Predictions of anisotropic thermal transport in non-linear-non-isothermal polymeric flows

Abstract

Over the last decades, significant efforts have been dedicated to include more complete rheological constitutive models into finite elements methods to simulate the complex flows in polymer manufacturing. However, while a remarkable portion of these processes are intrinsically non-isothermal, the study and implementation of non-isothermal flows has been very limited. The degree of complexity of such calculations is considerably increased by: 1) the addition to the problem of the energy equation; 2) a strong coupling to the momentum balance due to a highly temperature-dependent rheological behavior and 3) the strong influence that deformation-induced molecular orientation has on the thermo-physical properties of polymeric materials. Experimental evidence has shown that thermal conductivity becomes anisotropic in polymers subjected to deformation. Furthermore, a linear relationship between the thermal conductivity and stress tensors has been found to be universal (i.e. independent of polymer chemistry) and to extend beyond the finite extensibility limit. We make use of molecular simulation techniques to gain insights into the transport mechanisms behind these surprising results. On a more practical level, our work combines the thermal conductivity/stress response with two recent constitutive equations proposed for linear (Rolie Poly) and branched (eXtended Pom-Pom) polymers to venture predictions for the anisotropy in thermal conductivity in a number of interesting flows. These two constitutive models provide accurate descriptions of the available non-linear rheology and thermal transport data. 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. Our work represents a first step towards a molecular-to-continuum methodology for the simulation of industrially relevant non-isothermal flows to predict flow characteristics and the material final properties after processing