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## Effective flow of incompressible micropolar fluid through a system of thin pipes

Beneš, Michal; Pažanin, Igor
Effective flow of incompressible micropolar fluid through a system of thin pipes // Acta applicandae mathematicae, 143 (2016), 1; 29-43 doi:10.1007/s10440-015-0026-1 (međunarodna recenzija, članak, znanstveni)

Naslov
Effective flow of incompressible micropolar fluid through a system of thin pipes

Autori
Beneš, Michal ; Pažanin, Igor

Izvornik
Acta applicandae mathematicae (0167-8019) 143 (2016), 1; 29-43

Ključne riječi
Micropolar fluid; junction of thin pipes; strong coupling; micropolar Leray problem; asymptotic analysis

Sažetak
In this paper, we consider the incompressible micropolar fluid flowing through a multiple pipe system via asymptotic analysis. Introducing the ratio between pipes thickness and its length as a small parameter $\varepsilon$, we propose an approach leading to a macroscopic model describing the effective flow. In the interior of each pipe (far from the junction), we deduce that the fluid behavior is different depending on the magnitude of viscosity coefficients with respect to $\varepsilon$. In particular, we prove the solvability of the critical case characterized by the strong coupling between velocity and microrotation. In the vicinity of junction, an interior layer is observed so we correct our asymptotic approximation by solving an appropriate micropolar Leray's problem. The error estimates are also derived providing the rigorous mathematical justification of the constructed approximation. We believe that the obtained result could be instrumental for understanding the microstructure effects on the fluid flow in pipe networks.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekt / tema
HRZZ-IP-2013-11-3955 - Matematičko modeliranje i numeričke simulacije procesa u tankim i poroznim sredinama (Eduard Marušić-Paloka, )

Ustanove
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

Autor s matičnim brojem:
Igor Pažanin, (267385)

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

#### Uključenost u ostale bibliografske baze podataka:

• MathSciNet
• Zentrallblatt für Mathematik/Mathematical Abstracts