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Volume 16
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10.3390/sym16091144
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Article

Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel

by
Mary G. Thoubaan
1,†,
Dheia G. Salih Al-Khafajy
1,†,
Abbas Kareem Wanas
1,*,†,
Daniel Breaz
2,† and
Luminiţa-Ioana Cotîrlă
3,†
1
Department of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58001, Al-Qadisiyah, Iraq
2
Department of Mathematics, “1 Decembrie 1918” University of Alba-Iulia, 510009 Alba-Iulia, Romania
3
Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2024, 16(9), 1144; https://doi.org/10.3390/sym16091144
Submission received: 25 June 2024 / Revised: 22 July 2024 / Accepted: 24 July 2024 / Published: 3 September 2024
(This article belongs to the Special Issue Recent Advances in Mathematical Aspect in Engineering—Second Edition)
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Abstract

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters.
Keywords: Jeffrey fluid; peristaltic flow; streamline topologies; Hartman–Grobman theorem; stability; parameter space; bifurcation Jeffrey fluid; peristaltic flow; streamline topologies; Hartman–Grobman theorem; stability; parameter space; bifurcation

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MDPI and ACS Style

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

AMA Style

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 Style

Thoubaan, 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

APA Style

Thoubaan, M. G., Al-Khafajy, D. G. S., Wanas, A. K., Breaz, D., & Cotîrlă, L.-I. (2024). Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel. Symmetry, 16(9), 1144. https://doi.org/10.3390/sym16091144

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