  In this numerical study, an original approach to simulate non-isothermal
viscoelastic fluid flows at high Weissenberg numbers is presented. Stable
computations over a wide range of Weissenberg numbers are assured by using the
root conformation approach in a finite volume framework on general unstructured
meshes. The numerical stabilization framework is extended to consider
thermo-rheological properties in Oldroyd-B type viscoelastic fluids. The
temperature dependence of the viscoelastic fluid is modeled with the
time-temperature superposition principle. Both Arrhenius and WLF shift factors
can be chosen, depending on the flow characteristics. The internal energy
balance takes into account both energy and entropy elasticity. Partitioning is
achieved by a constant split factor. An analytical solution of the balance
equations in planar channel flow is derived to verify the results of the main
field variables and to estimate the numerical error. The more complex entry
flow of a polyisobutylene-based polymer solution in an axisymmetric 4:1
contraction is studied and compared to experimental data from the literature.
We demonstrate the stability of the method in the experimentally relevant range
of high Weissenberg numbers. The results at different imposed wall
temperatures, as well as Weissenberg numbers, are found to be in good agreement
with experimental data. Furthermore, the division between energy and entropy
elasticity is investigated in detail with regard to the experimental setup.
