An analytical technique for the determination of the thermal contact resistance between a solidifying metal and mold

In the classical solution to one-dimensional solidifications Schwarz showed that in the case of perfect thermal contact the interface temperature between the mold and solidifying material is constant. Adams hypothesized that in the case of real casting problems where there is imperfect thermal contact, that one could still use the interface temperature computed by Schwarz’s solution but now acting through a film resistance to the mold and a film resistance to the solidifying metal. The problem of solidifying a metal by a constant temperature source acting through a film resistance is solved by the method of successive approximations. The solution to the problem of a mold heated by a constant temperature source acting through a film resistance is well known. Taking experimental data for depth solidifiedvs time the first problem is solved inversely to determine the film resistance between the constant temperature source and the solidifying metal. Using experimental curves for temperaturevs depth at various times the second problem is also solved inversely in order to determine the film resistance between the mold and the constant temperature source. The overall film resistance between the mold and solidifying metal is the sum of the two resistances. Experiments indicate that the two resistances cannot be assumed equal.