  We successfully extend a multiscale simulation (MSS) method to nonisothermal
well-entangled polymer melt flows between two coaxial cylinders. In the
multiscale simulation, the macroscopic flow system is connected to a number of
microscopic systems through the velocity gradient tensor, stress tensor and
temperature. At the macroscopic level, in addition to the momentum balance
equation, we consider the energy balance equation, where heat generation plays
an important role not only in the temperature distribution but also in the flow
profile. At the microscopic level, a dual slip-link model is employed for
well-entangled polymers. To incorporate the temperature effect into the
microscopic systems, we used the time-temperature superposition rule for the
slip-link model, in which the temperature dependence of the parameters is not
known; on the other hand, the way to take into account the temperature effect
in the macroscopic equations has been well established. We find that the
extended multiscale simulation method is quite effective in revealing the
relation between nonisothermal polymeric flows for both steady and transient
cases and the microscopic states of polymer chains expressed by primitive paths
and slip-links. It is also found that the temperature-dependent
reptation-time-based Weissenberg number is a suitable measure for understanding
the extent of the polymer chain deformation in the range of the shear rate used
in this study.
