  The effect of shear flows on the thermal conductivity of polymer melts is
investigated using a reversed nonequilibrium molecular dynamics (RNEMD) method.
We extended the original RNEMD method to simultaneously produce spatial
gradients of temperature and flow velocity in a single direction. This method
enables accurate measurement of the thermal conductivity in the direction
transverse to shear flow.
  The Weissenberg number defined with the shear rate and the relaxation time of
the polymer conformation can uniformly differentiate the occurrence of shear
rate dependence of the thermal conductivity across different chain lengths. The
stress-thermal rule (STR) (i.e., the linear relationship between anisotropic
parts of the stress tensor and the thermal conductivity tensor) holds for
entangled polymer melts even under shear flows but not for unentangled polymer
melts. Furthermore, once entanglements form in polymer chains, the
stress-thermal coefficient in the STR remains independent of the polymer chain
length.
  These observations align with the theoretical foundation of the STR, which
focuses on energy transmission along the network structure of entangled polymer
chains [Brule, Rheol. Acta 28, 257 (1989)]. However, under driven shear flows,
the stress-thermal coefficient is notably smaller than that measured in the
literature for a quasi-quiescent state without external forces. Although the
mechanism of the STR in shear flows has yet to be fully elucidated, our study
confirmed the validity of the STR in shear flows. This allows us to use the STR
as a constitutive equation for computational thermo-fluid dynamics of polymer
melts, thus having broad engineering applications.
