The motion of a Carreau nanofluid past an infinite vertical non-linear permeable stretching sheet embedded in a non-Darcy porous medium is investigated. It is stressed by a uniform external magnetic field. The thermal radiation and heat generation are taken in consideration as well as Brownian motion with thermophoresis, chemical reaction and partial slip velocity at the boundary layer. The nonlinear partial differential equations describing the motion with heat and mass transfer are transformed to non-linear ordinary differential equations and solved by using Runge-Kutta method with approbriate boundary conditions. The effects of the physical parameters of the problem on the obtained solutions are discussed numerically and graphically. Through the section of discussion the skin friction and the rate of heat and mass transfer are computed. It is found that these physical parameters play an important rules to control the obtained velocity, temperature and concentration of the fluid.