New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate
Mathematics and Computer Science
Volume 1, Issue 2, July 2016, Pages: 29-35
Received: Jun. 28, 2016; Accepted: Aug. 5, 2016; Published: Aug. 25, 2016
Views 2778      Downloads 129
Author
Muhammet Yurusoy, Department of Mechanical Engineering, Afyon Kocatepe University, Afyon, Turkey
Article Tools
Follow on us
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.
Keywords
Fourth Grade Fluid Equations, Boundary Layer Analysis, Perturbation Methods
To cite this article
Muhammet Yurusoy, New Analytical Solutions for the Flow of a Fourth Grade Fluid Past a Porous Plate, Mathematics and Computer Science. Vol. 1, No. 2, 2016, pp. 29-35. doi: 10.11648/j.mcs.20160102.12
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186