Martin Burger,
"Modelling multi-dimensional crystallization of polymers in interaction with heat transfer"
, in Nonlinear Analysis: Real World Applications, 2001, M. Burger, V. Capasso, and C. Salani, Modelling multi-dimensional crystallization of polymers in interaction with heat transfer, Nonlinear Analysis: Real World Applications 3 (2001), 139-160
Original Titel:
Modelling multi-dimensional crystallization of polymers in interaction with heat transfer
Sprache des Titels:
Englisch
Englische Kurzfassung:
This paper is concerned with the mathematical modelling of crystallization processes in general non-homogenous situations. We apply the classical Avrami-Kolmogorov-Evans theory in the case of growth in a given field and verify
conditions for its validity. In addition, we discuss the problem of applying the theory in the case of interaction withthe heat transfer process, where the results obtained that way may be interpreted as an approximation, but not as an exact solution.
For the general situation we present a new direct approach based on averaging on a mesoscale; a coupled system of partial differential equations of parabolic and hyperbolic type is deduced, modelling the evolution of crystallinity
and temperature. Furthermore we give conditions upon scales and parameters, under which this approach yields a hybrid approximation on a mesoscale that corresponds to
classical deterministic models.
Journal:
Nonlinear Analysis: Real World Applications
Erscheinungsjahr:
2001
Notiz zum Zitat:
M. Burger, V. Capasso, and C. Salani, Modelling multi-dimensional crystallization of polymers in interaction with heat transfer, Nonlinear Analysis: Real World Applications 3 (2001), 139-160
Publikationstyp:
Aufsatz / Paper in sonstiger referierter Fachzeitschrift