Please use this identifier to cite or link to this item: https://hdl.handle.net/1822/59453

TitleTheoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries
Author(s)Ferrás, Luís Jorge Lima
Ford, Neville J.
Morgado, Maria Luisa
Rebelo, Magda
McKinley, Gareth H.
Nóbrega, J. M.
KeywordsFractional viscoelastic model
Annular flows
Numerical methods
Issue date30-Sep-2018
PublisherPergamon-Elsevier Science Ltd
JournalComputers & Fluids
Abstract(s)In this work we discuss the connection between classical and fractional viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the fractional Maxwell model. We then develop a numerical method for the solution of two coupled fractional differential equations (one for the velocity and the other for the stress), that appear in the pure tangential annular flow of fractional viscoelastic fluids. The numerical method is based on finite differences, with the approximation of fractional derivatives of the velocity and stress being inspired by the method proposed by Sun and Wu (2006) for the fractional diffusion-wave equation [ Z.Z. Sun, X. Wu, A fully discrete difference scheme for a diffusion-wave system, Applied Numerical Mathematics 56 (2006) 193-209]. We prove solvability, study numerical convergence of the method, and also discuss the applicability of this method for simulating the rheological response of complex fluids in a real concentric cylinder rheometer. By imposing a torsional step-strain, we observe the different rates of stress relaxation obtained with different values of alpha and beta (the fractional order exponents that regulate the viscoelastic response of the complex fluids). (C) 2018 Elsevier Ltd. All rights reserved.
TypeArticle
URIhttps://hdl.handle.net/1822/59453
DOI10.1016/j.compfluid.2018.07.004
ISSN0045-7930
Peer-Reviewedyes
AccessRestricted access (UMinho)
Appears in Collections:IPC - Artigos em revistas científicas internacionais com arbitragem

Files in This Item:
File Description SizeFormat 
FracViscModels-published.pdf
  Restricted access
2,94 MBAdobe PDFView/Open

Partilhe no FacebookPartilhe no TwitterPartilhe no DeliciousPartilhe no LinkedInPartilhe no DiggAdicionar ao Google BookmarksPartilhe no MySpacePartilhe no Orkut
Exporte no formato BibTex mendeley Exporte no formato Endnote Adicione ao seu ORCID