The study of laminar boundary layer flow over a stretching sheet has received considerable attention in the recent past due to its immense application in industry, for example, in extrusion processes such as the polymer extrusion from a dye and wire drawing. Other engineering applications of the stretching sheet problem include polymer sheet extrusion from a dye, drawing, tinning and annealing of copper wires, glass fiber and paper production, the cooling of a metallic plate in a cooling bath and so on. There has been tremendous amount of work on the stretching sheet problem in the past several decades (see Crane [1], Gupta and Gupta [2], Grubka and Bobba [3], Dutta and Gupta [4], Siddappa and Abel [5], Chen and Char [6], Laha *et al.* [7], Chakrabarti and Gupta [8], Anderson *et al.* [9], Siddheshwar and Mahabaleswar [10], Abel and Mahesha [11], Abel *et al.* [12] and the references therein).

The above studies concern the linear stretching sheet problem but most of the practical situations involve a non-linear stretching sheet such as an exponential one. With this in mind, several authors have considered the velocity of the sheet to vary exponentially with the distance from the slit. Elbashbeshy [13] was among the first to study the exponentially stretching sheet problem. He considered a perforated sheet and examined the effect of wall mass suction on the flow and heat transfer over an exponentially stretching surface. Using a suitable similarity transformation, he transformed the momentum equation into a non-linear Riccati type equation and solved it iteratively. Ishak [14] studied the MHD boundary layer flow due to an exponentially stretching sheet with radiation effect. He found that the local heat transfer rate at the surface decreased with increasing values of the magnetic and radiation parameters. The flow and heat transfer from an exponentially stretching surface was considered by Magyari and Keller [15]. They examined the heat and mass transfer characteristics and compared with the well-known results of the power-law models. Sanjayanand and Khan [16] studied the heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet. They found that the viscoelastic parameter enhances the thermal boundary layer thickness. The effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface was studied by Partha *et al.* [17]. They observed a rapid growth in the non-dimensional skin friction coefficient with the mixed convection parameter. The influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet is studied by Sajid and Hayat [18]. Khan [19] presented an elegant solution of the viscoelastic boundary layer flow over an exponentially stretching sheet in terms of Whittaker’s function.

The characteristics desired of the final product in an extrusion process depend on the rate of stretching and cooling. Hence, it is very important to have a controlled cooling environment where the flow over the stretching sheet can be regulated by external agencies like a magnetic field. An exponential variation of a magnetic field is used, among other applications, to determine the diamagnetic susceptibility of plasma. Steenbeck [20] determined the diamagnetic susceptibility of a cylindrical plasma for axial magnetic fields with various gas pressure and magnetic field strengths. Tonks [21] studied the effects of a magnetic field in the plasma of an arc. Pavlov [22] considered the magnetohydrodynamic flow of an incompressible viscous fluid over a linearly stretching surface. Sarpakaya [23] extended Pavlov’s work to non-Newtonian fluids. Subsequent studies by Andersson [24], Lawrence and Rao [25], Abel *et al.* [26], Cortell [27] concerned the magnetohydrodynamic flow of viscoelastic liquids over a stretching sheet. Radiation effects on MHD flow past an exponentially accelerated isothermal vertical plate with uniform mass diffusion in the presence of a heat source was studied by Reddy *et al.* [28]. They observed that the velocity decreases with an increase in the magnetic parameter due to a resistive drag force which tends to resist the fluid flow and thus reduces the velocity. The boundary layer thickness was also found to decrease with an increase in the magnetic parameter.

Most of the earlier work neglected radiation effects. If the polymer extrusion process is placed in a thermally controlled environment, radiation could become important. As with magnetohydrodynamics, careful control of thermal radiative heat transfer has an effect on the characteristics of the final product. Many researchers have considered the effect of thermal radiation on flows over stretching sheets. Studies by Raptis [29], Raptis and Perdikis [30] address the effect of radiation in various situations. Siddheshwar and Mahabaleswar [10] studied the effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet. Bidin and Nazar [31] studied the effects of numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation. They observed that the temperature profiles and the thermal boundary layer thickness increase slightly with an increase in the Eckert number. They also showed that an increase in *Pr* causes a decrease in temperature profiles and the thermal boundary layer thickness. Physically, if *Pr* increases, the thermal diffusivity decreases, and these phenomena lead to the decreasing of energy ability that reduces the thermal boundary layer. Elbashbeshy and Dimian [32] analyzed boundary layer flow in the presence of radiation effect and heat transfer over the wedge with a viscous coefficient. Thermal radiation effects on hydro-magnetic flow due to an exponentially stretching sheet were studied by Reddy and Reddy [33]. They found that as radiation increases, the temperature profiles and thermal boundary layer thickness also increase. They also observed that the temperature profiles and thermal boundary layer thickness increase slightly with an increase in the Eckert number. Raptis *et al.* [34] studied the effect of thermal radiation on the magnetohydrodynamic flow of a viscous fluid past semi-infinite stationary plate and Hayat *et al.* [35] extended the analysis for the second grade fluid.

In addition to a magnetic field and thermal radiation, one has to consider the viscous dissipation effects due to frictional heating between fluid layers. The effect of viscous dissipation in natural convection processes has been studied by Gebhart [36] and Gebhart and Mollendorf [37]. They observed that the effect of viscous dissipation is predominant in vigorous natural convection and mixed convection processes. They also showed the existence of a similarity solution for the external flow over an infinite vertical surface with an exponential variation of surface temperature. Vajravelu and Hadjinicalaou [38] studied the heat transfer characteristics over a stretching surface with viscous dissipation in the presence of internal heat generation or absorption.

In this paper, we investigate the effects of various physical and fluid parameters such as the magnetic parameter, radiation parameter and viscous dissipation parameter on the flow and heat transfer characteristics of an exponentially stretching sheet. The momentum, energy and concentration equations are coupled and nonlinear. By using suitable similarity variables, these equations are converted into coupled ordinary differential equations and are solved analytically and numerically by using the Runge-Kutta-Fehlberg and Newton-Raphson schemes.