Research Article Improved Analysis for Squeezing of Newtonian Material between Two Circular Plates Omar Khan, 1 Mubashir Qayyum, 2 Hamid Khan, 2 and Murtaza Ali 3 1 Department of Computer Science, National University of Computer & Emerging Sciences, Peshawar, Pakistan 2 Department of Mathematics, National University of Computer & Emerging Sciences, Peshawar, Pakistan 3 Department of Mathematics, University of Engineering & Technology, Mardan, Pakistan Correspondence should be addressed to Omar Khan; omar.khan@nu.edu.pk Received 4 September 2016; Revised 7 March 2017; Accepted 13 March 2017; Published 28 March 2017 Academic Editor: Wenbin Yi Copyright © 2017 Omar Khan et al. Tis 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. Tis article presents a scheme for the analysis of an unsteady axisymmetric fow of incompressible Newtonian material in the form of liquid squeezed between two circular plates. Te scheme combines traditional perturbation technique with homotopy using an adaptation of the Laplace Transform. Te proposed method is tested against other schemes such as the Regular Perturbation Method (RPM), Homotopy Perturbation Method (HPM), Optimal Homotopy Asymptotic Method (OHAM), and the fourth-order Explicit Runge-Kutta Method (ERK4). Comparison of the solutions along with absolute residual errors confrms that the proposed scheme surpasses HPM, OHAM, RPM, and ERK4 in terms of accuracy. Te article also investigates the efect of Reynolds number on the velocity profle and pressure variation graphically. 1. Introduction Te study of squeezing fows has signifcant applications in the areas of engineering, physics, biology, and material sciences. In the past few years, the study of rheometric prop- erties of fuids has garnered signifcant attention due to its vast industrial applications. Examples include modelling of lubrication systems involved in squeezing of fuids [1–3], compression moulding processes of metals and polymers [4], injection moulding processes, polymer processes [5], hydrodynamical tools and machines, modelling of chewing and eating [6], and modelling of the functions of heart valves and blood vessels. Many of these applications involve the adjustment of rheometric properties using external stimuli such as electric and magnetic felds. For instance, electrorhe- ological fuids (micron size polymer particles in silicon) may solidify or become extremely viscous under an electric feld. Te same can be said about magnetorheological fuids involving magnetic particles. Under an applied external feld, these particles remain suspended due to which fuid particles are not able to exhibit Brownian motion. As a result, the fuid can adopt viscous properties. Traditional approaches to study fow patterns involve the confguration of two plates of radius  that are separated by a narrow gap ℎ(). Tree modes of operations on the plates are commonly used; stationary plates resulting in Poiseuille fow, shear mode resulting in Couette fow, and squeeze mode resulting in compressed fow. Some properties of the fow such as mass and momentum are not afected by deforma- tions due to these operations and they remain conserved. Te resulting set of properties such as velocity and pressure can be modelled as various boundary value problems. Some confgurations may also focus on the interaction between the samples and the plates. Te interactions can result in diferent types of stresses identifed as slip, no-slip, or partial slip. Other confgurations may also focus on types of fuid such as viscous, plastics (or viscoplastics), and elastic (or viscoelastic) fuids. Te solutions to these diferent confgurations and boundary value problems can be obtained using well known analytical [7–14] and numerical schemes [15, 16]. Te most common approach involves the usage of perturbation tech- niques that assume small or large parameters, which may afect the solutions in diferent scenarios. To overcome this Hindawi Advances in Materials Science and Engineering Volume 2017, Article ID 5703291, 9 pages https://doi.org/10.1155/2017/5703291