17-03-2014, 09:51 PM
Abstract—The purpose of this study is to implement a new
analytical method (DTM-Padé technique which is a
combination of the differential transform method and the Padé
approximant) for solving magnetohydrodynamic boundarylayer
flow. We will show that the DTM solutions only valid for
small values of independent varible, therefore the DTM not
applicable for solving MHD boundary-layer equations.
Numerical comparisons between the DTM-Padé and the
classical fourth-order RungeKutta reveal that the new
technique is a promising tool for solving MHD boundary-layer
equations.
Keywords-DTM-Padé; MHD; Boundary-layer
I. INTRODUCTION
Magnetohydrodynamics (MHD) is the study of the
interaction of conducting fluids with electromagnetic
phenomena. The flow of an electrically conducting fluid in
the presence of a magnetic field is of importance in various
areas of technology and engineering such as MHD power
generation, MHD flow meters, MHD pumps, etc [1-6]. The
viscous flow due to stretching boundary is important in
extrusion processes where sheet material is pulled out of an
orifice with increasing velocity. If the boundary velocity is
linear with respect to a fixed point, exact solutions of the
Navier–Stokes equations may be obtained [7-8].
The concept of the DTM was first proposed by Zhou [9],
who solved linear and nonlinear problems in electrical
circuit problems. Chen and Ho [10] developed this method
for partial differential equations and Ayaz [11] applied it to
the system of differential equations, the validity of the DTM
is independent of whether or not there exist small
parameters in the considered equation. The motivation of
this letter is to extend the DTM to solve the MHD
boundary-layer equations, for this purpose, we introduce a
new analytical method (DTM-Padé). In this letter, DTMPadé
is employed to give series solution for MHD
boundary-layer flow.