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A Mathematical Model for the Melt Spinning of Polymer Fibers

In: Numerical Methods and Software Tools in Industrial Mathematics

Author

Listed:
  • Erik Andreassen

    (SINTEF)

  • Elisabeth Gundersen

    (University of Oslo, Dept. of Math.)

  • Einar L. Hinrichsen

    (SINTEF)

  • Hans Petter Langtangen

    (University of Oslo, Dept. of Math.)

Abstract

We derive a quasi one-dimensional mathematical model for the free surface flow of thin polymer fibers undergoing phase changes. The model is based on averaging the mass and momentum balance equations, while the energy equation is kept in the standard form. Various constitutive laws are introduced for crystallization kinetics, temperature and strain-rate dependent viscosity, air friction and heat transfer coefficients in cooling laws. Emphasis is put on the many approximations in the model. The resulting system of algebraic equations, partial differential equations and ordinary differential equations is solved numerically. We show how the numerical simulations can be used for fitting parameters in an empirical crystallization model.

Suggested Citation

  • Erik Andreassen & Elisabeth Gundersen & Einar L. Hinrichsen & Hans Petter Langtangen, 1997. "A Mathematical Model for the Melt Spinning of Polymer Fibers," Springer Books, in: Morten Dæhlen & Aslak Tveito (ed.), Numerical Methods and Software Tools in Industrial Mathematics, chapter 9, pages 195-212, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1984-2_9
    DOI: 10.1007/978-1-4612-1984-2_9
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