Iterative Methods for Solving the Fractional Form of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No-Slip Boundaries

A A Hemeda,E E Eladdad

doi:10.1155/2016/6021462

Abstract

An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is proposed with slip and no-slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations of motion is reduced to a single fourth-order nonlinear ordinary differential equation. By using the basic definitions of fractional calculus, we introduced the fractional order form of the fourth-order nonlinear ordinary differential equation. The resulting boundary value fractional problems are solved by the new iterative and Picard methods. Convergence of the considered methods is confirmed by obtaining absolute residual errors for approximate solutions for various Reynolds number. The comparisons of the solutions for various Reynolds number and various values of the fractional order confirm that the two methods are identical and therefore are suitable for solving this kind of problems. Finally, the effects of various Reynolds number on the solution are also studied graphically.

Highlights

The squeezing of an incompressible viscous fluid between two parallel plates is a fundamental type of flow that is frequently observed in many hydrodynamical tools and machines
An unsteady axisymmetric flow of nonconducting, incompressible Newtonian fluid squeezed between two circular plates is considered
Analysis of the residual errors confirms that the new iterative method (NIM) and Picard method (PM) are identical and efficient schemes

Summary

Introduction

The squeezing of an incompressible viscous fluid between two parallel plates is a fundamental type of flow that is frequently observed in many hydrodynamical tools and machines. The modeling and analysis of squeezing flow has been started in the nineteenth century and continues to receive significant attention due to its vast applications areas in biophysical and physical sciences. The first work in squeezing flows was laid down by Stefan [1] who developed an ad hoc asymptotic solution of Newtonian fluids. An explicit solution of the squeeze flow, considering inertial terms, has been established by Thorpe and Shaw [2]. Verma [4] and Singh et al [5] have established numerical solutions of the squeezing flow between parallel plates.

Objectives

Methods

Results

Conclusion