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

Sara Khamis; Oluwole Daniel Makinde; Yaw Nkansah-Gyekye

doi:doi:10.11648/j.acm.20140303.12

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

Sara Khamis, Oluwole Daniel Makinde, Yaw Nkansah-Gyekye

Published in Applied and Computational Mathematics (Volume 3, Issue 3)

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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[4]	Erdoğan , M. E., Imrak, C. E.,(2008), On the flow in a uniformly porous pipe, Int. J. Non-Linear Mech., 43, pp. 292–301.
[5]	Tsangaris, S. Kondaxakis, D., Vlachakis, N.W., (2007), Exact solution for flow in a porous pipe with unsteady wall suction and/or injection, Comm. Nonlinear Sci. Num. Simul., 12, pp. 1181–1189.
[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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[8]	Kaufui, V. W., Omar, D. L.(2003), Appli-cations of nanofluids: current and future, Adv. Mech. Eng. , 11 pp.
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[11]	Mutuku-Njane, W. N., Makinde, O. D., (2014), MHD nanofluid flow over a permeable vertical plate with convective heating, J. Compl Theor. Nanoscience, 3, pp. 667-675.
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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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[18]	Makinde, O. D., (2009), Hermite–Pade approach to thermal radiation effect on inherent irreversibility in a variable viscosity channel flow, Comp. Math. Appl., 58, pp. 2330-2338.
[19]	Kuppalapalle, V., Kerehalli, P. V., Chiu-on, NG., (2013), The effect of variable viscosity on the flow and heat transfer of a viscous Ag-water and Cu-water nanofluids, J. Hydro., 25, 8 pages.
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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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TY  - JOUR
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
AU  - Yaw Nkansah-Gyekye
Y1  - 2014/05/30
PY  - 2014
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
SP  - 75
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

Sara Khamis

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

Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
Yaw Nkansah-Gyekye

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
AU  - Yaw Nkansah-Gyekye
Y1  - 2014/05/30
PY  - 2014
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
SP  - 75
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  -

Copy | Download