World Applied Sciences Journal 16 (11): 1638-1648, 2012
ISSN 1818-4952
© IDOSI Publications, 2012
Corresponding Author: Muhammad Ashraf, Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin
Zakariya University, Multan, Pakistan
1638
Viscous Dissipation and Radiation Effects in MHD Stagnation Point
Flow towards a Stretching Sheet with Induced Magnetic Field
Kashif Ali, Muhammad Ashraf, Shahzad Ahmad and Kiran Batool
Centre for Advanced Studies in Pure and Applied Mathematics,
Bahauddin Zakariya University, Multan, Pakistan
Abstract: In this paper we present the numerical study of steady laminar two dimensional nonlinear MHD
stagnation point flow and heat transfer of an incompressible viscous fluid towards a stretching sheet, taking
the induced magnetic field, viscous dissipation and radiation effects into consideration. The study reveals
that the viscous dissipation may cause thermal reversal near the surface which is supported by the
stretching parameter of the sheet when greater than unity and the Prandtl number as well. On the other
hand, an opposite effect is observed for both the magnetic parameter and the radiation number.
Key words: Stagnation point flow • thermal reversal • stretching sheet • radiation • MHD • finite difference
method
INTRODUCTION
Hydromagnetic stagnation point flows with
thermal effects have applications in many
manufacturing processes in industry and engineering.
These applications include boundary layers along
material handling conveyers, the aerodynamic extrusion
of plastic sheets, blood flow problems, the cooling of an
infinite metallic plate in a cooling bath, textile and
paper industries etc.
The classical two dimensional stagnation point
flow impinging on a flat plate was first considered by
Hiemenz [1]. The flow of an electrically conducting
fluid past a porous substrate attached to the flat plate
with Beavers-Joseph boundary condition under the
influence of a uniform transverse magnetic field was
investigated by Jat and Santosh [2] using similarity
transformation method. Ishak et al . [3] discussed the
problem of steady two dimensional incompressible
stagnation point flow towards a stretching sheet with
variable surface temperature. Fang and Zhang [4]
studied the problem of a transverse magnetic field to
contain the vorticity over a shrinking sheet. Fang et al.
[5] and Fang & Zhang [6] discussed the problem of
mass and heat transfer characteristics on flow generated
by a shrinking sheet. Kumaran et al. [7] analyzed the
MHD boundary layer flow of an electrically conducting
fluid over a stretching permeable surface with suction/
injection. Kumaran et al . [8] studied the problem of two
dimensional stagnation point flow in a porous medium.
Hassanien and Al Arabi [9] presented the problem of
boundary layer unsteady mixed convection flow near
the stagnation point on a heated vertical plate through a
porous medium. Hayat et al. [10] investigated MHD
stagnation point flow and heat transfer through a porous
space bounded by a permeable surface. The problem of
two dimensional steady laminar MHD Hiemenz forced
flow over a flat plate through porous medium was
solved by Kechil and Hashim [11]. Ali et al . [12]
discussed steady two dimensional MHD stagnation
point flow and heat transfer towards a stretching sheet
with induced magnetic field by using shooting method.
The numerical solution of MHD steady laminar two
dimensional boundary layer stagnation flow of a
viscous incompressible electrically conducting fluid
over a stretching sheet with induced magnetic field was
investigated by Ali et al . [13] using Keller-box method.
Anwar et al . [14] studied the MHD two dimensional
boundary layer flow of an electrically conducting
forced convection liquid metal fluid flow with induced
magnetic field effects. Nadeem and Akbar [15]
considered the problem of two dimensional peristaltic
flow of an incompressible electrically conducting
Johnson Segalman fluid in a vertical asymmetric
channel which possesses the effects of induced
magnetic field.
Very little attention has been paid to the boundary
layer flow and heat transfer taking the effect of the
induced magnetic field and thermal radiation into
consideration. For example, Kumari et al. [16]
considered the MHD flow and heat transfer over a
stretching surface by considering the effect of the