This study investigates the hotness transport and entropy creation of a time-dependent Prandtl–Eyring half and half nanofluid (P-EHNF). The flow and heat transport features of P-EHNF are analysed by subjecting the nanofluid to the slippage heated surface. The effects of the shapes of the nanosolid molecule, porosity material, Cattaneo–Christov heat flux, and radiative transition are likewise associated with this assessment. In a system of partial differential equalities (PDEs), the transcendent stream conditions are planned. Keller box mathematical strategy is a technique used to recognise the self-similar answer for recipes changed into ordinary differential equalities (ODEs) utilising legitimate changes. Two types of nanoparticles, copper (Cu) and graphene oxide (GO)with engine oil (EO) as the base liquid are considered in this review. Significant outcomes for the various factors are drawn up graphically in the streaming, energy, surface friction, Nusselt sum and entropic estimation. The imperative consequence of this investigation is that the heat transmission pace of P-EHNF (GO–Cu/EO) is more than the customary nanofluid (Cu–EO). Likewise, heat transport is the highest for circular-shaped and the lowest for lamina-shaped nano strong particles. With the upgrade of nanoparticles size φ, the entropy is supported in the model. A similar impact likewise occurs with progress in radiative stream N$_r$ and Prandtl–Eyring variable α$^∗$.