This work investigates heat transfer and entropy generation of a turbulent flow of an Al2O3–Cu/water hybrid nanofluid in a plain tube (PT) with classical (TPT) and elliptical‑cut twisted tape (TECT) inserts. The heat transfer and pressure drop are investigated numerically at Re (7000–15,000), mass concentration (1–4%), and the inlet temperature of the fluid (300 K). Further, the total entropy generation and Bejan number are examined at Re = 7000 and a mass concentration of 4%. The obtained results indicate that heat transfer can be intensified when inserting classical and elliptical‑cut twisted tape. In addition, an increase in the thermal conductivity of the fluid may cause a slight increase in the heat transfer coefficient. Moreover, heat transfer and thermal performance factors increase when the mass concentration of nanoparticles increases. The Nusselt numbers for TECT and TPT are 1.7 and 1.57 times higher than those for PT, respectively. The Nusselt number and thermal performance factor of hybrid nanofluid are greatest at roughly 195 and 1.9, respectively, showing 3.9% and 7.73% improvement compared to CuO/water nanofluid at Re = 7000. The analysis of the generation of entropy is expressed as a function of thermal and frictional contributions. The results indicate the existence of a minimum entropy generation for each type of tubes for Al2O3–Cu/water hybrid nanofluid. Total entropy generation analysis demonstrates that thermal entropy generation dominates at high heat flux. Moreover, increasing the nanoparticles decreases the generation of total entropy, which is ascribed to the thermal conductivity increment. In addition, the rate of total entropy generation declines as the vortex flow increases.