigated. The liquidus and solidus lines of the phase diagram are used to relate the freezing temperature and composition of the alloy. The exact solutions of the temperature and concentration are established in series of products of functions in the error integral family and time t. The interfacial position and the freezing temperature are power series of t1/2. The existence and uniqueness of these series solutions are considered and proved. It is also shown that these series are convergent. The paper concludes with consideration of some special cases; one of these is the similarity solution.