Effective boundary condition for a quasi-Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition
We consider the quasi‐Newtonian flow in a domain with a periodic rough bottom Γϵ of period of order the small parameter ϵ and amplitude δϵ, such that δϵ 2. In the case δϵ>> ϵ2p‐1/p the effective boundary condition in the limit ϵ = 0 is the no‐slip condition, while if δϵ
Gespeichert in:
| Veröffentlicht in: | Zeitschrift für angewandte Mathematik und Mechanik 2015-05, Vol.95 (5), p.527-548 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 548 |
|---|---|
| container_issue | 5 |
| container_start_page | 527 |
| container_title | Zeitschrift für angewandte Mathematik und Mechanik |
| container_volume | 95 |
| creator | Suárez-Grau, F.J. |
| description | We consider the quasi‐Newtonian flow in a domain with a periodic rough bottom Γϵ of period of order the small parameter ϵ and amplitude δϵ, such that δϵ 2. In the case δϵ>> ϵ2p‐1/p the effective boundary condition in the limit ϵ = 0 is the no‐slip condition, while if δϵ |
| doi_str_mv | 10.1002/zamm.201300160 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1685792580</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1685792580</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3880-7093f0e5209522b33d0deb259fa3c30ae9d9ca7630d431aa3bc0a54e92893c603</originalsourceid><addsrcrecordid>eNqFkU1vEzEURS1EJULLlrUlNmwmPNvz5WVVlQJqwyYoiI314rFTl5lxa3tSwoLfjqOgFnXTlWXrnOd3dQl5y2DOAPiH3zgMcw5MALAaXpAZqzgrynx7SWYAZVlwXjevyOsYbyC_SiZm5M-5tUYntzV07aexw7Cj2o-dS86P1PpAkd5NGF2xMPfJjw5HunVR-ylS20-uo5gyEnu3uU79jgY_ba4fR8WEIblxQ23wQ-YWuHUmPP5wQo4s9tG8-Xcek28fz5dnn4rLrxefz04vCy3aFooGpLBgKg6y4nwtRAedWfNKWhRaABrZSY1NLaArBUMUaw1YlUbyVgpdgzgm7w9zb4O_m0xMasghTN_jaHIUxeq2aiSv2j367gl646cw5u32FGdNKZs2U_MDpYOPMRirboMbcmTFQO3rUPs61EMdWZAH4d71ZvcMrX6cXl397xYH18Vkfj24GH6quhFNpVaLC_V9tVzWK_5FLcVfADSfeQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1682174978</pqid></control><display><type>article</type><title>Effective boundary condition for a quasi-Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition</title><source>Wiley Online Library Journals Frontfile Complete</source><creator>Suárez-Grau, F.J.</creator><creatorcontrib>Suárez-Grau, F.J.</creatorcontrib><description>We consider the quasi‐Newtonian flow in a domain with a periodic rough bottom Γϵ of period of order the small parameter ϵ and amplitude δϵ, such that δϵ << ϵ. The flow is described by the 3D incompressible non‐Newtonian Navier‐Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening). Assuming that the fluid satisfies the Navier slip condition on Γϵ and letting ϵ → 0, we obtain three different macroscopic models depending on the magnitude of δϵ with respect to ϵ2p‐1/p, with p > 2. In the case δϵ>> ϵ2p‐1/p the effective boundary condition in the limit ϵ = 0 is the no‐slip condition, while if δϵ<< ϵ2p‐1/p there is no roughness‐induced effect. In the critical case when δϵ ∼ ϵ2p‐1/p we provide a more accurate effective boundary condition of Navier type. Finally, we also obtain corrector result for the pressure and velocity in every cases.
The author considers the quasi‐Newtonian flow in a domain with a periodic rough bottom Γε of period of order the small parameter ε and amplitude δε, such that . The flow is described by the 3D incompressible non‐Newtonian Navier‐Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening)….</description><identifier>ISSN: 0044-2267</identifier><identifier>EISSN: 1521-4001</identifier><identifier>DOI: 10.1002/zamm.201300160</identifier><language>eng</language><publisher>Weinheim: Blackwell Publishing Ltd</publisher><subject>Boundary conditions ; Computational fluid dynamics ; Finite element analysis ; Fluid flow ; Fluids ; Incompressible flow ; Mathematical models ; Navier boundary condition ; Navier-Stokes equations ; Quasi-Newtonian fluid ; rough boundary ; Three dimensional</subject><ispartof>Zeitschrift für angewandte Mathematik und Mechanik, 2015-05, Vol.95 (5), p.527-548</ispartof><rights>2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim</rights><rights>Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3880-7093f0e5209522b33d0deb259fa3c30ae9d9ca7630d431aa3bc0a54e92893c603</citedby><cites>FETCH-LOGICAL-c3880-7093f0e5209522b33d0deb259fa3c30ae9d9ca7630d431aa3bc0a54e92893c603</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fzamm.201300160$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fzamm.201300160$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Suárez-Grau, F.J.</creatorcontrib><title>Effective boundary condition for a quasi-Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition</title><title>Zeitschrift für angewandte Mathematik und Mechanik</title><addtitle>Z. Angew. Math. Mech</addtitle><description>We consider the quasi‐Newtonian flow in a domain with a periodic rough bottom Γϵ of period of order the small parameter ϵ and amplitude δϵ, such that δϵ << ϵ. The flow is described by the 3D incompressible non‐Newtonian Navier‐Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening). Assuming that the fluid satisfies the Navier slip condition on Γϵ and letting ϵ → 0, we obtain three different macroscopic models depending on the magnitude of δϵ with respect to ϵ2p‐1/p, with p > 2. In the case δϵ>> ϵ2p‐1/p the effective boundary condition in the limit ϵ = 0 is the no‐slip condition, while if δϵ<< ϵ2p‐1/p there is no roughness‐induced effect. In the critical case when δϵ ∼ ϵ2p‐1/p we provide a more accurate effective boundary condition of Navier type. Finally, we also obtain corrector result for the pressure and velocity in every cases.
The author considers the quasi‐Newtonian flow in a domain with a periodic rough bottom Γε of period of order the small parameter ε and amplitude δε, such that . The flow is described by the 3D incompressible non‐Newtonian Navier‐Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening)….</description><subject>Boundary conditions</subject><subject>Computational fluid dynamics</subject><subject>Finite element analysis</subject><subject>Fluid flow</subject><subject>Fluids</subject><subject>Incompressible flow</subject><subject>Mathematical models</subject><subject>Navier boundary condition</subject><subject>Navier-Stokes equations</subject><subject>Quasi-Newtonian fluid</subject><subject>rough boundary</subject><subject>Three dimensional</subject><issn>0044-2267</issn><issn>1521-4001</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNqFkU1vEzEURS1EJULLlrUlNmwmPNvz5WVVlQJqwyYoiI314rFTl5lxa3tSwoLfjqOgFnXTlWXrnOd3dQl5y2DOAPiH3zgMcw5MALAaXpAZqzgrynx7SWYAZVlwXjevyOsYbyC_SiZm5M-5tUYntzV07aexw7Cj2o-dS86P1PpAkd5NGF2xMPfJjw5HunVR-ylS20-uo5gyEnu3uU79jgY_ba4fR8WEIblxQ23wQ-YWuHUmPP5wQo4s9tG8-Xcek28fz5dnn4rLrxefz04vCy3aFooGpLBgKg6y4nwtRAedWfNKWhRaABrZSY1NLaArBUMUaw1YlUbyVgpdgzgm7w9zb4O_m0xMasghTN_jaHIUxeq2aiSv2j367gl646cw5u32FGdNKZs2U_MDpYOPMRirboMbcmTFQO3rUPs61EMdWZAH4d71ZvcMrX6cXl397xYH18Vkfj24GH6quhFNpVaLC_V9tVzWK_5FLcVfADSfeQ</recordid><startdate>201505</startdate><enddate>201505</enddate><creator>Suárez-Grau, F.J.</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201505</creationdate><title>Effective boundary condition for a quasi-Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition</title><author>Suárez-Grau, F.J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3880-7093f0e5209522b33d0deb259fa3c30ae9d9ca7630d431aa3bc0a54e92893c603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Boundary conditions</topic><topic>Computational fluid dynamics</topic><topic>Finite element analysis</topic><topic>Fluid flow</topic><topic>Fluids</topic><topic>Incompressible flow</topic><topic>Mathematical models</topic><topic>Navier boundary condition</topic><topic>Navier-Stokes equations</topic><topic>Quasi-Newtonian fluid</topic><topic>rough boundary</topic><topic>Three dimensional</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Suárez-Grau, F.J.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Suárez-Grau, F.J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Effective boundary condition for a quasi-Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition</atitle><jtitle>Zeitschrift für angewandte Mathematik und Mechanik</jtitle><addtitle>Z. Angew. Math. Mech</addtitle><date>2015-05</date><risdate>2015</risdate><volume>95</volume><issue>5</issue><spage>527</spage><epage>548</epage><pages>527-548</pages><issn>0044-2267</issn><eissn>1521-4001</eissn><abstract>We consider the quasi‐Newtonian flow in a domain with a periodic rough bottom Γϵ of period of order the small parameter ϵ and amplitude δϵ, such that δϵ << ϵ. The flow is described by the 3D incompressible non‐Newtonian Navier‐Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening). Assuming that the fluid satisfies the Navier slip condition on Γϵ and letting ϵ → 0, we obtain three different macroscopic models depending on the magnitude of δϵ with respect to ϵ2p‐1/p, with p > 2. In the case δϵ>> ϵ2p‐1/p the effective boundary condition in the limit ϵ = 0 is the no‐slip condition, while if δϵ<< ϵ2p‐1/p there is no roughness‐induced effect. In the critical case when δϵ ∼ ϵ2p‐1/p we provide a more accurate effective boundary condition of Navier type. Finally, we also obtain corrector result for the pressure and velocity in every cases.
The author considers the quasi‐Newtonian flow in a domain with a periodic rough bottom Γε of period of order the small parameter ε and amplitude δε, such that . The flow is described by the 3D incompressible non‐Newtonian Navier‐Stokes system where the viscosity is given by the non linear power law which is widely used for dilatant fluids (shear thickening)….</abstract><cop>Weinheim</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/zamm.201300160</doi><tpages>22</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0044-2267 |
| ispartof | Zeitschrift für angewandte Mathematik und Mechanik, 2015-05, Vol.95 (5), p.527-548 |
| issn | 0044-2267 1521-4001 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1685792580 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Boundary conditions Computational fluid dynamics Finite element analysis Fluid flow Fluids Incompressible flow Mathematical models Navier boundary condition Navier-Stokes equations Quasi-Newtonian fluid rough boundary Three dimensional |
| title | Effective boundary condition for a quasi-Newtonian viscous fluid at a slightly rough boundary starting from a Navier condition |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-18T23%3A19%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Effective%20boundary%20condition%20for%20a%20quasi-Newtonian%20viscous%20fluid%20at%20a%20slightly%20rough%20boundary%20starting%20from%20a%20Navier%20condition&rft.jtitle=Zeitschrift%20f%C3%BCr%20angewandte%20Mathematik%20und%20Mechanik&rft.au=Su%C3%A1rez-Grau,%20F.J.&rft.date=2015-05&rft.volume=95&rft.issue=5&rft.spage=527&rft.epage=548&rft.pages=527-548&rft.issn=0044-2267&rft.eissn=1521-4001&rft_id=info:doi/10.1002/zamm.201300160&rft_dat=%3Cproquest_cross%3E1685792580%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1682174978&rft_id=info:pmid/&rfr_iscdi=true |