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Flow of a Williamson Fluid over a Stretching Sheet Containing Nanoparticles

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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[12] Erickson, L. E., Fan, L. T. and Fox, V. G., Heat and mass transfer in the laminar boundary layer flow of a moving flat surface with constant surface velocity and temperature focusing on the effects of suction/injection. Industrial & Engineering Chemistry Research, 5, 19 (1966).
[13] Gupta, P. S. and Gupta, A. S., Heat and mass transfer on a stretching sheet with suction or blowing. Canadian Journal of Chemical Engineering, 55, No. 6, 744 (1977).
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[15] Nadeem, S., Hussain, A. and Khan, M., HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Communications in Nonlinear Science and Numerical Simulation, 15, No. 3, 475 (2010).
[16] S. Nadeem, Abdul Rehman, K. Vajravelu, Jinho Lee, Changhoon Lee, Axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder, Mathematical Problems in Engineering, Volume 2012, Article ID 378259.
[17] Abdul Rehman, S. Nadeem, Mixed convection heat transfer in micropolar nanofluid over a vertical slender cylinder, Chin. Phy. Lett. 29 (12) (2012) 124701-5.
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[20] S. Nadeem, Abdul Rehman, Axisymmetric stagnation flow of a nanofluid in a moving cylinder, Comp. Math. Mod. 24 (2) (2013) 293-306.
[21] Abdul Rehman, S. Nadeem, M. Y. Malik, Stagnation flow of couple stress nanofluid over an exponentially stretching sheet through a porous medium, J. Power Tech. 93(2) (2013) 122-132.
[22] Abdul Rehman, S. Nadeem, M. Y. Malik, Boundary layer stagnation-point flow of a third-grade fluid over an exponentially stretching sheet, Braz. J. Che. Eng. 30 (3) (2013) 611-618.
[23] Abdul Rehman, S. Nadeem, Heat transfer analysis of the boundary layer flow over a vertical exponentially stretching cylinder, Global J. Sci. Fron. Res. 13(11) (2013) 73-85.
[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.
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[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.
[29] Abdul Rehman, G. Farooq, I. Ahmed, M. Naseer, M. Zulfiqar, Boundary Layer Stagnation-Point Flow of Second Grade Fluid over an Exponentially Stretching Sheet, American J App Math Stat, 3(6) (2015) 211-219.
[30] Abdul Rehmana, S. Achakzai, S. Nadeem, S. Iqbal, Stagnation point flow of Eyring Powell fluid in a vertical cylinder with heat transfer, Journal of Power Technologies 96 (1) (2016) 57–62.
[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.
[32] Naheeda Iftikhar, Abdul Rehman, Peristaltic flow of an Eyring Prandtl fluid in a diverging tube with heat and mass transfer, International Journal of Heat and Mass Transfer 111 (2017) 667–676.
[33] Abdul Rehman, Naveed Sheikh, Boundary Layer Stagnation-Point Flow of Micropolar Fluid over an Exponentially Stretching Sheet, International Journal of Fluid Mechanics & Thermal Sciences, 2017; 3 (3): 25-31.
[34] Haroon Rasheed, Abdul Rehman, Naveed Sheikh, Saleem Iqbal, MHD Boundary Layer Flow of Nanofluid over a Continuously Moving Stretching Surface, Applied and Computational Mathematics, 2017; 6 (6): 265-270.
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Cite This Article
  • 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
  • Department of Mathematics, University of Balochistan, Quetta, Pakistan

  • Department of Mathematics, University of Balochistan, Quetta, Pakistan

  • Department of Mathematics, University of Balochistan, Quetta, Pakistan

  • Department of Mathematics, University of Balochistan, Quetta, Pakistan

  • Department of Mathematics, University of Balochistan, Quetta, Pakistan

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