An analysis is performed to investigate the effect of MHD and thermal radiation on the two-dimensional steady flow of an incompressible, upper-convected Maxwells (UCM) fluid in presence of external magnetic field. The governing system of partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and is solved numerically by efficient shooting technique. Velocity and temperature fields have been computed and shown graphically for various values of physical parameters. For a Maxwell fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for the higher elastic number which agrees with the results of Hayat et al. 2007 and Sadeghy et al. 2006. The objective of the present work is to investigate the effect of elastic parameter β, magnetic parameter Mn, Eckert number Ec, Radiation parameter N, and Prandtl number Pr on flow and heat transfer charecteristics. 1. Introduction In recent years, the studies of boundary layer flows of Newtonian and non-Newtonian fluids over a stretching surface have received considerable attention because of their numerous applications in the field of metallurgy and chemical engineering and, particularly, in the extrusion of polymer sheet, from a die or in the drawing of plastic films. During the manufacture of these sheets, the melt issues from a slit and is subsequently stretched to achieve the desired thickness. Such investigations of magnetohydrodynamic (MHD) flow are very important industrially and have applications in different areas of research such as petroleum production and metallurgical processes. The magnetic field has been used in the process of purification of molten metals from nonmetallic inclusions. The study of flow and heat transfer caused by a stretching surface is of great importance in many manufacturing processes such as in extrusion process, glass blowing, hot rolling, manufacturing of plastic and rubber sheets, crystal growing, continuous cooling, and fibers spinning. Water is amongst the most widely used coolant liquid. In all these cases, a study of flow field and heat transfer can be of significant importance because the quality of the final product depends to a large extent on the skin friction coefficient and the surface heat transfer rate [1]. Sarpakaya [2] was the first researcher to study the MHD flow a of non-Newtonian fluid. Prandtl’s boundary layer theory proved to be of great use in Newtonian fluids as Navier-Stokes equations can be converted into much simplified boundary layer equation which
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