# A Numerical Technique for Solving Magneto-Hydrodynamic Eyring-Powell Fluid Flow Over A Nonlinear Stretching Sheet

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Published on International Journal of Biology, Physics & Matematics
ISSN: 2721-3757, Volume 1, Issue 1, page 60 – 64
Publication Date: 24 September 2018

Zulqurnain Sabir, Muhammad Umar, & Canan Unlu

Zulqurnain Sabir & Muhammad Umar
Department of Mathematics, Unique Science College for Girls Dina
Jhelum, Pakistan

Canan Unlu
Department of Mathematics, Istanbul University
Istanbul, Turkey

Abstract
In this paper, magneto-hydrodynamic Eyring-Powell fluid flow over a nonlinear stretching sheet has analyzed. By using the similarity conditions, the nonlinear partial differential equation is renewed into ordinary differential equation. This ordinary differential equation is solved numerically with the use of shooting method and comparison of results is presented with the explicit Runge Kutta and implicit Runge Kutta numerical schemes. Some proficient parameters like magnetic parameter M, non-dimensional fluid parameter and stretching parameter have been discussed numerically and graphically.

Keywords: Erying-Powell Fluid, Stretched Sheet, Explicit Runge Kutta, Implicit Runge Kutta, Magneto-Hydrodynamic.

1. Introduction
The models of stretching sheet are of great significance because of their various applications in the field of engineering like multimedia feature, extrusion of polymer sheet, coating of liquid on photographic films. Sakiadis [1] first discussed the behavior of boundary layer on continuous solid flat faces. Tsou et al. [2] promoted the Sakiadis work and reflected the transfer of heat in the boundary layer flow over a continuous surface. Erickson et al. [3] did additional extension of Sakiadis work to consider the mass and heat transfer on a stretching surface with suction/injection. Crane [4] has done pioneering work for exponentially and linear stretching sheet. He extended the idea for steady the boundary layer flow of an incompressible fluid over a linear stretching plate and produced an exact comparable result in closed analytical form. Elbashbeshy [5] studied numerically the heat transfer flow passing over an exponentially stretching surface with the wall-mass suction. Ishak et al. [6] and Nazar et al. [7] studied the flow of stagnation point over a stretching sheet. Partha et al. [8] analyzed collective effects of mixed convection and viscous dissipation on the viscous fluid flow passing over an exponentially stretching sheet. In another study, Ishak et al. [9] discussed the analysis of heat transfer over a stretching surface using the variable heat flux in micropolar fluids. Nadeem and Hussain [10] presented the series solution results for the flow of boundary layer in the stagnation point state towards a stretching sheet. Recently, some progress on the relevant literature are therein [11–15]. Powell and Eyring presented in 1944 a new fluid model called as Eyring–Powell fluid model [15].
The main objective of this study is to solve magneto-hydrodynamic Eyring-Powell fluid flow over a nonlinear stretching sheet using a well-known shooting method. For the behavior of different parameters on velocity profile, a famous shooting method along with fourth order Runge-Kutta scheme has been analyzed.
The remaining portions of the paper is organized as follows: Section 2 narrates the formulation of the problem, the designed structures are presented in Section 3, the results of numerical are provided in Section 4 and conclusions are finally listed in the last Section ……..

2. Mathematical Formulation
The detailed discussion of the two-dimensional magneto-hydrodynamic Eyring-Powell fluid flow over a nonlinear stretching sheet is presented in this section. The equations of continuity and momentum of the Erying-Powell model are given as ……….