### Peter Wapperom and Martien A. Hulsen

### Numerical simulation of a viscoelastic fluid with anisotropic
heat conduction

#### In: Numerical simulation of nonisothermal flow of viscoelastic liquids
(eds. J.F. Dijksman and G.D.C. Kuiken), Kluwer Academic Publishers,
Dordrecht (1995) 37-55

#### Abstract

For the nonisothermal flow of a viscoelastic fluid we have taken into account
temperature dependency of the relaxation times and the viscosities in the
constitutive equation for the stress. In the energy equation the heat flux is
specified by Fourier's law, where anisotropic heat conduction has been taken
into account.
Furthermore one has to specify which part of the stress work is dissipated and
which part is stored as elastic energy. The equations are solved with a finite
element method for the balance equations and a streamline integration method
for the constitutive equation. The influence of the Deborah number,
the Péclet number and the cooling temperature are examined in a
flow through a 4 to 1 contraction.
#### Keywords

shift factors; dissipation; anisotropic heat conduction; finite
elements; streamline integration; axisymmetrical 4 to 1 contraction