A Combination of the eXtended Pom-Pom Model and the Stress-Thermal Rule to Predict Anisotropy in Thermal Conductivity in Non-Linear Polymeric Flows

Abstract

Advances in polymer processing enables more affordable technologies and significantly impacts the global plastics market which is expected to reach 654 billion USD by 2020. The cost/energy required to manufacture, recycle and dispose polymers is strongly affected by the thermo-physical properties and their dependence on state variables such as temperature and stress. The viscoelastic behavior of polymeric flows under isothermal conditions has been extensively researched. However, most of the processing of polymeric materials occurs under non-isothermal conditions and their implementation in simulations remains a challenge. In particular, flow-induced anisotropy in the thermal conductivity of polymers has been previously omitted in the study of industrially relevant flows. Our work combines evidence of a universal relationship between thermal conductivity and stress tensors (i.e. the stress-thermal rule) with differential constitutive equations for the viscoelastic behavior of polymers to provide predictions for the anisotropy in thermal conductivity in uniaxial, planar, equibiaxial and shear flow in commercial polymers. Special focus is placed on the eXtended Pom-Pom model which captures the non-linear behavior in both shear and elongation flows. The predictions provided by this approach are easily implemented in finite elements packages since the viscoelastic and thermal behavior is described by a single equation. Our results include predictions for the flow-induced anisotropy in thermal conductivity for low density polyethylene as well as validation of the method by comparison with available measurements. Remarkably, this approach allows universal predictions of anisotropy in thermal conductivity to be used in simulations of complex flows in which only the most fundamental rheological behavior of the material has been previously characterized (i.e. no adjusting parameters are needed in addition to those in the constitutive model