Applied Engineering

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Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method

Received: 13 October 2023    Accepted: 31 October 2023    Published: 11 November 2023
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Abstract

The present study involves a numerical investigation of laminar boundary layer flow over a flat plate, controlled by the Prandtl equations. The flow is governed by a dimensionless third-order system of nonlinear ordinary differential equations. The finite difference method is employed to solve the system, which serves as an approximation technique. The study explores the properties of the finite difference method and discusses its efficacy in solving the boundary layer flow problem. Additionally, we discuss an inverse problem related to the Falkner-Skan equation, aiming to obtain precise values for the second derivative's initial value. This inverse problem is successfully resolved using an appropriate initial value procedure. The results obtained from the finite difference method and the inverse problem resolution is compared with those from cubic spline interpolation, proposed by Alavi and Aminikhan. By doing so, the reliability and accuracy of present approach is demonstrated. Overall, this study contributes to a better understanding of boundary layer flow and presents a viable numerical technique for tackling similar fluid dynamics problems. The findings shed light on the significance of choosing appropriate numerical methods for solving complex systems of equations in fluid mechanics.

DOI 10.11648/j.ae.20230702.11
Published in Applied Engineering (Volume 7, Issue 2, December 2023)
Page(s) 27-36
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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), 2024. Published by Science Publishing Group

Keywords

Boundary Layer Flow, Falkner-Skan Equation, Finite Difference Method

References
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[27] 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.
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Cite This Article
  • APA Style

    Rafiq, M., Rehman, A., Sheikh, N., Saleem, M., Umar Farooq, M. (2023). Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method. Applied Engineering, 7(2), 27-36. https://doi.org/10.11648/j.ae.20230702.11

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    ACS Style

    Rafiq, M.; Rehman, A.; Sheikh, N.; Saleem, M.; Umar Farooq, M. Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method. Appl. Eng. 2023, 7(2), 27-36. doi: 10.11648/j.ae.20230702.11

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    AMA Style

    Rafiq M, Rehman A, Sheikh N, Saleem M, Umar Farooq M. Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method. Appl Eng. 2023;7(2):27-36. doi: 10.11648/j.ae.20230702.11

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  • @article{10.11648/j.ae.20230702.11,
      author = {Muhammad Rafiq and Abdul Rehman and Naveed Sheikh and Muhammad Saleem and Muhammad Umar Farooq},
      title = {Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method},
      journal = {Applied Engineering},
      volume = {7},
      number = {2},
      pages = {27-36},
      doi = {10.11648/j.ae.20230702.11},
      url = {https://doi.org/10.11648/j.ae.20230702.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ae.20230702.11},
      abstract = {The present study involves a numerical investigation of laminar boundary layer flow over a flat plate, controlled by the Prandtl equations. The flow is governed by a dimensionless third-order system of nonlinear ordinary differential equations. The finite difference method is employed to solve the system, which serves as an approximation technique. The study explores the properties of the finite difference method and discusses its efficacy in solving the boundary layer flow problem. Additionally, we discuss an inverse problem related to the Falkner-Skan equation, aiming to obtain precise values for the second derivative's initial value. This inverse problem is successfully resolved using an appropriate initial value procedure. The results obtained from the finite difference method and the inverse problem resolution is compared with those from cubic spline interpolation, proposed by Alavi and Aminikhan. By doing so, the reliability and accuracy of present approach is demonstrated. Overall, this study contributes to a better understanding of boundary layer flow and presents a viable numerical technique for tackling similar fluid dynamics problems. The findings shed light on the significance of choosing appropriate numerical methods for solving complex systems of equations in fluid mechanics.
    },
     year = {2023}
    }
    

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    T1  - Numerical Study of the Boundary Layer Flow Problem over a Flat Plate by Finite Difference Method
    AU  - Muhammad Rafiq
    AU  - Abdul Rehman
    AU  - Naveed Sheikh
    AU  - Muhammad Saleem
    AU  - Muhammad Umar Farooq
    Y1  - 2023/11/11
    PY  - 2023
    N1  - https://doi.org/10.11648/j.ae.20230702.11
    DO  - 10.11648/j.ae.20230702.11
    T2  - Applied Engineering
    JF  - Applied Engineering
    JO  - Applied Engineering
    SP  - 27
    EP  - 36
    PB  - Science Publishing Group
    SN  - 2994-7456
    UR  - https://doi.org/10.11648/j.ae.20230702.11
    AB  - The present study involves a numerical investigation of laminar boundary layer flow over a flat plate, controlled by the Prandtl equations. The flow is governed by a dimensionless third-order system of nonlinear ordinary differential equations. The finite difference method is employed to solve the system, which serves as an approximation technique. The study explores the properties of the finite difference method and discusses its efficacy in solving the boundary layer flow problem. Additionally, we discuss an inverse problem related to the Falkner-Skan equation, aiming to obtain precise values for the second derivative's initial value. This inverse problem is successfully resolved using an appropriate initial value procedure. The results obtained from the finite difference method and the inverse problem resolution is compared with those from cubic spline interpolation, proposed by Alavi and Aminikhan. By doing so, the reliability and accuracy of present approach is demonstrated. Overall, this study contributes to a better understanding of boundary layer flow and presents a viable numerical technique for tackling similar fluid dynamics problems. The findings shed light on the significance of choosing appropriate numerical methods for solving complex systems of equations in fluid mechanics.
    
    VL  - 7
    IS  - 2
    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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