Ribau, Ângela M.Ferrás, Luís L.Morgado, Maria L.Rebelo, MagdaAfonso, Alexandre M.2020-06-032020-06-032019-07-122311-5521PURE: 16196449PURE UUID: 6c285390-28a7-463e-88b0-ce7ad2f13ef7Scopus: 85071481535WOS: 000488029400035ORCID: /0000-0003-4115-3516/work/101442143http://hdl.handle.net/10362/98743PTDC/EMS-ENE/3362/2014 POCI-01-0145-FEDER-016665 SFRH/BPD/100353/2014 UID/MAT/00297/2019This 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.1957921engCouette flowGeneralised simplified PTTMittag–LefflerPhan-Thien–Tanner (PTT) modelPoiseuille–Couette flowCondensed Matter PhysicsMechanical EngineeringFluid Flow and Transfer Processesjournal article10.3390/fluids4030129https://www.scopus.com/pages/publications/85071481535