Boundary Layer Flow past a stretching surface with constant wall temperature, of a nanofluid is studied for heat transfer characteristics. The system of partial differential equations describing such a flow is subjected to similarity transformations gives rise to a boundary value problem involving a system of ordinary differential equations. This system is solved by a shooting method. Effect of the non-dimensional parameters on temperature and concentration profiles are displayed graphically for different values of the parameters, namely, Brownian motion parameter, Lewis number, Prandtl number and thermophoresis parameter. The reduced Nusselt number and the reduced Sherwood number are also shown in a tabular form. The main objective of this paper is to extend the numerical investigation of boundary-layer flow of steady state, two-dimensional flow of nanofluid over a stretching surface with the impact of viscous dissipation. The ordinary differential equations are obtained by applying similarity transformation on partial differential equations. Then, the system is solved by applying the shooting techniques together with Adams-Bashforth Moulton Method. Software Fortran is used to compute the numerical results and the resulting values are indicated through graphs and tables.