In this article, the three-dimensional (3D) flow and heat transport of viscous dissipating Cu-H2O nanoliquid over an elongated plate in a rotating frame of reference is studied by considering the modified Buongiorno model. The mechanisms of haphazard motion and thermo-migration of nanoparticles along with effective nanoliquid properties are comprised in the modified Buongiorno model (MBM). The Rosseland radiative heat flux and prescribed heat flux at the boundary are accounted. The governing nonlinear problem subjected to Prandtl’s boundary layer approximation is solved numerically. The consequence of dimensionless parameters on the velocities, temperature, and nanoparticles volume fraction profiles is analyzed via graphical representations. The temperature of the base liquid is improved significantly owing to the existence of copper nanoparticles in it. The phenomenon of rotation improves the structure of the thermal boundary layer, while, the momentum layer thickness gets reduced. The thermal layer structure gets enhanced due to the Brownian movement and thermo-migration of nanoparticles. Moreover, it is shown that temperature enhances owing to the presence of thermal radiation. In addition, it is revealed that the haphazard motion of nanoparticles decays the nanoparticle volume fraction layer thickness. Also, the skin friction coefficients found to have a similar trend for larger values of rotation parameter. Furthermore, the results of the single-phase nanoliquid model are limiting the case of this study.