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## A note on the Kirchhoff's junction rule for power-law fluids

Marušić-Paloka, Eduard; Pažanin, Igor
A note on the Kirchhoff's junction rule for power-law fluids // Zeitschrift für Naturforschung. A, A journal of physical sciences, 70 (2015), 9; 695-702 doi:10.1515/zna-2015-0148 (međunarodna recenzija, članak, znanstveni)

Naslov
A note on the Kirchhoff's junction rule for power-law fluids

Autori
Marušić-Paloka, Eduard ; Pažanin, Igor

Izvornik
Zeitschrift für Naturforschung. A, A journal of physical sciences (0932-0784) 70 (2015), 9; 695-702

Ključne riječi
Power-law fluid; junction of thin pipes; Kirchhoff's law; matched asymptotic solution

Sažetak
We study a multiple pipe system filled with non- Newtonian fluid being in stationary regime and obeying the power-law. Introducing the small parameter $\varepsilon$, being the ratio between the cross-section area and the length of the pipes, we find the effective flow via singular perturbation as $\varespilon$ tends to zero. The flow in each pipe of the system remains in the power-law Poiseuille form governed by the pressure drop between pipe's end and the junction. The Kirchhoff's law providing the value of pressure at the junction point is derived and its solvability is discussed. In the vicinity of junction, an interior layer appears so we correct the asymptotic solution by introducing a non-Newtonian Leray's problem. The error analysis is also provided.

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

#### 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