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Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder

Received: 14 September 2015     Accepted: 26 September 2015     Published: 15 October 2015
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Abstract

The current paper offers an analysis of the steady boundary layer flow and heat transfer of a non-Newtonian micropolar fluid flowing through a vertical exponentially stretching cylinder along its axial axis. The obtained system of nonlinear partial differential equations along with the appropriate boundary conditions is abridged to dimensionless form by means of the boundary layer estimates and a suitable similarity transformation. The subsequent nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved numerically with the help of Keller-box method. The effects of the involved parameters are presented through graphs. The allied physical features for the flow and heat transfer characteristics that is the skinfriction coefficient and Nusselt numbers are presented for different parameters.

Published in Applied and Computational Mathematics (Volume 4, Issue 6)
DOI 10.11648/j.acm.20150406.15
Page(s) 424-430
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), 2015. Published by Science Publishing Group

Keywords

Boundary Layer Flow, Vertical Cylinder, Micropolar Fluid, Heat Dissipation, Keller-Box Method

References
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[2] H. Rosali, A. Ishak, I. Pop, Micropolar fluid flow towards a stretching/shrinking sheet in a porous medium with suction, Int. Commun. Heat Mass Tran. 39 (2012) 826-829.
[3] H. A. Attia, Heat transfer in a stagnation point flow of a micropolar fluid over a stretching surface with heat generation/absorption, Tamkang J. Sci. Eng. 9 (4) (2006) 299-305.
[4] R. Nazar, A. Ishak, I. Pop, Unsteady boundary layer flow over a stretching sheet in a micropolar fluid, Int. J. Eng. App. Sci. 4 (7) (2008) 406-410.
[5] S. Nadeem, Abdul Rehman, K. Vajravelu, J. Lee, C. Lee, Axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder, Math. Prob. Eng. Volume 2012 (2012), Article ID 378259, 17 pages, doi:10.1155/2012/378259.
[6] S. Nadeem, N. S. Akbar, M. Y. Malik, Exact and numerical solutions of a micropolar fluid in a vertical Annulus, Num. Meth. Part. Diff. Equ. 26 (2010) 1660-1674.
[7] A. Ishak, R. Nazar, I. Pop, Magnetohydrodynamic stagnation point flow towards a stretching vertical sheet in a micropolar fluid, Magnetohydrodynamics, 43 (1) (2007) 83-97.
[8] A. Ishak, R. Nazar, I. Pop, Heat transfer over a stretching surface with variable surface heat flux in micropolar fluids, Phys. Lett. A, 372 (2008) 559-561.
[9] S. Nadeem, M. Hussain, M. Naz, MHD Stagnation flow of a micropolar fluid through porous medium, Meccanica 45 (2010) 869-880.
[10] S. Nadeem, S. Abbasbandy, M. Hussain, Series solutions of boundary layer flow of a Micropolar fluid near the stagnation point towards a shrinking sheet, Zeitschrift fur Naturforschung. 64a (2009) 575-582.
[11] N. Bachok, A. Ishak, Flow and heat transfer over a stretching cylinder with prescribed surface heat flux, Malaysian Journal of Mathematical Sciences 4 (2) (2010) 159-169.
[12] T. G. Fang, J. Zhang, Y. F. Zhong, H. Tao, Unsteady viscous flow over an expanding stretching cylinder, Chin. Phys. Lett. 28 (12) (2011) 124707-1-4.
[13] T. Fang, S. Yao, Viscous swirling flow over a stretching cylinder, Chin. Phys. Lett. 28 (11) (2011) 114702-1-4.
[14] C. Y. Wang, Natural convection on a vertical stretching cylinder, Commun. Nonlinear Sci. Numer. Simulat, 17 (2012) 1098-1103.
[15] B. J. Gireesha, B. Mahanthesh, P. T. Manjunatha, R. S. R. Gorla, Numerical solution for hydromagnetic boundary layer flow and heat transfer past a stretching surface embedded in non-Darcy porous medium with fluid-particle suspension, J. Nigerian Math. Society, doi:10.1016/j.jnnms.2015.07.003.
[16] S. Mukhopadhyay, MHD boundary layer slip flow along a stretching cylinder, Ain Shams Eng. J. 4(2) (2013) 317-324.
[17] Abdul Rehman, S. Nadeem, Heat Transfer Analysis of the Boundary Layer Flow over a Vertical Exponentially Stretching Cylinder, Global J. Sci. Frontier Res. Math. Decision Sci. 13(11) (2013) 73-85.
[18] Abdul Rehman, S. Nadeem, S. Iqbal, M. Y. Malik, M. Naseer, Nanoparticle effect over the boundary layer flow over an exponentially stretching cylinder, Proc IMechE Part N: J Nanoengineering and Nanosystems, (2014) 1-6.
[19] M. Naseer, M. Y. Malik, Abdul Rehman, Numerical Study of Convective Heat Transfer on the Power Law Fluid over a Vertical Exponentially Stretching Cylinder, Applied and Comp.Math. 4(5) (2015) 346-350.
[20] X. Si, Lin Li, L. Zheng, X. Zhang, B. Liu, The exterior unsteady viscous flow and heat transfer due to a porous expanding stretching cylinder, Computers & Fluids, 105(10) (2014) 280-284.
[21] K. Vajravelu, K. V. Prasad, S. R. Santhi, Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder, App. Math. Comp. 219(8) (2012) 3993-4005.
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Cite This Article
  • APA Style

    Abdul Rehman, Razmak Bazai, Sallahuddin Achakzai, Saleem Iqbal, Muhammad Naseer. (2015). Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder. Applied and Computational Mathematics, 4(6), 424-430. https://doi.org/10.11648/j.acm.20150406.15

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    ACS Style

    Abdul Rehman; Razmak Bazai; Sallahuddin Achakzai; Saleem Iqbal; Muhammad Naseer. Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder. Appl. Comput. Math. 2015, 4(6), 424-430. doi: 10.11648/j.acm.20150406.15

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    AMA Style

    Abdul Rehman, Razmak Bazai, Sallahuddin Achakzai, Saleem Iqbal, Muhammad Naseer. Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder. Appl Comput Math. 2015;4(6):424-430. doi: 10.11648/j.acm.20150406.15

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  • @article{10.11648/j.acm.20150406.15,
      author = {Abdul Rehman and Razmak Bazai and Sallahuddin Achakzai and Saleem Iqbal and Muhammad Naseer},
      title = {Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder},
      journal = {Applied and Computational Mathematics},
      volume = {4},
      number = {6},
      pages = {424-430},
      doi = {10.11648/j.acm.20150406.15},
      url = {https://doi.org/10.11648/j.acm.20150406.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150406.15},
      abstract = {The current paper offers an analysis of the steady boundary layer flow and heat transfer of a non-Newtonian micropolar fluid flowing through a vertical exponentially stretching cylinder along its axial axis. The obtained system of nonlinear partial differential equations along with the appropriate boundary conditions is abridged to dimensionless form by means of the boundary layer estimates and a suitable similarity transformation. The subsequent nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved numerically with the help of Keller-box method. The effects of the involved parameters are presented through graphs. The allied physical features for the flow and heat transfer characteristics that is the skinfriction coefficient and Nusselt numbers are presented for different parameters.},
     year = {2015}
    }
    

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    T1  - Boundary Layer Flow and Heat Transfer of Micropolar Fluid over a Vertical Exponentially Stretched Cylinder
    AU  - Abdul Rehman
    AU  - Razmak Bazai
    AU  - Sallahuddin Achakzai
    AU  - Saleem Iqbal
    AU  - Muhammad Naseer
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    PY  - 2015
    N1  - https://doi.org/10.11648/j.acm.20150406.15
    DO  - 10.11648/j.acm.20150406.15
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20150406.15
    AB  - The current paper offers an analysis of the steady boundary layer flow and heat transfer of a non-Newtonian micropolar fluid flowing through a vertical exponentially stretching cylinder along its axial axis. The obtained system of nonlinear partial differential equations along with the appropriate boundary conditions is abridged to dimensionless form by means of the boundary layer estimates and a suitable similarity transformation. The subsequent nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved numerically with the help of Keller-box method. The effects of the involved parameters are presented through graphs. The allied physical features for the flow and heat transfer characteristics that is the skinfriction coefficient and Nusselt numbers are presented for different parameters.
    VL  - 4
    IS  - 6
    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, Quaid-i-Azam University, Islamabad, Pakistan

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