In recent years, significant patents have been devoted to developing nanotechnology in industry since materials with sizes of nanometers possess unique physical and chemical properties. Due to recent advances in nanotechnology, a new class of heat transfer fluids called nanofluids was discovered. A nanofluid is a mixture produced by dispersing metallic nanoparticles in low thermal conductivity liquids such as water, oils, lubricants and others to enhance the heat transfer performance. Many patents have been devoted to the methods of preparation of new nanofluids heat transfer. Nanofluids are now being developed for medical applications, including cancer therapy and safer surgery by cooling. In this paper, a study of a boundary layer flow and heat transfer characteristics of an incompressible nanofluid flowing over a permeable uniform heat flux surface moving continuously in the presence of radiation is reported. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The resulting system of non-linear ordinary differential equations are solved numerically using a finite difference method. Numerical results are obtained for the velocity, temperature and nanoparticles volume fraction profiles, as well as the friction factor, local Nusselt number and local Sherwood number for several values of the parameters, namely the velocity ratio parameter, suction/injection parameter, Brownian motion parameter, thermophoresis parameter and radiation parameter. It is found that an increase in either of the Brownian motion parameter or the thermophoresis parameter leads to reductions in the local Nusselt number and the local Sherwood number. In addition, increasing either of the suction/injection parameter or the radiation parameter causes enhancements in both the local Nusselt number and the local Sherwood number.