In this study, the heat transfer and entropy of transient non‐Newtonian Powell–Eyring nanofluid flow is studied. The nanofluid flows over a stretched flat surface, moving nonuniformly. The flow and heat transfer properties are analyzed subject to a convective heated slippery surface. This study also examined the thermal radiation, nanoparticle shapes, inclined magnetic field (B), and joule heating. The governing equations of flow are formulated in partial differential equations (PDEs). A numerical technique utilizes the Keller Box Method to find the similarity solution of the reduced ordinary differential equations, converted from PDEs by using an appropriate transformation. Two different nanofluids, copper–methanol (Cu–MeOH) and silicon carbide–methanol (SiC–MeOH), are considered in the analysis. Significant results of various parameters for the flow, heat, Skin friction (Cf), Nusselt number (Nu), and entropy analysis are described graphically. This study's remarkable finding is that the thermal conductivity in Powell–Eyring phenomena gradually increases compared to the conventional fluid. The Cu–MeOH based nanofluid is found to be a superior thermal conductor instead of the SiC–MeOH based nanofluid. The entropy of the system exaggerates with the incorporation of nanoparticle volume fraction
ϕ, thermal radiation Nr, and material parameter
normalΔ. It is found that the slip parameters work as a retarded force to the system and decrease the system's entropy.