Semi-Analytical Solutions for the Poiseuille–Couette Flow of a Generalised Phan-Thien–Tanner Fluid
Ângela M. Ribau,
Luís L. Ferrás,
Maria L. Morgado,
Magda Rebelo,
Alexandre M. Afonso
Affiliations
Ângela M. Ribau
Centro de Estudos de Fenómenos de Transporte, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
Luís L. Ferrás
Centro de Matemática & Departamento de matemática da Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
Maria L. Morgado
Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, Universidade de Lisboa & Department of Mathematics, University of Trás-os-Montes e Alto Douro, UTAD, 5001-801 Vila Real, Portugal
Magda Rebelo
Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal
Alexandre M. Afonso
Centro de Estudos de Fenómenos de Transporte, Departamento de Engenharia Mecânica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille−Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien−Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien−Tanner constitutive equation. This generalised version considers the Mittag−Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification.
