Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles

Farah Deba; Abdul Rehman; Zahida Khan; Saleem Iqbal; Naveed Sheikh

doi:doi:10.11648/j.ijse.20210501.12

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Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles

Farah Deba, Abdul Rehman, Zahida Khan, Saleem Iqbal, Naveed Sheikh

Published in International Journal of Systems Engineering (Volume 5, Issue 1)

Received: 18 November 2020 Accepted: 14 April 2021 Published: 30 April 2021

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Abstract

In this article, an attempt has been made to study the behavior of non-Newtonian viscoelastic model of a Williamson fluid flow problem containing nanoparticles and is assumed to be flowing over a stretching sheet stretched along its surface in both directions with the same constant surface stretching velocity. The boundary layer governing equations of the conservation of mass, conservation of linear momentum and the energy are first modeled into a set of nonlinear coupled partial differential equations along with the appropriate boundary conditions. A numerical study of impact of nanofluid flow over a stretching sheet is tabulated. The basic equations of Williamson fluid are modeled with the help of Navier-Stokes equations for momentum and heat transfer. With the assistance of appropriate similarity transformations these pair of PEDs is transformed into up-to-date system of coupled nonlinear ODEs. These transformed systems of equations are evaluated numerically with the assistance of shooting method using forth order. The dominant physical properties for system of equations of the model that is wall shear stress, and the coefficient of skin friction are acquired. The behavior of nondimensional velocity and thermal flow profiles are discussed for the important involved dimensionless parameters like the Williamson fluid parameter and the nanoparticles volume fraction through tables and graphs.

Published in	International Journal of Systems Engineering (Volume 5, Issue 1)
DOI	10.11648/j.ijse.20210501.12
Page(s)	13-17
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Boundary Layer Flow, Williamson Fluid, Nanoparticles, Stretching Sheet

References

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[24]	M. Y. Malik, M. Naseer, S. Nadeem, Abdul Rehman, The boundary layer flow of Casson nanofluid over a vertical exponentially stretching cylinder, Appl. NanoSci. DOI: 10.1007/s13204-012-0267-0
[25]	Abdul Rehman, S. Nadeem, S. Iqbal, M. Y. Malik, M. Naseer, Nanoparticle effect over the boundary layer flow over an exponentially stretching cylinder, J. NanoEngineering and NanoSystems (2014) 1-6.
[26]	M. Y. Malik, M. Naseer, S. Nadeem, Abdul Rehman, The boundary layer flow of hyperbolic tangent fluid over a vertical exponentially stretching cylinder, Alexandria Eng. J., 53 (2014) 747-750.
[27]	M. Y. Malik, M. Naseer, Abdul Rehman, Numerical study of convective heat transfer on the Power Law fluid over a vertical exponentially stretching cylinder, App Comp Math, 4(5), (2015) 346-350.
[28]	Abdul Rehman, R. Bazai, S. Achakzai, S. Iqbal, M. Naseer, Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder, App Comp Math, 4(6) (2015) 424-430.
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[31]	Abdul Rehman, Saleem Iqbal, Syed Mohsin Raza, Axisymmetric Stagnation Flow of a Micropolar Fluid in a Moving Cylinder: An Analytical Solution, Fluid Mechanics, 2(1) (2016) 1-7.
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[38]	Amina Panezai, Abdul Rehman, Naveed Sheikh, Saleem Iqbal, Israr Ahmed, Manzoor Iqbal, Muhammad Zulfiqar, Mixed Convective Magnetohydrodynamic Heat Transfer Flow of Williamson Fluid Over a Porous Wedge, American Journal of Mathematical and Computer Modelling, 4(3) (2019) 66-73.
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APA Style

Farah Deba, Abdul Rehman, Zahida Khan, Saleem Iqbal, Naveed Sheikh. (2021). Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles. International Journal of Systems Engineering, 5(1), 13-17. https://doi.org/10.11648/j.ijse.20210501.12

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ACS Style

Farah Deba; Abdul Rehman; Zahida Khan; Saleem Iqbal; Naveed Sheikh. Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles. Int. J. Syst. Eng. 2021, 5(1), 13-17. doi: 10.11648/j.ijse.20210501.12

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AMA Style

Farah Deba, Abdul Rehman, Zahida Khan, Saleem Iqbal, Naveed Sheikh. Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles. Int J Syst Eng. 2021;5(1):13-17. doi: 10.11648/j.ijse.20210501.12

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@article{10.11648/j.ijse.20210501.12,
  author = {Farah Deba and Abdul Rehman and Zahida Khan and Saleem Iqbal and Naveed Sheikh},
  title = {Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles},
  journal = {International Journal of Systems Engineering},
  volume = {5},
  number = {1},
  pages = {13-17},
  doi = {10.11648/j.ijse.20210501.12},
  url = {https://doi.org/10.11648/j.ijse.20210501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijse.20210501.12},
  abstract = {In this article, an attempt has been made to study the behavior of non-Newtonian viscoelastic model of a Williamson fluid flow problem containing nanoparticles and is assumed to be flowing over a stretching sheet stretched along its surface in both directions with the same constant surface stretching velocity. The boundary layer governing equations of the conservation of mass, conservation of linear momentum and the energy are first modeled into a set of nonlinear coupled partial differential equations along with the appropriate boundary conditions. A numerical study of impact of nanofluid flow over a stretching sheet is tabulated. The basic equations of Williamson fluid are modeled with the help of Navier-Stokes equations for momentum and heat transfer. With the assistance of appropriate similarity transformations these pair of PEDs is transformed into up-to-date system of coupled nonlinear ODEs. These transformed systems of equations are evaluated numerically with the assistance of shooting method using forth order. The dominant physical properties for system of equations of the model that is wall shear stress, and the coefficient of skin friction are acquired. The behavior of nondimensional velocity and thermal flow profiles are discussed for the important involved dimensionless parameters like the Williamson fluid parameter and the nanoparticles volume fraction through tables and graphs.},
 year = {2021}
}

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TY  - JOUR
T1  - Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles
AU  - Farah Deba
AU  - Abdul Rehman
AU  - Zahida Khan
AU  - Saleem Iqbal
AU  - Naveed Sheikh
Y1  - 2021/04/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ijse.20210501.12
DO  - 10.11648/j.ijse.20210501.12
T2  - International Journal of Systems Engineering
JF  - International Journal of Systems Engineering
JO  - International Journal of Systems Engineering
SP  - 13
EP  - 17
PB  - Science Publishing Group
SN  - 2640-4230
UR  - https://doi.org/10.11648/j.ijse.20210501.12
AB  - In this article, an attempt has been made to study the behavior of non-Newtonian viscoelastic model of a Williamson fluid flow problem containing nanoparticles and is assumed to be flowing over a stretching sheet stretched along its surface in both directions with the same constant surface stretching velocity. The boundary layer governing equations of the conservation of mass, conservation of linear momentum and the energy are first modeled into a set of nonlinear coupled partial differential equations along with the appropriate boundary conditions. A numerical study of impact of nanofluid flow over a stretching sheet is tabulated. The basic equations of Williamson fluid are modeled with the help of Navier-Stokes equations for momentum and heat transfer. With the assistance of appropriate similarity transformations these pair of PEDs is transformed into up-to-date system of coupled nonlinear ODEs. These transformed systems of equations are evaluated numerically with the assistance of shooting method using forth order. The dominant physical properties for system of equations of the model that is wall shear stress, and the coefficient of skin friction are acquired. The behavior of nondimensional velocity and thermal flow profiles are discussed for the important involved dimensionless parameters like the Williamson fluid parameter and the nanoparticles volume fraction through tables and graphs.
VL  - 5
IS  - 1
ER  -

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Author Information

Farah Deba

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Abdul Rehman

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Zahida Khan

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Saleem Iqbal

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Naveed Sheikh

Department of Mathematics, University of Balochistan, Quetta, Pakistan

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Plain Text BibTeX RIS

APA Style

Farah Deba, Abdul Rehman, Zahida Khan, Saleem Iqbal, Naveed Sheikh. (2021). Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles. International Journal of Systems Engineering, 5(1), 13-17. https://doi.org/10.11648/j.ijse.20210501.12

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ACS Style

Farah Deba; Abdul Rehman; Zahida Khan; Saleem Iqbal; Naveed Sheikh. Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles. Int. J. Syst. Eng. 2021, 5(1), 13-17. doi: 10.11648/j.ijse.20210501.12

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AMA Style

Farah Deba, Abdul Rehman, Zahida Khan, Saleem Iqbal, Naveed Sheikh. Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles. Int J Syst Eng. 2021;5(1):13-17. doi: 10.11648/j.ijse.20210501.12

Copy | Download

@article{10.11648/j.ijse.20210501.12,
  author = {Farah Deba and Abdul Rehman and Zahida Khan and Saleem Iqbal and Naveed Sheikh},
  title = {Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles},
  journal = {International Journal of Systems Engineering},
  volume = {5},
  number = {1},
  pages = {13-17},
  doi = {10.11648/j.ijse.20210501.12},
  url = {https://doi.org/10.11648/j.ijse.20210501.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijse.20210501.12},
  abstract = {In this article, an attempt has been made to study the behavior of non-Newtonian viscoelastic model of a Williamson fluid flow problem containing nanoparticles and is assumed to be flowing over a stretching sheet stretched along its surface in both directions with the same constant surface stretching velocity. The boundary layer governing equations of the conservation of mass, conservation of linear momentum and the energy are first modeled into a set of nonlinear coupled partial differential equations along with the appropriate boundary conditions. A numerical study of impact of nanofluid flow over a stretching sheet is tabulated. The basic equations of Williamson fluid are modeled with the help of Navier-Stokes equations for momentum and heat transfer. With the assistance of appropriate similarity transformations these pair of PEDs is transformed into up-to-date system of coupled nonlinear ODEs. These transformed systems of equations are evaluated numerically with the assistance of shooting method using forth order. The dominant physical properties for system of equations of the model that is wall shear stress, and the coefficient of skin friction are acquired. The behavior of nondimensional velocity and thermal flow profiles are discussed for the important involved dimensionless parameters like the Williamson fluid parameter and the nanoparticles volume fraction through tables and graphs.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles
AU  - Farah Deba
AU  - Abdul Rehman
AU  - Zahida Khan
AU  - Saleem Iqbal
AU  - Naveed Sheikh
Y1  - 2021/04/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ijse.20210501.12
DO  - 10.11648/j.ijse.20210501.12
T2  - International Journal of Systems Engineering
JF  - International Journal of Systems Engineering
JO  - International Journal of Systems Engineering
SP  - 13
EP  - 17
PB  - Science Publishing Group
SN  - 2640-4230
UR  - https://doi.org/10.11648/j.ijse.20210501.12
AB  - In this article, an attempt has been made to study the behavior of non-Newtonian viscoelastic model of a Williamson fluid flow problem containing nanoparticles and is assumed to be flowing over a stretching sheet stretched along its surface in both directions with the same constant surface stretching velocity. The boundary layer governing equations of the conservation of mass, conservation of linear momentum and the energy are first modeled into a set of nonlinear coupled partial differential equations along with the appropriate boundary conditions. A numerical study of impact of nanofluid flow over a stretching sheet is tabulated. The basic equations of Williamson fluid are modeled with the help of Navier-Stokes equations for momentum and heat transfer. With the assistance of appropriate similarity transformations these pair of PEDs is transformed into up-to-date system of coupled nonlinear ODEs. These transformed systems of equations are evaluated numerically with the assistance of shooting method using forth order. The dominant physical properties for system of equations of the model that is wall shear stress, and the coefficient of skin friction are acquired. The behavior of nondimensional velocity and thermal flow profiles are discussed for the important involved dimensionless parameters like the Williamson fluid parameter and the nanoparticles volume fraction through tables and graphs.
VL  - 5
IS  - 1
ER  -

Copy | Download