Annular flow of viscoelastic fluids: Analytical and numerical solutions
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/39255 |
Resumo: | This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem |
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Annular flow of viscoelastic fluids: Analytical and numerical solutionsAnnular flowAnalytical solutionsPTT modelSlip boundary conditionsEngenharia e Tecnologia::Engenharia dos MateriaisScience & TechnologyThis work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problemCOMPETE, FEDER and Fundação para a Ciência e a Tecnologia (FCT) through projects PEst-C/CTM/LA0025/2013 (Strategic Project – LA 25 – 2013-2014), PTDC/EQU-FTT/113811/2009 and PTDC/EME-MFE/113988/2009. LLF and AMA would also like to thank FCT for financial support through the scholarships SFRH/BD/37586/2007 and SFRH/BPD/75436/2010, respectively.ElsevierUniversidade do MinhoFerrás, Luís Jorge LimaAfonso, A. M.Alves, M. A.Nóbrega, J. M.Pinho, F. T.2014-102014-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/39255engFerrás, L.L., Afonso, A.M., Alves, M.A., Nóbrega, J.M., Pinho, F.T., Annular flow of viscoelastic fluids: Analytical and numerical solutions, Journal of Non-Newtonian Fluid Mechanics, Vol 212, pp. 80-91, 2014.0377-02510.1016/j.jnnfm.2014.07.004http://www.sciencedirect.com/science/article/pii/S0377025714001128info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:40:28Zoai:repositorium.sdum.uminho.pt:1822/39255Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:37:17.137871Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
title |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
spellingShingle |
Annular flow of viscoelastic fluids: Analytical and numerical solutions Ferrás, Luís Jorge Lima Annular flow Analytical solution sPTT model Slip boundary conditions Engenharia e Tecnologia::Engenharia dos Materiais Science & Technology |
title_short |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
title_full |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
title_fullStr |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
title_full_unstemmed |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
title_sort |
Annular flow of viscoelastic fluids: Analytical and numerical solutions |
author |
Ferrás, Luís Jorge Lima |
author_facet |
Ferrás, Luís Jorge Lima Afonso, A. M. Alves, M. A. Nóbrega, J. M. Pinho, F. T. |
author_role |
author |
author2 |
Afonso, A. M. Alves, M. A. Nóbrega, J. M. Pinho, F. T. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Ferrás, Luís Jorge Lima Afonso, A. M. Alves, M. A. Nóbrega, J. M. Pinho, F. T. |
dc.subject.por.fl_str_mv |
Annular flow Analytical solution sPTT model Slip boundary conditions Engenharia e Tecnologia::Engenharia dos Materiais Science & Technology |
topic |
Annular flow Analytical solution sPTT model Slip boundary conditions Engenharia e Tecnologia::Engenharia dos Materiais Science & Technology |
description |
This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problem |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-10 2014-10-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/39255 |
url |
http://hdl.handle.net/1822/39255 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Ferrás, L.L., Afonso, A.M., Alves, M.A., Nóbrega, J.M., Pinho, F.T., Annular flow of viscoelastic fluids: Analytical and numerical solutions, Journal of Non-Newtonian Fluid Mechanics, Vol 212, pp. 80-91, 2014. 0377-025 10.1016/j.jnnfm.2014.07.004 http://www.sciencedirect.com/science/article/pii/S0377025714001128 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799132905944907776 |