Heat transport and entropy generation of steady Prandtl-Eyring hybrid nanofluids (P-EHNF) are explored in a recent article. As the hybrid nanofluid is subjected to a slippery hot surface, the flow and thermal transport characteristics of P-EHNF are investigated. For this study, we are also looking at the effects of hydrodynamical forces, nanosolid particle morphologies, magnetic field and joule heating, as well as changing thermal conductivity and radiative flux. Partial differential equations (PDE) are used to define most of the flow equations in a system of PDE. Numerical scheme of Keller box is implemented on the system of nonlinear ordinary differential equations, which are resultant after application of similarity transformation to governing nonlinear partial differential equations. With Engine Oil (EO) as base fluid, this study examines two different types of nano solid-particles: Copper (Cu) and Zirconium dioxide (ZrO2). Graphical representations of important results for the different variables may be found in the flow, temperature, drag force, Nusselt amount, and entropy measurement sections of the website. The noteworthy result of this analysis is that the comparing rate of heat transfer of P-EHNF (ZrO2–Cu/EO) progressively more upsurges as compared to traditional nanofluid (ZrO2-EO). The model's entropy increases as the nanoparticle size increases. Improved radiative flow NE and Prandtl-Eyring variable ε1 have the same effect on the radiative field.