Unsteady Incompressible Couette Flow Problem for the Eyring-Powell Model with Porous Walls

Haider Zaman,Muhammad Ibrahim,Murad Ali Shah

doi:10.4236/ajcm.2013.34041

Haider Zaman, Muhammad Ibrahim + Show 1 more

Open Access

https://doi.org/10.4236/ajcm.2013.34041

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Abstract

This work is concerned with the influence of uniform suction or injection on unsteady incompressible Couette flow for the Eyring-Powell model. The resulting unsteady problem for horizontal velocity field is solved by means of homotopy analysis method (HAM). The characteristics of the horizontal velocity field and wall shear stress are analyzed and discussed. Pade approximants and Taylor polynomials are also found for velocity profile and are used to make the maximum error as small as possible. The graphs of the error for the Pade approximation and Taylor approximation are drawn and discussed. Convergence of the series solution is also discussed with the help of h-curve and interval of convergence is also found.

Highlights

The study of non-Newtonian fluids has generated much interest in recent years in view of their numerous industrial applications, especially in polymer and chemical industries
Some important studies about this flow are as follows: Fang [21] studied Couette flow problem for unsteady incompressible viscous fluid bounded by porous walls
The Eyring-Powell model is derived from the theory of rate processes, which describes the shear of a non-Newtonian flow

Summary

Introduction

The study of non-Newtonian fluids has generated much interest in recent years in view of their numerous industrial applications, especially in polymer and chemical industries. Eldabe et al [34] and Zueco and Beg [35] discussed the non-Newtonian fluid flow under the effect of couple stresses between two parallel plates using Eyring-Powell model. Noreen and Qasim [40] analyzed peristaltic flow of MHD Eyring- Powell fluid in a channel. Keeping this all in view, in the present paper, the authors envisage studying the time-dependent Couette flow of incompressible non-Newtonian Eyring-Powell model with porous walls. Our goal is to make the maximum error as small as possible For this purpose, Pade approximants and Taylor polynomials are found. The series solution clearly demonstrates how various physical parameters play their part in determining properties of the flow

Mathematical Description of the Problem

Analytic Solution

Pade Approximation

Graphs and Discussion

Conclusions