| Issue |
Math. Model. Nat. Phenom.
Volume 17, 2022
|
|
|---|---|---|
| Article Number | 18 | |
| Number of page(s) | 36 | |
| DOI | https://doi.org/10.1051/mmnp/2022005 | |
| Published online | 29 June 2022 | |
Steady state non-Newtonian flow with strain rate dependent viscosity in thin tube structure with no slip boundary condition
1
University of Lyon, UJM, Institute Camille Jordan UMR CNRS 5208, 23 rue P. Michelon, 42023, Saint-Etienne, France
2
Institute of Applied Mathematics, Vilnius University, Naugarduko Str., 24, Vilnius 03225, Lithuania
3
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA
* Corresponding author: grigory.panasenko@univ-st-etienne.fr
Received:
22
October
2021
Accepted:
24
January
2022
The steady state non-Newtonian flow, with strain rate dependent viscosity in a thin tube structure, with no slip boundary condition, is considered. Applying the Banach fixed point theorem we prove the existence and uniqueness of a solution. An asymptotic approximation is constructed and justified by an error estimate.
Mathematics Subject Classification: 35Q35 / 76D07
Key words: Non-Newtonian flow / strain rate dependent viscosity / asymptotic approximation / quasi-Poiseuille flows / boundary layers / method of asymptotic partial decomposition
© The authors. Published by EDP Sciences, 2022
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