International Journal of Engineering and Manufacturing Science. ISSN 2249-3115 Volume 8, Number 1 (2018), pp. 1-14 © Research India Publications http://www.ripublication.com MHD Flow of Non-Newtonian Viscoelastic Fluid on Stretching Sheet With The Effect of Slip Velocity Adamu Gizachew 1* , Bandari Shankar 2 1 Department of Mathematics, College of Science Osmania University, Hyderabad, India & Addis Ababa Science and Technology University 2 Department of Mathematics, University College of Science Osmania University, Hyderabad, India. *Corresponding Author Abstract In this study, MHD steady laminar flow and heat transfer in non-Newtonian viscoelastic fluid expanded on a horizontal plane is considered. The governing non-linear momentum and thermal boundary layer equations are reduced to a set of non-linear ordinary differential equations by appropriate transformation. To evaluate the temperature and velocity profiles of the problem we used Optimal Homotopy Asymptotic Method (OHAM). The influence of various parameters such as, magnetic parameter, viscoelastic parameter, Prandtl number, and viscous dissipation parameter on curves, speed, and temperature are investigated through graphs and tables. It is observed magentic parameter, and viscoelastic parameter increases the thickness of thermal boundary layer. Keywords: laminar flow; non-Newtonian fluid; viscoelastic, MHD; Spread sheet. 1. INTRODUCTION The study of laminar boundary layer flow of non-Newtonian fluids over continuous moving surfaces is an important type of flow occurring in a number of engineering processes. Aerodynamic extrusion of plastic sheets, cooling of an infinite metallic plate in a cooling bath, the boundary layer along a liquid film in condensation processes and a polymer sheet or filament extruded continuously from a die are examples of practical importance. Also, glass blowing, continuous casting, and spinning of fibers involve the flow due to a stretching surface. Furthermore, it has several practical applications in the field of metallurgy and chemical engineering such as the material manufactured by the extrusion process and heat-treated materials traveling between a feed roll and a wind-up roll or on conveyor belt possess the feature of a moving continuous surface.