Simulations of two-dimensional steady isothermal and non-isothermal steady flows with slip for a viscoelastic memory-integral fluid

Abstract

Purpose – The purpose of this paper is to compute flow effects of the transition from adherence-to-slip in two-dimensional flows, for a polymer melt obeying a memory-integral viscoelastic equation, in isothermal and non-isothermal cases. Design/methodology/approach – Temperature dependence is expressed by Arrhenius and William-Landel-Ferry models. A coupling approach is defined. For the dynamic equations, the Stream-Tube Method (STM) is used with finite differences in a mapped rectangular domain of the real domain, where streamlines are parallel and straight. STM avoids particle-tracking problems and allows simple formulae to evaluate stresses resulting from the constitutive equation. For the temperature field, a finite-element method is carried out to solve the energy equation in the real domain. Findings – The approach avoids numerical problems arising with classical formulations and proves to be robust and efficient. Large elasticity levels are attained without convergence and refinement difficulties that may arise close to the “stick-slip” transition section. The method highlights the role of temperature conditions and reveals interesting differences for the ducts considered. Practical implications – The results of the study are of interest for polymer processing where slip at the wall can be encountered, in relation with the physical properties of the materials. Originality/value – The paper presents a simple approach that limits considerably numerical problems coming from stick-slip boundary conditions and avoids particle-tracking. Results are obtained at flow rates encountered in industrial conditions. Keywords Finite elements, Viscoelasticity, Stick-slip problem, Adherence-to-slip, Non-isothermal two-dimensional flows, Memory-integral models