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Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate

Received: 21 January 2017     Accepted: 6 February 2017     Published: 4 March 2017
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Abstract

In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method with shooting technique for better accuracy. The effects of the governing parameters on the flow and thermal fields are investigated numerically and displayed graphically. The skin-friction coefficient, heat transfer coefficient have also been obtained and presented in tabular form.

Published in Applied and Computational Mathematics (Volume 6, Issue 1)
DOI 10.11648/j.acm.20170601.15
Page(s) 60-67
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), 2017. Published by Science Publishing Group

Keywords

Boundary Layer, Heat Generation, Thermal Radiation, Buoyancy Force, Similarity Solution, Vertical Plate

References
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[3] G. D. Callahan, W. J. Marner, Transient free convection with mass transfer on an isothermal vertical flat plate, Int. J. Heat Mass Transfer 19 (1976) 165–174.
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[17] Ali M. Yeakub, Hossain, M. M. Touhid, Similarity solution for unsteady laminar natural convection boundary layer flow around a vertical heated curvilinear surface, Int.j. of Appl. Math and Stat.(2012)0973_1377.
[18] A. Aziz, A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 1064-1068.
[19] E. Magyari, Comment on “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition” by A. Aziz, Nonlinear Sci. Numer. Simul. 14 2009 1064-1068, Nonlinear Sci. Numer. Simul. (2010), doi:10.1016/j.cnsns.2010.03.020.
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Cite This Article
  • APA Style

    N. M. Ridwan Zahed, Md. Yeakub Ali, Md. Jashim Uddin, Mohammed Nasir Uddin. (2017). Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate. Applied and Computational Mathematics, 6(1), 60-67. https://doi.org/10.11648/j.acm.20170601.15

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    ACS Style

    N. M. Ridwan Zahed; Md. Yeakub Ali; Md. Jashim Uddin; Mohammed Nasir Uddin. Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate. Appl. Comput. Math. 2017, 6(1), 60-67. doi: 10.11648/j.acm.20170601.15

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    AMA Style

    N. M. Ridwan Zahed, Md. Yeakub Ali, Md. Jashim Uddin, Mohammed Nasir Uddin. Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate. Appl Comput Math. 2017;6(1):60-67. doi: 10.11648/j.acm.20170601.15

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  • @article{10.11648/j.acm.20170601.15,
      author = {N. M. Ridwan Zahed and Md. Yeakub Ali and Md. Jashim Uddin and Mohammed Nasir Uddin},
      title = {Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate},
      journal = {Applied and Computational Mathematics},
      volume = {6},
      number = {1},
      pages = {60-67},
      doi = {10.11648/j.acm.20170601.15},
      url = {https://doi.org/10.11648/j.acm.20170601.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170601.15},
      abstract = {In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method with shooting technique for better accuracy. The effects of the governing parameters on the flow and thermal fields are investigated numerically and displayed graphically. The skin-friction coefficient, heat transfer coefficient have also been obtained and presented in tabular form.},
     year = {2017}
    }
    

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    T1  - Possible Similarity Cases for Internal Heat Generation, Thermal Radiation and Free Convection of Unsteady Boundary Layer Flow Over a Vertical Plate
    AU  - N. M. Ridwan Zahed
    AU  - Md. Yeakub Ali
    AU  - Md. Jashim Uddin
    AU  - Mohammed Nasir Uddin
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    N1  - https://doi.org/10.11648/j.acm.20170601.15
    DO  - 10.11648/j.acm.20170601.15
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    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20170601.15
    AB  - In this paper we analyze the effects of free convection for internal heat generation and thermal radiation of an unsteady boundary layer flow over a vertical plate. We have applied free parameter method to obtain possible similarity cases. One of these cases have been investigated analytically and numerically. In this case, the governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta method with shooting technique for better accuracy. The effects of the governing parameters on the flow and thermal fields are investigated numerically and displayed graphically. The skin-friction coefficient, heat transfer coefficient have also been obtained and presented in tabular form.
    VL  - 6
    IS  - 1
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Author Information
  • Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh

  • Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh

  • Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh

  • Department of Mathematics, Chittagong University of Engineering & Technology, Chittagong, Bangladesh

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