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.
| Published in | Applied Engineering (Volume 7, Issue 2) |
| DOI | 10.11648/j.ae.20230702.11 |
| Page(s) | 27-36 |
| 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), 2024. Published by Science Publishing Group |
Boundary Layer Flow, Falkner-Skan Equation, Finite Difference Method
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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
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
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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Download@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}
}
TY - JOUR 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 -
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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