Anisotropic thermal transport in non-linear-non-isothermal polymeric flows

Abstract

Over the last decades, the use of finite elements methods to simulate the complex flows occurring in polymer manufacturing has grown considerably. However, while significant efforts have been dedicated to include more complete rheological constitutive models into these numeric packages, the study of the underlying phenomena and implementation of non-isothermal flows has been very limited. The degree of complexity of such calculations is caused by the addition to the problem of the energy equation, which is strongly coupled to the momentum balance because viscosity is highly dependent on temperature. To further complicate this scheme, the thermo-physical properties of polymeric materials are strongly influenced by the deformation-induced molecular orientation. As a result, thermal conductivity needs to be treated as an anisotropic tensor when polymers are subjected to deformation. Furthermore, a linear relationship between the thermal conductivity and stress tensors, known as the stress-thermal rule, has been found to be universal (i.e. independent of polymer chemistry). Our work takes advantage of this universality to combine the stress-thermal rule with two recent constitutive equations proposed for linear (Rolie Poly) and branched (eXtended Pom-Pom) polymers to obtain predictions for the anisotropy in thermal conductivity. We demonstrate how these two constitutive models provide accurate descriptions of the available non-linear rheology and thermal transport data, and venture predictions for a number of interesting flows. Remarkably, our approach allows implementation of anisotropy in thermal conductivity into finite elements simulations without adding any adjusting parameters to those of the viscoelastic model. We present this work as a first step towards a molecular-to-continuum methodology for the simulation of industrially relevant non-isothermal flows to predict not only the flow characteristics but also the final properties of the material after processing.