Combined Analytical-Numerical Solution for MHD Viscous Flow over a Stretching Sheet

We studied the two-dimensional flow of viscous and electrically conducting fluid over a stretching sheet under the influence of constant magnetic field. Approximate analytical solution of governing nonlinear boundary layer equation via optimal homotopy asymptotic method (OHAM) is obtained. For numerical comparison we used Runge-Kutta-Fehlberg fourth-fifth-order method. The effect of different parameters on fluid flow is analyzed. It is found that the OHAM solution is very close to the numerical solution for different assigned values of parameters; this thus indicates the feasibility of the proposed method (OHAM). 1. Introduction Magnetohydrodynamics (MHD) is the study of interaction of conducting fluids with electromagnetic phenomena. The flow of an electrically conducting fluid in the presence of magnetic field has many applications in engineering. Also the flow influence by a moving boundary is of crucial importance in the extrusion processes in chemical industries [1, 2]. Sakiadis [3, 4] is a pioneer in this area who has investigated the boundary layer flow with uniform speed over continuously stretching surface. Later on, Tsou et al. [5] experimentally verified the work of Sakiadis. Crane [6] studied the steady-state two-dimensional boundary layer flow caused by a stretching sheet whose velocity varies linearly with the distance from a fixed point on the sheet. Chiam [7] and Dandapat and Gupta [8] considered the motion of micropolar and power-law fluids, respectively. Most attention has so far been devoted to the analysis of flow of viscoelastic fluids [9–13] and the joint effect of viscoelasticity and magnetic field has been worked out by Ariel [14]. Beside this, Liao [15, 16] has provided solution for impermeable and permeable stretching sheets, which shows that multiple solutions for the stretching surfaces are possible under definite conditions. The optimal homotopy asymptotic method is a powerful approximate analytical technique that is straightforward to use and does not require the existence of any small or large parameter. Optimal homotopy asymptotic method (OHAM) is employed to construct the series solution of the problem. This method is a consistent analytical tool and it has already been applied to a number of nonlinear differential equations arising in science and engineering [17–19]. So far, as we are aware, there have been no solutions for MHD viscous flow over stretching sheet via OHAM. This paper is organized as follows. First, in Section 2, we formulate the problem. In Section 3 we present basic principles of OHAM. The OHAM solution