Flow in a two dimensional channel with deforming and peristaltically moving walls

In this paper, effects of deforming walls on peristaltic flow in a two dimensional channel have been investigated. The two dimensional form of the governing equations is simplified by using appropriate transformations and well established approximations, which are used extensively for solution of su...

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Published in:SN applied sciences Vol. 1; no. 12; p. 1534
Main Authors: Laila, Roohi, Khan Marwat, Dil Nawaz, Khan, Kamran, Ali, Aamir, Shah, Zahir
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2019
Springer Nature B.V
Subjects:
Applied and Technical Physics
Approximation
Chemistry/Food Science
Computational Fluid Dynamics and Fluid Interaction
Deformation
Deformation effects
Differential equations
Earth Sciences
Engineering
Engineering: Fluid Mechanics
Environment
Fluid flow
Geometry
Magnetic fields
Materials Science
Moving walls
Perturbation methods
Research Article
Reynolds number
Shear stress
Transformations (mathematics)
Two dimensional flow
Variables
Velocity
Velocity distribution
Viscosity
Surface deformation
Peristaltic pumping
ISSN:2523-3963, 2523-3971
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Abstract In this paper, effects of deforming walls on peristaltic flow in a two dimensional channel have been investigated. The two dimensional form of the governing equations is simplified by using appropriate transformations and well established approximations, which are used extensively for solution of such models. The transformations are designed so that the complex problem is reduced into an ordinary differential equation (ODE). New and simple non-linear ODE is formed in view of adopted procedures and techniques. Its solutions are exactly matched with the solutions of classical problems. Solutions of the final problem are provided for small values of the surface expansion (contraction) ratio and Reynolds number with the help of the perturbation technique and non-linear shooting method. The velocity field, pressure and shear stress are evaluated analytically and numerically. Meanwhile, effects of all parameters are observed on the velocity field, pressure rise per wavelength and shear stress profiles with the help of tables and different figures. Excellent agreement between solutions is found. Current results are apparently matched with the classical problems of peristaltic flow in deforming and non-deforming walls.
AbstractList In this paper, effects of deforming walls on peristaltic flow in a two dimensional channel have been investigated. The two dimensional form of the governing equations is simplified by using appropriate transformations and well established approximations, which are used extensively for solution of such models. The transformations are designed so that the complex problem is reduced into an ordinary differential equation (ODE). New and simple non-linear ODE is formed in view of adopted procedures and techniques. Its solutions are exactly matched with the solutions of classical problems. Solutions of the final problem are provided for small values of the surface expansion (contraction) ratio and Reynolds number with the help of the perturbation technique and non-linear shooting method. The velocity field, pressure and shear stress are evaluated analytically and numerically. Meanwhile, effects of all parameters are observed on the velocity field, pressure rise per wavelength and shear stress profiles with the help of tables and different figures. Excellent agreement between solutions is found. Current results are apparently matched with the classical problems of peristaltic flow in deforming and non-deforming walls.
ArticleNumber 1534
Author Shah, Zahir
Ali, Aamir
Khan, Kamran
Khan Marwat, Dil Nawaz
Laila, Roohi
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  givenname: Dil Nawaz
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  organization: Department of Mathematics, Faculty of Technology and Engineering Sciences, Islamia College Peshawar
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  organization: Department of Mathematics, Faculty of Technology and Engineering Sciences, Islamia College Peshawar
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  givenname: Aamir
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  organization: Department of Mathematics, COMSATS University Islamabad
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  organization: Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)
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Cites_doi 10.1017/S0022112071000958
10.1142/S0219887818501815
10.1088/0253-6102/70/5/534
10.1146/annurev.fl.03.010171.000305
10.1016/j.matcom.2017.12.009
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Peristaltic pumping
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Snippet In this paper, effects of deforming walls on peristaltic flow in a two dimensional channel have been investigated. The two dimensional form of the governing...
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SubjectTerms Applied and Technical Physics
Approximation
Chemistry/Food Science
Computational Fluid Dynamics and Fluid Interaction
Deformation
Deformation effects
Differential equations
Earth Sciences
Engineering
Engineering: Fluid Mechanics
Environment
Fluid flow
Geometry
Magnetic fields
Materials Science
Moving walls
Perturbation methods
Research Article
Reynolds number
Shear stress
Transformations (mathematics)
Two dimensional flow
Variables
Velocity
Velocity distribution
Viscosity
Title Flow in a two dimensional channel with deforming and peristaltically moving walls
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