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