%0 Journal Article
%T Application of Homotopy Analysis Method to the Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates
%A Mohammad Mehdi Rashidi
%A Abdul Majid Siddiqui
%A Mostafa Asadi
%J Mathematical Problems in Engineering
%D 2010
%I Hindawi Publishing Corporation
%R 10.1155/2010/706840
%X We investigated an axisymmetric unsteady two-dimensional flow of nonconducting, incompressible second grade fluid between two circular plates. The similarity transformation is applied to reduce governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE) in dimensionless form. The resulting nonlinear boundary value problem is solved using homotopy analysis method and numerical method. The effects of appropriate dimensionless parameters on the velocity profiles are studied. The total resistance to the upper plate has been calculated. 1. Introduction Squeezing flows are induced by externally normal stresses or vertical velocities by means of moving boundary. Squeezing flows have many applications in food industry, especially in chemical engineering. Some practical examples of squeezing flow include polymer processing, compression and injection molding. In addition, the lubrication system can also be modeled by squeezing flows. The study of squeezing flows has its origins in the 19th century and continues to receive considerable attention due to the practical applications in physical and biophysical areas. Stefan [1] published a classical paper on squeezing flow by using lubrication approximation. Such types of flow exist in lubrication when there is squeezing flow between two parallel plates. The tackiness of liquid adhesives also reflects squeeze film effects [2]. The squeeze film geometry has been studied extensively since 1947. Other applications in the biomechanics area relate to squeezing flow between parallel plates and the alternation between contraction and expansion of the blood vessels. In addition, polymer extrusion processes are modeled using squeezing flow of viscous fluids [3]. The squeezing flow between parallel plates when the confining walls have a transverse motion has great importance in hydrodynamic lubrication theory Langlois [4] and Salbu [5] have analyzed isothermal compressible squeeze films neglecting inertial effects. Thorpe [6] presented an explicit solution of the squeeze flow problem taking inertial terms into account. Later, P. S. Gupta and A. S. Gupta [7] showed that the solution given by [6] fails to satisfy the boundary conditions. Gupta solution, however, is restricted only to small Reynolds number. Squeeze film between two plane annuli with fluid inertia effects has been studied by Elkouh [8]. Some numerical solutions of squeezing flow between parallel plates has been conducted by Verma [9] and later by Singh et al. [10]. In addition, Hamza [11] has considered suction and injection
%U http://www.hindawi.com/journals/mpe/2010/706840/