Optimal cooling strategies in polymer crystallization

An optimal control problem for cooling strategies in polymer crystallization processes described by a deterministic model is solved in the framework of a free boundary problem. The strategy of cooling both sides of a one dimensional sample is introduced for the first time in this model, and is shown to be well approximated by the sum of the solutions of two one-phase Stefan problems, even for arbitrary applied temperature profiles. This result is then used to show that cooling both sides is always more effective in polymer production than injecting the same amount of cold through only one side. The optimal cooling strategy, focused in avoiding low temperatures and in shortening cooling times, is derived, and consists in applying the same constant temperature at both sides. Explicit expressions of the optimal controls in terms of the parameters of the material are also obtained.