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Symmetry Analysis to f'''+βff''-αf'2=0 Arising in Boundary Layer Theory

Received: 10 September 2013     Published: 20 October 2013
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Abstract

In this paper we analyze the boundary layer equation f^'''+βff^''-α〖f'〗^2=0 using a group theoretical method known as symmetry method. We obtain the symmetry group admitted by the boundary layer equation. We then construct exact invariant solutions and outline a symmetry reduction. The invariant solution is examined under common boundary conditions.

Published in Science Journal of Applied Mathematics and Statistics (Volume 1, Issue 5)
DOI 10.11648/j.sjams.20130105.12
Page(s) 47-49
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), 2013. Published by Science Publishing Group

Keywords

Lie Symmetries, Group-Invariant Solutions, Analytic Solution, Boundary Layer Equation

References
[1] E. Magyari, B. Keller, Exact solutions for self-similary boundary-layer flows induced by permeable stretching walls.Eur. J. Mech. B Fluids 19 (2000) 109–122.
[2] P. Weidman, E. Magyari, Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities, Acta Mech 209, (2010) 353–362.
[3] C.Y. Wang, Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Analysis: Real World Appplications 10 (2009) 375-380.
[4] G. Bognar, Analytic solutions to the boundary layer problem over a stretching wall, Computers and Mathematics with Applications 61 (2011) 2256-2261.
[5] R.B. Kudenatti, V.B. Awati, N.M. Bujurke, Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface, Applied Mathematics and Computation 218 (2011) 2952-2959.
[6] E. Aly, A. Ebaid, On the exact analytical and numerical solutions of Nano boundary layer fluid flows, Hindawi Publishing Corporation, Abstract and Applied Analysis, Vol. 2012 (2012), Article ID 415431, 22 pages.
[7] Z. Belhachmi, B. Brighi, K. Taous, On a family of differential equations for boundary layer approximations in porous media, European J. Appl. Math. 12(2001) 513–528.
[8] S. Liao, I. Pop, Explicit analytic solution for similarity boundary layer equations, International Journal of Heat and Mass Transfer 47 (2004) 75-85.
[9] V.B. Awati, N.M. Bujurke, R.B. Kudenatti, An exponential series method for the solution of free convection boundary layer flow in a saturated porous medium, American Journal of Computational Mathematics 1 (2011) 104-110.
[10] B. Brighi, J.-D. Hoernel, Similarity solutions for high frequency excitation of liquid metal in an antisymmetric magnetic field, in: J.A. Goldstein (Ed.),Self-Similar Solutions of Nonlinear PDE, in: Banach Center Publ., vol. 74, Institute of Mathematics, Polish Academy of Sciences, Warszawa, 2006.
[11] Je-Chiang Tsai, Similarity solutions for liquid metal systems near a 8sharply cornered conductive region, J. Math.Anal. Appl. 355 (2009) 364–384.
[12] G. Bulman, S. Kumei, Symmetries and differential equations, Springer-Verlag, New York, 1989.
[13] J. Olver, Applications of Lie group to differential equations, Springer-Verlag, New York, 1986.
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    Salma Mohammad Al-Tuwairqi, Anisa Mukhtar Hassan. (2013). Symmetry Analysis to f'''+βff''-αf'2=0 Arising in Boundary Layer Theory. Science Journal of Applied Mathematics and Statistics, 1(5), 47-49. https://doi.org/10.11648/j.sjams.20130105.12

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    ACS Style

    Salma Mohammad Al-Tuwairqi; Anisa Mukhtar Hassan. Symmetry Analysis to f'''+βff''-αf'2=0 Arising in Boundary Layer Theory. Sci. J. Appl. Math. Stat. 2013, 1(5), 47-49. doi: 10.11648/j.sjams.20130105.12

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    AMA Style

    Salma Mohammad Al-Tuwairqi, Anisa Mukhtar Hassan. Symmetry Analysis to f'''+βff''-αf'2=0 Arising in Boundary Layer Theory. Sci J Appl Math Stat. 2013;1(5):47-49. doi: 10.11648/j.sjams.20130105.12

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  • @article{10.11648/j.sjams.20130105.12,
      author = {Salma Mohammad Al-Tuwairqi and Anisa Mukhtar Hassan},
      title = {Symmetry Analysis to f'''+βff''-αf'2=0 Arising in Boundary Layer Theory},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {1},
      number = {5},
      pages = {47-49},
      doi = {10.11648/j.sjams.20130105.12},
      url = {https://doi.org/10.11648/j.sjams.20130105.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20130105.12},
      abstract = {In this paper we analyze the boundary layer equation f^'''+βff^''-α〖f'〗^2=0 using a group theoretical method known as symmetry method. We obtain the symmetry group admitted by the boundary layer equation. We then construct exact invariant solutions and outline a symmetry reduction. The invariant solution is examined under common boundary conditions.},
     year = {2013}
    }
    

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    AB  - In this paper we analyze the boundary layer equation f^'''+βff^''-α〖f'〗^2=0 using a group theoretical method known as symmetry method. We obtain the symmetry group admitted by the boundary layer equation. We then construct exact invariant solutions and outline a symmetry reduction. The invariant solution is examined under common boundary conditions.
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Author Information
  • Department of Mathematics, King Abdulaziz University, Jeddah 21551, Saudi Arabia

  • Department of Mathematics, King Abdulaziz University, Jeddah 21551, Saudi Arabia

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