The effect of variable thermal conductivity on the characteristics of heat transfer and mechanical properties of a moving surface on a casson-nanofluid flow as a coolant has been studied in this paper. We used similarity transformation method to transform the equations of the governing boundary layer into ordinary differential equations which are solved numerically using a mix of fourth order Runge Kutta method and find root technique. Different values relevant parameters have been studied on the features of velocity, temperature and the profiles of concentration and discussed in details for different values of various parameter as shape parameter, heat source parameter, radiation parameter and magnetic parameter. The results were compared with previous published researches and obtained it in a good agreement and the results were tabulated. Furthermore, Nusselt number, Sherwood number and the Skin friction values with different parameters were calculated and the influence of theses physical quantities on the mechanical properties on the surface are analyzed and discussed in details.