Meccanica (2007) 42:375–386
DOI 10.1007/s11012-006-9051-5
Temperature dependent viscosity and thermal conductivity
effects on combined heat and mass transfer in MHD
three-dimensional flow over a stretching surface with
Ohmic heating
Mohamed Abd El-Aziz
Received: 4 February 2006 / Accepted: 6 December 2006 / Published online: 24 April 2007
© Springer Science+Business Media B.V. 2007
Abstract An analysis has been carried out to
obtain the flow, heat and mass transfer character-
istics of a viscous electrically conducting fluid hav-
ing temperature dependent viscosity and thermal
conductivity past a continuously stretching sur-
face, taking into account the effect of Ohmic heat-
ing. The flow is subjected to a uniform transverse
magnetic field normal to the plate. The resulting
governing three-dimensional equations are trans-
formed using suitable three-dimensional transfor-
mations and then solved numerically by using fifth
order Runge–Kutta–Fehlberg scheme with a modi-
fied version of the Newton–Raphson shooting
method. Favorable comparisons with previously
published work are obtained. The effects of the
various parameters such as magnetic parameter M,
the viscosity/temperature parameter θ
r
, the ther-
mal conductivity parameter S and the Eckert
number Ec on the velocity, temperature, and con-
centration profiles, as well as the local skin-
friction coefficient, local Nusselt number, and the
local Sherwood number are presented graphically
and in tabulated form.
Keywords Heat transfer · Stretching surface ·
Variable Viscosity · Ohmic heating · Fluid
mechanics
M. Abd El-Aziz (B )
Department of Mathematics, Faculty of Science,
Helwan University, P.O. Box 11795, Cairo, Egypt
e-mail: m_abdelaziz999@yahoo.com
1 Introduction
The study of flow, heat and mass transfer in the
boundary layer induced by a surface moving with
a uniform or non-uniform velocity in a quiescent
ambient fluid is important in several manufactur-
ing process in industry which include the bound-
ary layer along material handling conveyers, the
extrusion of plastic sheets, the cooling of an infinite
metallic plate in a cooling path. Glass blowing, con-
tinuous casting, and spinning of fibers also involve
the flow due to a stretching surface. After Sakiadis
[1, 2] initiated the study of the boundary layer flow
over a continuous solid surface moving with con-
stant speed, the boundary layer flow caused by a
stretching surface has attracted the attention of
many researchers (Tsou et al. [3], Erickson et al.
[4], Soundalgekar and Murthy [5], Ishak et al. [6]).
Early studies dealing with coupled heat and mass
transfer include the works of Gebhart and Pera [7]
on vertical plate, Pera and Gebhart [8], and Chen
and Yuh [9] on inclined plates. Gupta and Gupta
[10] studied heat and mass transfer on a stretch-
ing sheet with suction or blowing. Hydromagnetic
flows and heat transfer have become more impor-
tant in recent years because of many important
applications. For example, in many metallurgical
processes which involve cooling of continuous
strips or filaments, these elements are drawn
through a quiescent fluid. During this process, these
strips are sometimes stretched. The properties of