The rheology of non-Newtonian fluids is of an immense importance in wide range of engineering applications involving flows over stretching surfaces along with heat and mass transfer. The present thesis focuses on examining steady two dimensional nonlinear flows in the presence of heat and mass transfer effects. Mathematical formulations for nonlinear flows over vertical and horizontal stretching surfaces in the presence of viscosity variation, magnetic field, magnetic dipole, convective and mass flux boundary conditions are carried out in Cartesian coordinate system. Nanoparticles presence is very beneficial for enhancing thermal properties of base fluids and has importance in engineering processes. The shape and size of the nanoparticles play vital role in improving thermal conductivity and this thesis emphasis on examining these effects. The close form and numerical solutions are presented for emerging nonlinear coupled partial differential equations by using shooting algorithm embedded with Runge- Kutta Fehlberg method. The validity of numerical results is performed through comparison tables in the limiting sense with available literature. The effects of pertinent physical parameters are discussed through graphs and tabulated results are presented for skin friction coefficient, Nusselt and Sherwood numbers