48 Emerging Trends in Computational and Applied Mathematics Introduction Production of polymers of fixed cross-sectional profiles, cooling of metallic and glass plates, the production of sheeting material (which includes both metals and polymers), the drawing of strips which are extruded from a die (with some prescribed velocity) are sometime stretched. The stretching surfaces undergo cooling or heating which causes variations in surface velocities and temperatures. Aforementioned issue has attracted the attention of many researchers in recent years due to its applications in a variety of situations. Sakiadis [1] initiated the study of the boundary layer flow over a continuous solid surface moving with constant speed. He assumed inextensible surface whereas most of the physical situations concern with extensible surfaces moving in a cooling liquid. Crane [2] reported an exact solution for the steady two-dimensional flow of viscous and incompressible fluid induced in the stretching of an elastic flat sheet. He reported that the uniform stress causes the stretching of sheet in its own plane with linear velocity variation along the distance from a fixed point. The pioneering works of Crane are subsequently extended by many authors to explore various aspects of the flow and heat transfer occurring in an infinite domain of the fluid surrounding the stretching sheet. Most of the work reported in the literature is for the case when fluid at rest but, in some practical applications fluid can have some prescribed velocity. Mahapatra and Gupta [3] analyzed stagnation-point flow towards a stretching surface in presence of free stream velocity. They have reported that a boundary layer is formed when stretching velocity is less than the free stream velocity. As the stretching velocity exceeds the free stream velocity then, an inverted boundary layer is formed. Singh et al. [4], [5], [6], [7] reported effect of stretching parameter for orthogonal flow and oblique flow under different conditions. Bachok et al. [8] studied the boundary layer stagnation point flow towards a 11 Effect of variable heat flux and constant suction of a viscous and incompressible MHD fluid flow on a stretching sheet Aryan Kaushik 1 , Anoop Kumar Vashisth 2 , N. S. Tomer 3 , Shri Dhar Kaushik 1 1 ITM University, Gurgaon, Haryana, India-122017 2 GITM, Gurgaon, Haryana, India-122017 3 F. G. M. F. C., Adampur, Hisar, Haryana, India-122017 er.aryankaushik@gmail.com Abstract : This paper deals with steady two-dimensional MHD flow of a viscous and incompressible fluid past a stretching sheet. The flow carries a free stream velocity. Effect of variable heat flux and constant suction has been addressed in this paper. The influence of transverse magnetic field is considered for the fluid flow. The stream function splits into a Hiemenz and a tangential component. Using similarity variables, the governing partial differential equations are transformed into a set of two non-dimensional ordinary differential equations. Runge- Kutta Fehlberg method with shooting technique provides the numerical solutions for these equations. Moreover, the effect of magnetic parameter, suction parameter, heat generation parameter and heat flux parameter on flow and heat transfer characteristics has been discussed and their variations with the stretching sheet parameter have been graphically presented. The results are in good agreement with the previous published work of the researchers working in the same field. Keywords: MHD flow, Stream function, Stretching sheet, Heat flux, Constant suction