European Scientific Journal November 2014 edition vol.10, No.33 ISSN: 1857 – 7881 (Print) e - ISSN 1857- 7431 383 EFFECTS OF VISCOUS DISSIPATION AND JOULE HEATING ON MHD FLOW OF A FLUID WITH VARIABLE PROPERTIES PAST ASTRETCHING VERTICAL PLATE Khaled K. Jaber Department of Mathematics, Faculty of Science and information technology, Zarqa University, Zarqa, Jordan Abstract An analysis is presented to study the combined effects of viscous dissipation and Joule heating on MHD free-convective flow of a fluid with variable properties near a linearly stretching isothermal vertical sheet. The flow is subjected to a uniform transverse magnetic field, with high temperature differences between the plate and ambient fluid. The Boussinesq approximation is neglected due to the large temperature differences between the plate and the ambient fluid. The resulting coupled nonlinear differential equations are solved numerically. The effects of magnetic parameter, Grashof number, Eckert number and other involved parameters on the velocity and temperature functions are investigated. Keywords: Astretching Vertical Plate, Viscous Dissipation Introduction The interest in studying the effect of viscous and Joule heating on the MHD flow and heat transfer is due to the important role of this flow in various devices which are subjected to large variations of gravitational force, its application on heat exchanger designs, wire and glass fiber drawing and its application in nuclear engineering in connection with the cooling of reactors. The flow of anelectrically conducting fluid past a continuously moving plate was initiated in 1969 by Sakiadis and then extended by Erickson et al. to include blowing or suction at the plate. After thatmany investigations have focused on the problems of a stretched sheet oriented in the horizontal direction with a linear velocity and a different thermal boundary layer conditions (see for instance Crane and Gupta and Gupta). Vayjravelu and Hadyinicolaou studied the convective heat transfer in an