The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid

Binyam Zigta; Purnachandra Rao Koya

doi:doi:10.11648/j.ajam.20170503.13

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The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid

Binyam Zigta, Purnachandra Rao Koya

Published in American Journal of Applied Mathematics (Volume 5, Issue 3)

Received: 14 April 2017 Accepted: 27 April 2017 Published: 23 June 2017

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Abstract

In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.

Published in	American Journal of Applied Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.ajam.20170503.13
Page(s)	78-90
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), 2017. Published by Science Publishing Group

Keywords

Viscoelastic Fluid, MHD, Couette Channel Walls, Permeability of Porous Medium

References

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APA Style

Binyam Zigta, Purnachandra Rao Koya. (2017). The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. American Journal of Applied Mathematics, 5(3), 78-90. https://doi.org/10.11648/j.ajam.20170503.13

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ACS Style

Binyam Zigta; Purnachandra Rao Koya. The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. Am. J. Appl. Math. 2017, 5(3), 78-90. doi: 10.11648/j.ajam.20170503.13

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AMA Style

Binyam Zigta, Purnachandra Rao Koya. The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. Am J Appl Math. 2017;5(3):78-90. doi: 10.11648/j.ajam.20170503.13

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@article{10.11648/j.ajam.20170503.13,
  author = {Binyam Zigta and Purnachandra Rao Koya},
  title = {The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {78-90},
  doi = {10.11648/j.ajam.20170503.13},
  url = {https://doi.org/10.11648/j.ajam.20170503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170503.13},
  abstract = {In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.},
 year = {2017}
}

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TY  - JOUR
T1  - The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid
AU  - Binyam Zigta
AU  - Purnachandra Rao Koya
Y1  - 2017/06/23
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170503.13
DO  - 10.11648/j.ajam.20170503.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 78
EP  - 90
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170503.13
AB  - In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.
VL  - 5
IS  - 3
ER  -

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Author Information

Binyam Zigta

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia
Purnachandra Rao Koya

School of Mathematical and Statistical Sciences, Hawassa University, Hawassa, Ethiopia

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APA Style

Binyam Zigta, Purnachandra Rao Koya. (2017). The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. American Journal of Applied Mathematics, 5(3), 78-90. https://doi.org/10.11648/j.ajam.20170503.13

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ACS Style

Binyam Zigta; Purnachandra Rao Koya. The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. Am. J. Appl. Math. 2017, 5(3), 78-90. doi: 10.11648/j.ajam.20170503.13

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AMA Style

Binyam Zigta, Purnachandra Rao Koya. The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid. Am J Appl Math. 2017;5(3):78-90. doi: 10.11648/j.ajam.20170503.13

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@article{10.11648/j.ajam.20170503.13,
  author = {Binyam Zigta and Purnachandra Rao Koya},
  title = {The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {78-90},
  doi = {10.11648/j.ajam.20170503.13},
  url = {https://doi.org/10.11648/j.ajam.20170503.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170503.13},
  abstract = {In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.},
 year = {2017}
}

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TY  - JOUR
T1  - The Effect of Physical Parameters on Flow Variables of an Electrically Conducting Viscoelastic Fluid
AU  - Binyam Zigta
AU  - Purnachandra Rao Koya
Y1  - 2017/06/23
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170503.13
DO  - 10.11648/j.ajam.20170503.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 78
EP  - 90
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170503.13
AB  - In this paper the effect physical parameters on flow variables of unsteady, incompressible, electrically conducting viscoelastic fluid flowing between a pair of infinite vertical Couette porous channel walls embedded in a porous medium is analyzed. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall varies periodically. The temperature difference between the two walls is high enough due to thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. This technique is applied on partial differential equations that are difficult to solve. These partial differential equations are reduced to a set of ordinary differential equations in dimensionless form and thus they can be solved analytically. The effects of physical parameters on the flow variables are studied and the results have been discussed. The physical parameters considered include Hartmann number, viscoelastic parameter, Permeability of porous medium, chemical reaction parameter, radiative parameter, thermal Grashof number for heat transfer, modified Grashof number for mass transfer, frequency parameter, Prandtl number, mass diffusivity and Schmidt number. The flow variables considered include velocity, temperature and concentration. The theoretical results have been supported by simulation study. The observations include: (i) velocity decreases with increasing values of frequency, Hartmann number and viscoelastic parameter (ii) velocity increases with increasing values of temperature, thermal Grashof number, modified Grashof number and permeability of porous medium, (iii) the temperature decreases near the moving channel wall when the radiative parameter increases (iv) the temperature approaches to zero in the region near to the boundary layer of the stationary channel wall when the radiative parameter increases (v) concentration decreases with an increment in both chemical reaction and Schmidt number and (vi) The velocity of fluid increases as thermal Grashof number and modified Grashof number increases.
VL  - 5
IS  - 3
ER  -

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