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In this work, the numerical simulation of the non-isothermal steady co-extrusion fiber spinning with flow-induced crystallization is explored. The model is based on the formulation originally proposed by China et al. in which Newtonian and Phan-Thien-Tanner (PTT) fluids are considered the core and the skin layer, respectively. The polymeric flow rate fraction, Deborah dimensionless number and the PTTs parameters on the temperature, the velocity and the crystallization profiles are analyzed. The numerical results show: the temperature profile is sensitive to the polymeric layer flow rate and the deformation parameters (shear thinning and extensional), the tensile stress induced crystallization parameter has a strong influence at the onset of the process, increasing drastically temperature and crystallinity.

A numerical solution for axis-symmetrical fluid flow through a smooth constriction using the alternating direction implicit finite volume method and the fractional-step-method is presented. The wall is modelled with a smooth contraction mapped by a sinusoidal function and the flow is supposed to be axis-symmetric. A pressure boundary condition is set at the inlet and the resulting pressure gradient field drives fluid flow which is always in laminar regime. This study presents results for a non-Newtonian fluid using the Ostwaldde Waele constitutive model. Moreover, a transient network representing three different microstructures, immersed in the fluid, is evolved by viscous dissipation and an isothermal process is considered. The time dependent evolution of the transient network is represented by a set of kinetic equations with their respective forward and reversed constants. The numerical predictions show that, at a fixed Reynolds number, the viscous dissipation and the grade of structure restoration or breakage is influenced by constriction severity due to the energy generated during fluid flow. A 50% reduction in transversal section generates secondary flow downstream and vortex shedding, whereas a 10% and 25% constrictions presents a thin boundary layer and no secondary flow near the constricted wall.