Analytical Approximate Solution of Nonlinear Differential Equation Governing Jeffery-Hamel Flow with High Magnetic Field by Adomian Decomposition Method

D D Ganji,H R Ashorynejad,M Sheikholeslami

doi:10.5402/2011/937830

Abstract

The magnetohydrodynamic Jeffery-Hamel flow is studied analytically. The traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations reduce to nonlinear ordinary differential equations to model this problem. The analytical tool of Adomian decomposition method is used to solve this nonlinear problem. The velocity profile of the conductive fluid inside the divergent channel is studied for various values of Hartmann number. Results agree well with the numerical (Runge-Kutta method) results, tabulated in a table. The plots confirm that the method used is of high accuracy for different α, Ha, and Re numbers.

Highlights

The flow of fluid through a divergent channel is called Jeffery-Hamel flow since introducing this problem by Jeffery 1 and Hamel 2 in 1915 and 1916, respectively
We introduce the Reynolds number and the Hartmann number based on the electromagnetic parameter as follows, respectively: Re fmaxα υ
The magnetic field acts as a control parameter such as the flow Reynolds number and the angle of the walls, in MHD JefferyHamel problems

Summary

Introduction

The flow of fluid through a divergent channel is called Jeffery-Hamel flow since introducing this problem by Jeffery 1 and Hamel 2 in 1915 and 1916, respectively. The term of magnetohydrodynamic MHD was first introduced by Bansal 3 in 1994. The theory of magnetohydrodynamics is inducing current in a moving conductive fluid in presence of magnetic field; such induced current results in force on ions of the conductive fluid. The theoretical study of magnetohydrodynamic MHD channel has been a subject of great interest due to its extensive applications in designing cooling systems with liquid metals, MHD generators, accelerators, pumps, and flow meters 4–7. In fluid mechanics most of the problems are nonlinear. It is very important to develop efficient methods to solve them. It is very difficult to obtain analytical

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Conclusion