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dc.contributor.authorFerras, Luis L.*
dc.contributor.authorFord, Neville J.*
dc.contributor.authorMorgado, Maria L.*
dc.contributor.authorRebelo, Magda S.*
dc.contributor.authorMcKinley, Gareth H.*
dc.contributor.authorNobrega, Joao M.*
dc.date.accessioned2018-11-20T14:42:55Z
dc.date.available2018-11-20T14:42:55Z
dc.date.issued2018-07-12
dc.identifier.citationFerrás, L. L., Ford, N. J., Morgado, M. L., Rebelo, M., McKinley, G. H. & Nóbrega, J. M. (2018). Theoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries. Computers and Fluids, 174, 14-33en
dc.identifier.issn0045-7930
dc.identifier.doi10.1016/j.compfluid.2018.07.004
dc.identifier.urihttp://hdl.handle.net/10034/621579
dc.descriptionAuthor copy of accepted articleen
dc.description.abstractIn 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 ow 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 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).
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttps://www.sciencedirect.com/science/article/pii/S0045793018303931en
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectfractional differential equationsen
dc.subjectnumerical methodsen
dc.subjectviscoelastic modelsen
dc.titleTheoretical and numerical analysis of unsteady fractional viscoelastic flows in simple geometries.en
dc.typeArticleen
dc.contributor.departmentUniversity of Chester, University of Minho, UTAD, Universidade Nova de Lisboaen
dc.identifier.journalComputers and Fluids
dc.date.accepted2018-07-06
or.grant.openaccessYesen
rioxxterms.funderFCT Portugalen_US
rioxxterms.identifier.projectUnfunded at Chesteren_US
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2019-07-12
rioxxterms.publicationdate2018-07-12


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