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Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling

Received: 13 May 2014     Accepted: 27 May 2014     Published: 30 May 2014
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Abstract

In this paper, the combined effects of variable viscosity, Brownian motion, thermophoresis and convective cooling on unsteady flow of nanofluids in a pipe with permeable wall are investigated. It is assumed that the pipe surface exchange heat with the ambient following the Newton’s law of cooling. Using a semi discretization finite difference method coupled with Runge-Kutta Fehlberg integration scheme, the nonlinear governing equations of momentum and energy balance, and the equation for nanoparticles concentration are tackled numerically. Useful results for the velocity, temperature, nanoparticles concentration profiles, skin friction and Nusselt number are obtained graphically and discussed quantitatively.

Published in Applied and Computational Mathematics (Volume 3, Issue 3)
DOI 10.11648/j.acm.20140303.12
Page(s) 75-84
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), 2014. Published by Science Publishing Group

Keywords

Porous Pipe Flow, Variable Viscosity, Nanofluids, Heat Transfer, Convective Cooling

References
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[6] Mutuku-Njane, W. N., Makinde, O. D., (2014), Hydromagnetic bioconvection of nanofluid over a permeable vertical plate due to gy-rotactic microorganisms, Comp. Fluids, 95, pp. 88–97.
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[13] Makinde, O. D., (2013), Effects of viscous dissipation and New-tonian heating on boundary layer flow of nanofluids over a flat plate, Int. J. Num. Meth. Heat and Fluid flow 23, pp. 1291-1303.
[14] Makinde, O. D., Khamis, S. A., Tshehla, M. S., Franks, O. (2014), Analysis of Heat Transfer in Berman Flow of Nanofluids with Navier Slip, Viscous Dissipa-tion, and Convective Cooling, Adv. Math. Phys., 2014, 13 pages.
[15] Makinde, O. D., (2013), Computational modelling of nanofluids flow over a convectively heated unsteady stretching sheet, Curr. Nanoscience, 9, pp. 673-678.
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Cite This Article
  • APA Style

    Sara Khamis, Oluwole Daniel Makinde, Yaw Nkansah-Gyekye. (2014). Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling. Applied and Computational Mathematics, 3(3), 75-84. https://doi.org/10.11648/j.acm.20140303.12

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    ACS Style

    Sara Khamis; Oluwole Daniel Makinde; Yaw Nkansah-Gyekye. Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling. Appl. Comput. Math. 2014, 3(3), 75-84. doi: 10.11648/j.acm.20140303.12

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    AMA Style

    Sara Khamis, Oluwole Daniel Makinde, Yaw Nkansah-Gyekye. Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling. Appl Comput Math. 2014;3(3):75-84. doi: 10.11648/j.acm.20140303.12

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  • @article{10.11648/j.acm.20140303.12,
      author = {Sara Khamis and Oluwole Daniel Makinde and Yaw Nkansah-Gyekye},
      title = {Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {3},
      pages = {75-84},
      doi = {10.11648/j.acm.20140303.12},
      url = {https://doi.org/10.11648/j.acm.20140303.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140303.12},
      abstract = {In this paper, the combined effects of variable viscosity, Brownian motion, thermophoresis and convective cooling on unsteady flow of nanofluids in a pipe with permeable wall are investigated. It is assumed that the pipe surface exchange heat with the ambient following the Newton’s law of cooling.  Using a semi discretization finite difference method coupled with Runge-Kutta Fehlberg integration scheme, the nonlinear governing equations of momentum and energy balance, and the equation for nanoparticles concentration are tackled numerically. Useful results for the velocity, temperature, nanoparticles concentration profiles, skin friction and Nusselt number are obtained graphically and discussed quantitatively.},
     year = {2014}
    }
    

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    T1  - Modelling the Effects of Variable Viscosity in Unsteady Flow of Nanofluids in a Pipe with Permeable Wall and Convective Cooling
    AU  - Sara Khamis
    AU  - Oluwole Daniel Makinde
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    Y1  - 2014/05/30
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    N1  - https://doi.org/10.11648/j.acm.20140303.12
    DO  - 10.11648/j.acm.20140303.12
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    EP  - 84
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20140303.12
    AB  - In this paper, the combined effects of variable viscosity, Brownian motion, thermophoresis and convective cooling on unsteady flow of nanofluids in a pipe with permeable wall are investigated. It is assumed that the pipe surface exchange heat with the ambient following the Newton’s law of cooling.  Using a semi discretization finite difference method coupled with Runge-Kutta Fehlberg integration scheme, the nonlinear governing equations of momentum and energy balance, and the equation for nanoparticles concentration are tackled numerically. Useful results for the velocity, temperature, nanoparticles concentration profiles, skin friction and Nusselt number are obtained graphically and discussed quantitatively.
    VL  - 3
    IS  - 3
    ER  - 

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Author Information
  • Nelson Mandela African Institution of Science and Technology (NM-AIST), P. O. Box 447, Arusha, Tanzania

  • Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa

  • Nelson Mandela African Institution of Science and Technology (NM-AIST), P. O. Box 447, Arusha, Tanzania

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