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Mathematical Problems in Engineering
Volume 2017, Article ID 1421862, 16 pages
https://doi.org/10.1155/2017/1421862
Research Article

Solution of the Fractional Form of Unsteady Squeezing Flow through Porous Medium

Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

Correspondence should be addressed to A. A. Hemeda; moc.oohay@ademehaa

Received 21 March 2017; Revised 17 May 2017; Accepted 15 June 2017; Published 1 August 2017

Academic Editor: Mauro Gaggero

Copyright © 2017 A. A. Hemeda et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose two friendly analytical techniques called Adomian decomposition and Picard methods to analyze an unsteady axisymmetric flow of nonconducting, Newtonian fluid. This fluid is assumed to be squeezed between two circular plates passing through porous medium channel with slip and no-slip boundary conditions. A single fractional order nonlinear ordinary differential equation is obtained by means of similarity transformation with the help of the fractional calculus definitions. The resulting fractional boundary value problems are solved by the proposed methods. Convergence of the two methods’ solutions is confirmed by obtaining various approximate solutions and various absolute residuals for different values of the fractional order. Comparison of the results of the two methods for different values of the fractional order confirms that the proposed methods are in a well agreement and therefore they can be used in a simple manner for solving this kind of problems. Finally, graphical study for the longitudinal and normal velocity profiles is obtained for various values of some dimensionless parameters and fractional orders.