Couette Flow Problem for an Unsteady MHD Fourth-Grade Fluid with Hall Currents

Haider Zaman,Tarique Abbas,Arif Sohail,Azhar Ali

doi:10.4236/jamp.2014.24001

Haider Zaman, Tarique Abbas + Show 2 more

Open Access

https://doi.org/10.4236/jamp.2014.24001

Copy DOI

Abstract

In this work, we analyze Couette flow problem for an unsteady magnetohydrodynamic (MHD) fourth-grade fluid in presence of pressure gradient and Hall currents. The existing literature on the topic shows that the effect of Hall current on Couette flow of an unsteady MHD fourth-grade fluid with pressure gradient has not been investigated so far. The arising non-linear problem is solved by the homotopy analysis method (HAM) and the convergence of the obtained complex series solution is carefully analyzed. The influence of pressure number, Hartmann number, Hall parameter and fourth-grade material parameters on the unsteady velocity is discussed through plots and on local skin-friction coefficient discussed through numerical values presented in tabular form.

Highlights

In fluid mechanics, everyone is familiar with Couette flow problem, the flow between two parallel plates in which bottom plate is fixed and upper plate is initially at rest and is suddenly set into motion in its own plane with a constant velocity, is termed as Couette flow [1] [2]
In order to understand the interaction of electric, magnetic, and hydrodynamic forces in the unsteady fourth-grade fluid, we considered a simple flow problem, known as the Couette flow
The Couette flow between two parallel plates filled with MHD unsteady fourth-grade fluid is studied analytically

Summary

Introduction

Everyone is familiar with Couette flow problem, the flow between two parallel plates in which bottom plate is fixed and upper plate is initially at rest and is suddenly set into motion in its own plane with a constant velocity, is termed as Couette flow [1] [2]. Hayat et al [7] used Laplace transform method to determine the analytic solutions of Couette flows of a second grade fluid. How to cite this paper: Zaman, H., et al (2014) Couette Flow Problem for an Unsteady MHD Fourth-Grade Fluid with Hall Currents. When a strong magnetic field is applied in an ionized gas of low density, the conductivity normal to the magnetic field is decreased by free spiraling of electrons and ions about the magnetic lines of force before suffering collisions This phenomenon is known as Hall effect and a current induced in a direction normal to the electric and magnetic fields is called Hall current [15]. In order to understand the interaction of electric, magnetic, and hydrodynamic forces in the unsteady fourth-grade fluid, we considered a simple flow problem, known as the Couette flow. The effects of the pertinent parameters on the local skin friction coefficient at the surface of the wall are presented numerically in tabular form

Formulation of the Problem and Its Analytic Solution

Conclusion