Prilozi asimptotičkom modeliranju toka mikropolarnog fluida

doctoral thesis

• Title (english): Contributions to asymptotic modelling of the micropolar fluid flow
• Author: Borja Rukavina
• Mentor: Igor Pažanin (mentor)
• Committee member: Eduard Marušić-Paloka (predsjednik povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Committee member: Marija Galić (član povjerenstva)
• Committee member: Marko Radulović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-06-21, 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: mikropolarni fluid; nestacionarni tok
• Keywords (english): micropolar fluid; unsteady flow
• Language: croatian
• URN:NBN: urn:nbn:hr:217:679772
• Promotion: 2024
• Project: Number: 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 programme: Title: 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 resource: Text
• Extent: viii, 156 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-06-28 12:25:58