  The present paper develops an isothermal model for fast (high Deborah number)
contraction flows of polymers from a reservoir to a die of circular or
rectangular cross-sections. Two components of composite flow models in
different regions of the flow domain are connected in succession with the use
of asymptotic matching boundary conditions. These components are inhomogeneous
elongation and a modified unsteady shearing. It is constructed based on a
stable and descriptive set of viscoelastic constitutive equations with the
specified material parameters. The present model demonstrates a reasonable good
agreement to the experimental/direct numerical data and improves for the higher
values of Deborah number and contraction ratio cases without any adjustable
parameters. Also it is applicable to any constitutive equation and performs
with easy PC numerical calculations.
