<p>Non-Newtonian fluid keeps the significant impact in everyday life, economic growth, technological advancement essentially on human health including blood flow, biomedical uses etc. Moreover, application of Stefan blowing on non-Newtonian fluid flow over a stretching disk makes it more acceptable due to its optimized capacity of heat and mass transfer, enhanced capacity of lubrication etc. These facts motivate us to consider this research. The aim of this investigation is to explore the effects of nonlinear thermal radiation and Newtonian heating on heat transfer of Eyring–Powell nanofluid flow past a radially stretching disk in presence of Stefan blowing. Two phase model for nanofluid has been considered. Inclusion of nonlinear radiation and Stefan blowing makes this research distinct from others. The governing partial differential equations are converted into a system of ordinary differential equations with the help of similarity transformations. Then, these equations are solved numerically by fourth order Runge–Kutta method with shooting technique. The effects of fluid controlling pertinent parameters on fluid velocity, temperature and concentration of the fluid, skin friction coefficient, Nusselt number and Sherwood number are explored graphically and numerically. Improvement in flow velocity is observed for stretching parameter as well as Stefan blowing. Temperature enhancement is noted for rising values of stretching parameter. But the temperature reduces with the rise in Stefan blowing parameter as well as radiation parameter. The reduction of Nusselt number by the enhancement of temperature ratio parameter and radiation parameter which can be used in controlling the rate of heat dissipation in cooling system, in improving thermal insulation, in the design of heat exchanger for minimizing heat transfer rate. For the important findings of flow over stretched disk problems, these are generally used for the understanding of the dynamics of hurricanes, tornados and rotor–stator systems of turbines.</p>