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The effect of shear flows on the thermal conductivity of polymer melts isinvestigated using a reversed nonequilibrium molecular dynamics (RNEMD) method.We extended the original RNEMD method to simultaneously produce spatialgradients of temperature and flow velocity in a single direction. This methodenables the accurate measurement of thermal conductivity in the transversedirection to shear flow.  Our main finding is that the stress-thermal rule (STR) (i.e., the linearrelationship between anisotropic parts of the stress tensor and the thermalconductivity tensor) holds for entangled polymer melts even under shear flowsbut not for unentangled polymer melts. Furthermore, once entanglements form inpolymer chains, the coefficient of the STR (i.e., the stress-thermalcoefficient) remains independent of the polymer chain length.  These observations align with the theoretical foundation of the STR, whichfocuses on energy transmission along the network structure of entangled polymerchains [Brule, Rheol. Acta \textbf{28}, 257 (1989)]. However, under drivenshear flows, the stress-thermal coefficient is notably smaller than thatmeasured in the literature for a quasi-quiescent state without external forces.Although the mechanism of the STR in shear flows has yet to be fullyelucidated, our study confirmed the validity of the STR in shear flows. Thisallows us to use the STR as a constitutive equation for computationalthermo-fluid dynamics of polymer melts, thus offering broad engineeringapplications.

Effect of shear flow on the transverse thermal conductivity of polymer melts