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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 4293721, 14 pages
http://dx.doi.org/10.1155/2016/4293721
Research Article

Unsteady Squeezing Flow of Casson Fluid with Magnetohydrodynamic Effect and Passing through Porous Medium

1Department of Mathematics, National University of Computer and Emerging Sciences, Peshawar, Pakistan
2Department of Computer Sciences, National University of Computer and Emerging Sciences, Peshawar, Pakistan
3Department of Basic Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan

Received 22 August 2016; Revised 26 October 2016; Accepted 1 December 2016

Academic Editor: Michael Vynnycky

Copyright © 2016 Hamid Khan 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

An unsteady squeezing flow of Casson fluid having magnetohydrodynamic (MHD) effect and passing through porous medium channel is modeled and investigated. Similarity transformations are used to convert the partial differential equations (PDEs) of non-Newtonian fluid to a highly nonlinear fourth-order ordinary differential equation (ODE). The obtained boundary value problem is solved analytically by Homotopy Perturbation Method (HPM) and numerically by explicit Runge-Kutta method of order 4. For validity purpose, we compare the analytical and numerical results which show excellent agreement. Furthermore, comprehensive graphical analysis has been made to investigate the effects of various fluid parameters on the velocity profile. Analysis shows that positive and negative squeeze number have opposite effect on the velocity profile. It is also observed that Casson parameter shows opposite effect on the velocity profile in case of positive and negative squeeze number . MHD parameter and permeability constant have similar effects on the velocity profile in case of positive and negative squeeze numbers. It is also seen that, in case of positive squeeze number, similar velocity profiles have been obtained for , and . Besides this, analysis of skin friction coefficient has also been presented. It is observed that squeeze number, MHD parameter, and permeability parameter have direct relationship while Casson parameter has inverse relationship with skin friction coefficient.