Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel
Abstract
:1. Introduction
2. Mathematical Formulations
3. Solution Method
4. Rate of Volume Flow
5. Solution of the Problem
6. The Nonlinear System and Its Bifurcation
- ,
- ,
- ,
- .
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
List of Symbols
geometry of the flow channel | dimensionless stream function | ||
U | velocity field | stream function | |
Cartesian coordinate in the fixed frame | dimensionless volume flow rate | ||
dimensionless cartesian coordinate in the wave frame | volume of flow rate | ||
Cartesian coordinate in the wave frame | extra stress tensor | ||
average radius of the tube | shear rate | ||
d | amplitude of a peristaltic wave | material derivative | |
wavelength | gradient of velocity | ||
wave propagation speed | fluid density | ||
time | pressure in the fixed frame | ||
velocity components in the fixed frame | pressure in the wave frame | ||
velocity components in the wave frame | p | dimensionless pressure in the wave frame | |
elocity components in the wave frame | fluid dynamic viscosity | ||
ratio of relaxation to retardation times | retartation time | ||
instantaneous volume of the flow rate in a wave frame | dimensionless volume of the flow rate | ||
instantaneous volume of the flow rate in a fixed frame | dimensionless wave number |
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Thoubaan, M.G.; Al-Khafajy, D.G.S.; Wanas, A.K.; Breaz, D.; Cotîrlă, L.-I. Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel. Symmetry 2024, 16, 1144. https://doi.org/10.3390/sym16091144
Thoubaan MG, Al-Khafajy DGS, Wanas AK, Breaz D, Cotîrlă L-I. Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel. Symmetry. 2024; 16(9):1144. https://doi.org/10.3390/sym16091144
Chicago/Turabian StyleThoubaan, Mary G., Dheia G. Salih Al-Khafajy, Abbas Kareem Wanas, Daniel Breaz, and Luminiţa-Ioana Cotîrlă. 2024. "Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel" Symmetry 16, no. 9: 1144. https://doi.org/10.3390/sym16091144