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doctoral thesis
Prilozi asimptotičkom modeliranju toka mikropolarnog fluida
Zagreb: University of Zagreb, Faculty of Science, 2024. urn:nbn:hr:217:679772
Rukavina, Borja
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Rukavina, B. (2024). Prilozi asimptotičkom modeliranju toka mikropolarnog fluida (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:679772

Rukavina, Borja. "Prilozi asimptotičkom modeliranju toka mikropolarnog fluida." Doctoral thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:679772

Rukavina, Borja. "Prilozi asimptotičkom modeliranju toka mikropolarnog fluida." Doctoral thesis, University of Zagreb, Faculty of Science, 2024. https://urn.nsk.hr/urn:nbn:hr:217:679772

Rukavina, B. (2024). 'Prilozi asimptotičkom modeliranju toka mikropolarnog fluida', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 07 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:679772

Rukavina B. Prilozi asimptotičkom modeliranju toka mikropolarnog fluida [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2024 [cited 2024 December 07] Available at: https://urn.nsk.hr/urn:nbn:hr:217:679772

B. Rukavina, "Prilozi asimptotičkom modeliranju toka mikropolarnog fluida", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:217:679772

Metadata
TitlePrilozi asimptotičkom modeliranju toka mikropolarnog fluida
Title (english)Contributions to asymptotic modelling of the micropolar fluid flow
AuthorBorja Rukavina
MentorIgor Pažanin (mentor)
Committee memberEduard Marušić-Paloka (predsjednik povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
Committee memberMarija Galić (član povjerenstva)
Committee memberMarko Radulović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2024-06-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
Cilj ove disertacije je provesti asimptotičku analizu toka mikropolarnog fluida u fizikalno relevantnim tankim domenama (zakrivljeni kanali, cijevi, sustavi cijevi) i režimima (nestacionarni tok, neizotermni tok, tok s nestandardnim rubnim uvjetima). Najprije predlažemo asimptotičku aproksimaciju za neizoterman tok mikropolarnog fluida u tankom zakrivljenom kanalu koju rigorozno opravdavamo dokazujući ocjenu greške. Zatim dokazujemo egzistenciju i jedinstvenost rješenja inicijalno-rubne zadaće za nestacionarni tok u tankoj cijevi s ne-nul rubnim uvjetom za mikrorotaciju. Temeljem dobivenih rezultata te koristeći homogenizaciju i analizu rubnog sloja, izvodimo asimptotički model višeg reda točnosti koji opisuje efektivno ponašanje fluida u cijevi, te izvodimo ocjenu greške. Konačno, opisujemo problem nestacionarnog toka mikropolarnog fluida u sustavu tankih cijevi. Homogenizacijom te analizom rubnog i unutarnjeg sloja izvodimo asimptotički model proizvoljnog reda točnosti, te dobivenu aproksimaciju rigorozno opravdavamo ocjenom greške.
Abstract (english)
The goal of this dissertation is to perform the asymptotic analysis of the micropolar fluid flow in physically relevant thin domains (curvilinear channels, pipes, pipe systems) and regimes (unsteady flow, non-isothermal flow, flow with non-standard boundary conditions). First, we propose an asymptotic approximation for the non-isothermal flow of a micropolar fluid in a thin curvilinear channel, which we rigorously justify by proving the error estimates. Then we prove the existence and uniqueness of the solution of the initial-boundary problem for the unsteady flow in a thin pipe with a non-zero boundary condition for microrotation. Based on the obtained results and using homogenization and boundary layer analysis, we derive an asymptotic model of a higher order of accuracy that describes the effective behavior of the fluid in the pipe, and prove the error estimates. Finally, we describe the problem of the unsteady flow of a micropolar fluid in a system of thin pipes. Using homogenization and analysis of the boundary and interior layer, we derive an asymptotic model of arbitrary order of accuracy, and rigorously justify the obtained approximation by proving the error estimates.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:679772
Promotion2024
ProjectNumber: IP-2019-04-1140
Title: Višeskalni problemi u mehanici fluida
Title: Multiscale problems in fluid mechanics
Acronym: MultiFM
Leader: Igor Pažanin
Jurisdiction: Croatia
Funder: Hrvatska zaklada za znanost
Funding stream: Research Projects
Study programmeTitle: Doctoral study
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica u području prirodnih znanosti (doktor/doktorica u području prirodnih znanosti)
Type of resourceText
Extentviii, 156 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-06-28 12:25:58