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Open AccessArticle

Semi-Analytical Solutions for the Poiseuille–Couette Flow of a Generalised Phan-Thien–Tanner Fluid

1
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
2
Centro de Matemática & Departamento de matemática da Universidade do Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
3
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
4
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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Fluids 2019, 4(3), 129; https://doi.org/10.3390/fluids4030129
Received: 3 June 2019 / Revised: 3 July 2019 / Accepted: 9 July 2019 / Published: 12 July 2019
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Abstract

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. View Full-Text
Keywords: generalised simplified PTT; Phan-Thien–Tanner (PTT) model; Mittag–Leffler; Couette flow; Poiseuille–Couette flow generalised simplified PTT; Phan-Thien–Tanner (PTT) model; Mittag–Leffler; Couette flow; Poiseuille–Couette flow
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MDPI and ACS Style

Ribau, Â.M.; Ferrás, L.L.; Morgado, M.L.; Rebelo, M.; Afonso, A.M. Semi-Analytical Solutions for the Poiseuille–Couette Flow of a Generalised Phan-Thien–Tanner Fluid. Fluids 2019, 4, 129.

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