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

Abdul Rehman; Razmak Bazai; Sallahuddin Achakzai; Saleem Iqbal; Muhammad Naseer

doi:doi:10.11648/j.acm.20150406.15

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

Abdul Rehman, Razmak Bazai, Sallahuddin Achakzai, Saleem Iqbal, Muhammad Naseer

Published in Applied and Computational Mathematics (Volume 4, Issue 6)

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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[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.
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[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.
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[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.
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[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.
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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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TY  - JOUR
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
Y1  - 2015/10/15
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
SP  - 424
EP  - 430
PB  - Science Publishing Group
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

Abdul Rehman

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Razmak Bazai

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Sallahuddin Achakzai

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Saleem Iqbal

Department of Mathematics, University of Balochistan, Quetta, Pakistan
Muhammad Naseer

Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
Y1  - 2015/10/15
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
SP  - 424
EP  - 430
PB  - Science Publishing Group
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  -

Copy | Download