A numerical study is carried out to study the effects of variable fluid properties on the boundary layer flow and heat transfer of a nanofluid at a flat sheet. The effects of Brownian motion, thermophoresis and viscous dissipation due to frictional heating are also considered. The temperature-dependent variable fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function and a linear function of temperature. Using a similarity transformation, the governing non-linear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and these equations are solved numerically by Keller-Box method. Velocity, temperature, and nanoparticles volume fraction profiles are presented and analyzed for several sets of values of the governing parameters; namely, variable fluid viscosity, variable thermal conductivity, Brownaian motion, thermophoresis and plate-velocity parameters with changes in the Prandtl and Schmidt numbers. It is observed that there is an increase in the skin friction in the upstream movement of the plate: But quite the opposite is true in the downstream movement of the plate. Also, the effect of the Schmidt number and the Brownian motion parameter is to reduce the Sherwood number, where as the effect of thermophoresis parameter is to enhance it.