Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium

Wissam Sadiq Khudair; Dheia Gaze Salih Al-Khafajy

doi:doi:10.11648/j.ijfmts.20180401.12

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Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium

Wissam Sadiq Khudair, Dheia Gaze Salih Al-Khafajy

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 4, Issue 1)

Received: 21 February 2018 Accepted: 9 March 2018 Published: 3 April 2018

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Abstract

The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We <<1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 4, Issue 1)
DOI	10.11648/j.ijfmts.20180401.12
Page(s)	11-17
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), 2018. Published by Science Publishing Group

Keywords

Williamson Fluid, Variable Viscosity, Heat Transfer, (MHD), Porous Medium

References

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[2]	K. M. Joseph, S. Daniel, and G. M. Joseph, “Unsteady MHD Couette Flow between Two Infinite Parallel Porous Plates in an Inclined Magnetic Field with Heat Transfer,” Int. J. Math. Stat. Invent., vol. 2, no. 3, pp. 103–110, 2014.
[3]	B. S. D. Nigamf and S. N. Singhj, “Heat Transfer By Laminar Flow Between Parallel Plates Under the Action of transverse magnetic field,” Quart. Journ. Mech Applied. Math, vol. XIII, no. 5, 1960.
[4]	M. Y. Malik, I. Zehra, and S. Nadeem, “Flows of Carreau fluid with pressure dependent viscosity in a variable porous medium : Application of polymer melt,” Alexandria Eng. J., 2014.
[5]	I. Zehra, M. M. Yousaf, and S. Nadeem, “Numerical solutions of Williamson fluid with pressure dependent viscosity,” Results Phys., vol. 5, pp. 20–25, 2015.
[6]	S. Nadeem and M. Awais, “Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity,” Phys. Lett. A, vol. 372, pp. 4965–4972, 2008.
[7]	D. G. S. Al-khafajy, “Influence of MHD and Wall Properties on the Peristaltic Transport of a Williamson Fluid with Variable Viscosity Through Porous Medium,” Iraqi J. Sci., vol. 58, no. 2, pp. 1076–1089, 2017.
[8]	W. S. Khudair and D. G. S. Al-khafajy, Influence of heat transfer on Magneto hydrodynamics oscillatory flow for Williamson fluid through a porous medium, Iraqi J. Sci., vol. 59, no. 1B, pp. 389–397, 2018.
[9]	A. A. Khan, R. Ellahi, and K. Vafai, “Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel,” vol. 2012.
[10]	T. Hayat, S. Nawaz, A. Alsaedi, and M. Rafiq, “Results in Physics Influence of radial magnetic field on the peristaltic flow of Williamson fluid in a curved complaint walls channel,” Results Phys., vol. 7, pp. 982–990, 2017.
[11]	S. E. G. A. C. Cogley. W. G. Vincenti, “Differential approximation for radiative transfer in a Nongrey gas near equilbrium,” Am. Inst. Aeronaut. Astronaut., vol. 6, no. 3, pp. 551–553, 1968.
[12]	J. D. Kevorkian, Jirair, Cole, Perturbation Methods in Applied Mathematics. Springer-Verlag New York, 1981.

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Wissam Sadiq Khudair, Dheia Gaze Salih Al-Khafajy. (2018). Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium. International Journal of Fluid Mechanics & Thermal Sciences, 4(1), 11-17. https://doi.org/10.11648/j.ijfmts.20180401.12

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ACS Style

Wissam Sadiq Khudair; Dheia Gaze Salih Al-Khafajy. Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium. Int. J. Fluid Mech. Therm. Sci. 2018, 4(1), 11-17. doi: 10.11648/j.ijfmts.20180401.12

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AMA Style

Wissam Sadiq Khudair, Dheia Gaze Salih Al-Khafajy. Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium. Int J Fluid Mech Therm Sci. 2018;4(1):11-17. doi: 10.11648/j.ijfmts.20180401.12

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@article{10.11648/j.ijfmts.20180401.12,
  author = {Wissam Sadiq Khudair and Dheia Gaze Salih Al-Khafajy},
  title = {Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {4},
  number = {1},
  pages = {11-17},
  doi = {10.11648/j.ijfmts.20180401.12},
  url = {https://doi.org/10.11648/j.ijfmts.20180401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20180401.12},
  abstract = {The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We <<1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.},
 year = {2018}
}

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TY  - JOUR
T1  - Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium
AU  - Wissam Sadiq Khudair
AU  - Dheia Gaze Salih Al-Khafajy
Y1  - 2018/04/03
PY  - 2018
N1  - https://doi.org/10.11648/j.ijfmts.20180401.12
DO  - 10.11648/j.ijfmts.20180401.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 11
EP  - 17
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20180401.12
AB  - The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We <<1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.
VL  - 4
IS  - 1
ER  -

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Author Information

Wissam Sadiq Khudair

Faculty of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaneyah, Iraq
Dheia Gaze Salih Al-Khafajy

Faculty of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaneyah, Iraq

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APA Style

Wissam Sadiq Khudair, Dheia Gaze Salih Al-Khafajy. (2018). Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium. International Journal of Fluid Mechanics & Thermal Sciences, 4(1), 11-17. https://doi.org/10.11648/j.ijfmts.20180401.12

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ACS Style

Wissam Sadiq Khudair; Dheia Gaze Salih Al-Khafajy. Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium. Int. J. Fluid Mech. Therm. Sci. 2018, 4(1), 11-17. doi: 10.11648/j.ijfmts.20180401.12

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AMA Style

Wissam Sadiq Khudair, Dheia Gaze Salih Al-Khafajy. Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium. Int J Fluid Mech Therm Sci. 2018;4(1):11-17. doi: 10.11648/j.ijfmts.20180401.12

Copy | Download

@article{10.11648/j.ijfmts.20180401.12,
  author = {Wissam Sadiq Khudair and Dheia Gaze Salih Al-Khafajy},
  title = {Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {4},
  number = {1},
  pages = {11-17},
  doi = {10.11648/j.ijfmts.20180401.12},
  url = {https://doi.org/10.11648/j.ijfmts.20180401.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20180401.12},
  abstract = {The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We <<1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium
AU  - Wissam Sadiq Khudair
AU  - Dheia Gaze Salih Al-Khafajy
Y1  - 2018/04/03
PY  - 2018
N1  - https://doi.org/10.11648/j.ijfmts.20180401.12
DO  - 10.11648/j.ijfmts.20180401.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 11
EP  - 17
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20180401.12
AB  - The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We <<1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.
VL  - 4
IS  - 1
ER  -

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