Journal of Mathematical Chemistry

, Volume 50, Issue 2, pp 313–324 | Cite as

Optimal cooling strategies in polymer crystallization

Original Paper

Abstract

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.

Keywords

Optimal control Stefan problem Polymer crystallization 

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References

  1. 1.
    Alexiades V., Solomon A.D.: Mathematical Modeling of Melting and Freezing Processes. Hemisphere Publishing Co., Washington DC (1993)Google Scholar
  2. 2.
    V. Capasso, in Mathematical Models for Polymer Crystallization Processes, ed. by V. Capasso, H. Engl, J. Periaux. Computational Mathematics Driven by Industrial Problems (Springer, Berlin, 2000), pp. 39–67Google Scholar
  3. 3.
    Escobedo R., Capasso V.: Moving bands and moving boundaries with decreasing speed in polymer crystallization. Math. Mod. Meth. Appl. Sci. (M3AS) 15(3), 325–341 (2005)CrossRefGoogle Scholar
  4. 4.
    Escobedo R., Fernández L.A.: Optimal control of chemical birth and growth processes in a deterministic model. J. Math. Chem. 48, 118–127 (2010)CrossRefGoogle Scholar
  5. 5.
    R. Escobedo, L.A. Fernández, A classical one-phase Stefan problem for describing a polymer crystallization process (2010, submitted)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Departamento Matemática Aplicada y CC. de la ComputaciónUniversidad de CantabriaSantanderSpain
  2. 2.Departamento Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain

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