New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate

Muhammet Yurusoy

doi:doi:10.11648/j.mcs.20160102.12

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New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate

Muhammet Yurusoy

Published in Mathematics and Computer Science (Volume 1, Issue 2)

Received: 28 June 2016 Accepted: 5 August 2016 Published: 25 August 2016

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Abstract

The flow of fourth grade fluid flow over a porous plate with heat transfer is considered. By using the perturbation techniques, approximate analytical solutions for velocity and temperature profiles have been obtained. Comparing with the Newtonian effect, it turns out that if the second grade, third grade and fourth grade effects are small, an ordinary perturbation problem occurs. To find fourth grade fluids, velocity and temperature profiles, which are attained, are compared with numerical solutions. The approximate solutions run in well with the numerical solutions. This is to demonstrate us that the perturbation technique is a robust tool to find great approximations to nonlinear equations of fourth grade fluids. Velocity and temperature profiles are calculated for diverse second grade, third grade and fourth grade non-Newtonian fluid parameters.

Published in	Mathematics and Computer Science (Volume 1, Issue 2)
DOI	10.11648/j.mcs.20160102.12
Page(s)	29-35
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), 2016. Published by Science Publishing Group

Keywords

Fourth Grade Fluid Equations, Boundary Layer Analysis, Perturbation Methods

References

[1]	R. L. Fosdick and K. R. Rajagopal, Thermodynamics and stability of fluids of third grade, Proceedings of the Royal Society A 1, 351-377, 1980.
[2]	K. R. Rajagopal, On the stability of third-grade fluids, Arch. Mech. 32, 867-875. 1980.
[3]	A. Z. Szeri and K. R. Rajagopal, Flow of a non-Newtonian fluid between heated parallel plates, Int. J. Non-Linear Mech. 20, 91-101, 1985.
[4]	K. R. Rajagopal, A. Z. Szeri and W. Troy, An existence theorem for the flow of a non-Newtonian fluid past an infinite porous plate, Int. J. Non-Linear Mech. 21, 279-289. 1986.
[5]	C. E. Maneschy, M. Massoudi and A. Ghoneimy, Heat transfer analysis of a non-Newtonian fluid past a porous plate, International Journal of Non-Linear Mechanics, 28, 131-143, 1993.
[6]	T. Hayat and M. Khan, Homotopy solutions for a generalized second-grade fluid past a porous plate, Nonlinear Dynamics, 42, 395-405, 2005.
[7]	M. Pakdemirli, T. Hayat, M. Yürüsoy, S. Abbasbandy and S. Asghar, Perturbation analysis of a modified second grade fluid over a porous plate, Nonlinear Analysis: Real World Applications, 12, 1774-1785, 2011.
[8]	M. Massoudi and I. Christie, Effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a pipe, Int. J. Non-Linear Mech. 30, 687-699, 1995.
[9]	M. Yurusoy and M. Pakdemirli, Approximate analytical solutions for the flow of a third-grade fluid in a pipe. Int. J. Nonlinear Mech. 37, 187–195, 2002.
[10]	T. Hayat, A. H. Kara, and E. Momoniat, Exact flow of a third grade fluid on a porous wall. Int. J. Non-Linear Mech. 38, 1533–1537, 2003.

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Muhammet Yurusoy. (2016). New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate. Mathematics and Computer Science, 1(2), 29-35. https://doi.org/10.11648/j.mcs.20160102.12

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ACS Style

Muhammet Yurusoy. New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate. Math. Comput. Sci. 2016, 1(2), 29-35. doi: 10.11648/j.mcs.20160102.12

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AMA Style

Muhammet Yurusoy. New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate. Math Comput Sci. 2016;1(2):29-35. doi: 10.11648/j.mcs.20160102.12

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@article{10.11648/j.mcs.20160102.12,
  author = {Muhammet Yurusoy},
  title = {New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate},
  journal = {Mathematics and Computer Science},
  volume = {1},
  number = {2},
  pages = {29-35},
  doi = {10.11648/j.mcs.20160102.12},
  url = {https://doi.org/10.11648/j.mcs.20160102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160102.12},
  abstract = {The flow of fourth grade fluid flow over a porous plate with heat transfer is considered. By using the perturbation techniques, approximate analytical solutions for velocity and temperature profiles have been obtained. Comparing with the Newtonian effect, it turns out that if the second grade, third grade and fourth grade effects are small, an ordinary perturbation problem occurs. To find fourth grade fluids, velocity and temperature profiles, which are attained, are compared with numerical solutions. The approximate solutions run in well with the numerical solutions. This is to demonstrate us that the perturbation technique is a robust tool to find great approximations to nonlinear equations of fourth grade fluids. Velocity and temperature profiles are calculated for diverse second grade, third grade and fourth grade non-Newtonian fluid parameters.},
 year = {2016}
}

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TY  - JOUR
T1  - New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate
AU  - Muhammet Yurusoy
Y1  - 2016/08/25
PY  - 2016
N1  - https://doi.org/10.11648/j.mcs.20160102.12
DO  - 10.11648/j.mcs.20160102.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 29
EP  - 35
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20160102.12
AB  - The flow of fourth grade fluid flow over a porous plate with heat transfer is considered. By using the perturbation techniques, approximate analytical solutions for velocity and temperature profiles have been obtained. Comparing with the Newtonian effect, it turns out that if the second grade, third grade and fourth grade effects are small, an ordinary perturbation problem occurs. To find fourth grade fluids, velocity and temperature profiles, which are attained, are compared with numerical solutions. The approximate solutions run in well with the numerical solutions. This is to demonstrate us that the perturbation technique is a robust tool to find great approximations to nonlinear equations of fourth grade fluids. Velocity and temperature profiles are calculated for diverse second grade, third grade and fourth grade non-Newtonian fluid parameters.
VL  - 1
IS  - 2
ER  -

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Author Information

Muhammet Yurusoy

Department of Mechanical Engineering, Afyon Kocatepe University, Afyon, Turkey

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APA Style

Muhammet Yurusoy. (2016). New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate. Mathematics and Computer Science, 1(2), 29-35. https://doi.org/10.11648/j.mcs.20160102.12

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ACS Style

Muhammet Yurusoy. New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate. Math. Comput. Sci. 2016, 1(2), 29-35. doi: 10.11648/j.mcs.20160102.12

Copy | Download

AMA Style

Muhammet Yurusoy. New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate. Math Comput Sci. 2016;1(2):29-35. doi: 10.11648/j.mcs.20160102.12

Copy | Download

@article{10.11648/j.mcs.20160102.12,
  author = {Muhammet Yurusoy},
  title = {New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate},
  journal = {Mathematics and Computer Science},
  volume = {1},
  number = {2},
  pages = {29-35},
  doi = {10.11648/j.mcs.20160102.12},
  url = {https://doi.org/10.11648/j.mcs.20160102.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20160102.12},
  abstract = {The flow of fourth grade fluid flow over a porous plate with heat transfer is considered. By using the perturbation techniques, approximate analytical solutions for velocity and temperature profiles have been obtained. Comparing with the Newtonian effect, it turns out that if the second grade, third grade and fourth grade effects are small, an ordinary perturbation problem occurs. To find fourth grade fluids, velocity and temperature profiles, which are attained, are compared with numerical solutions. The approximate solutions run in well with the numerical solutions. This is to demonstrate us that the perturbation technique is a robust tool to find great approximations to nonlinear equations of fourth grade fluids. Velocity and temperature profiles are calculated for diverse second grade, third grade and fourth grade non-Newtonian fluid parameters.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate
AU  - Muhammet Yurusoy
Y1  - 2016/08/25
PY  - 2016
N1  - https://doi.org/10.11648/j.mcs.20160102.12
DO  - 10.11648/j.mcs.20160102.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 29
EP  - 35
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20160102.12
AB  - The flow of fourth grade fluid flow over a porous plate with heat transfer is considered. By using the perturbation techniques, approximate analytical solutions for velocity and temperature profiles have been obtained. Comparing with the Newtonian effect, it turns out that if the second grade, third grade and fourth grade effects are small, an ordinary perturbation problem occurs. To find fourth grade fluids, velocity and temperature profiles, which are attained, are compared with numerical solutions. The approximate solutions run in well with the numerical solutions. This is to demonstrate us that the perturbation technique is a robust tool to find great approximations to nonlinear equations of fourth grade fluids. Velocity and temperature profiles are calculated for diverse second grade, third grade and fourth grade non-Newtonian fluid parameters.
VL  - 1
IS  - 2
ER  -

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