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DOI: 10.1615/ICHMT.2008.CHT.980
page 18

Juan I. Ramos
Escuela de Ingenierias Industriales, Universidad de Malaga, Dr. Ortiz Ramos, s/n 29071 Malaga, Spain


A two--dimensional low Reynolds number model for bicomponent fibres that includes the effects of molecular orientation, crystallization and latent heat, is presented and used to assess the accuracy of an asymptotic one--dimensional model developed by the author for slender fibres at low Biot numbers which employs the slenderness ratio as the perturbation parameter. The two--dimensional model involves two free surfaces and its equations are solved numerically by means of a domain decomposition technique that maps the curvilinear geometries of the inner and outer jets into rectangles, and employs strong conservation--law, finite differences and an iterative procedure. It is reported that, owing to the nonlinearities and coupling between the equations and the free--surface characteristics of the problem, the convergence is very slow even when small relaxation factors are used. Convergence is sped--up by employing a pseudo--time approach. It is found that the differences between the results of the one-- and two--dimensional are less than six percent for the molecular orientation, degree of crystallization and temperature at the outer jet's outer surface. However, large differences have been found in the axial velocity and and fibre's geometry prior to the fibre solidification. The differences in axial velocity are largest at the inflection point of this velocity component, whereas those in the geometry are located between the die's exit and the inflection point of the axial velocity component, i.e., where the fibre's contraction is largest. It is also found that the differences between the two models decrease as the Biot is increased.

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