The present investigation of the rotating disk system is highly significant due to its many applications, such as in fluid thermal reactors, regulating fluidic systems and fluid stirring. Subject to the upper functions of the rotating disk, the Stefan blowing into the three-dimensional Reiner–Rivlin (R–R) fluid flow by the rotating disk affect the vertical direction. Thermal radiation and Cattaneo–Christov (CC) energy diffusion effects are examined into considering energy transport. The chemical reaction is accommodated in the concentration equation. The convective boundary conditions are considered in the disk surfaces. The ensuing nonlinear systems are determined by applying the Bvp4c routine along with the shooting method. The obtained outcomes are shown graphically with physical justification. The results show that R–R parameters cause a downturn in the radial and tangential velocity profiles as well as the temperature field. The curves of the temperature profile enhance with higher values of radiation parameter. Although this radiation falls onto the fluid surface and increases the temperature of the liquid as hot particles collide with cold particles, the skin friction coefficients decrease with suction. However, the heat and mass transfer rates are enhanced. The current model has been validated by comparing the simplified version of the investigation to a previously published article and a close agreement has been found.