A novel EMHD dissipative second-grade nanofluid flow model is proposed exclusively in this numerical inspection for radiating copper-based ethylene glycol nanofluids to reveal the dynamical and thermal aspects of the studied homogeneous mixture during its unsteady two- dimensional stagnation point flow towards a horizontal electromagnetic actuator. Based on admissible physical assumptions and authenticated experimental correlations, the governing PDEs and BCs are derived appropriately for the nanofluid flow problem under consideration. After numerous rearrangements and non-dimensionalization treatments, the resulting ODEs and BCs are handled computationally with the help of a robust GDQ algorithm under the parametric control of several influencing factors, whose strengthening magnitudes affect probably the flow control process and heat transport mechanism. In this context, it proved graphically that the nanoparticles’ loading process exhibits dissimilar dynamical and thermal impacts as compared with the influences of the nanoparticles’ diameter size. Besides, the resistive dynamical effect of the utilized electromagnetic actuator reinforces thermally the enhancing role of the thermal radiative heat flux and Joule’s heating process within the nanofluidic medium.