Owing to higher thermal conductivity, nanofluids have the potential to be the coolant for various applications ranging from internal to external flows. A two-phase model is implemented to model the interaction between nanoparticles and base fluid to obtain accurate results. Heat transfer and entropy generation characteristics of nanofluid (Al2O3 and water) flow over bluff bodies such as circular and square cylinders for steady (20 < Re < 100) and unsteady (Re = 150 and 300) flow conditions have been carried out for various volume fractions (0.5–2 %). The same has been expressed in quantitative and qualitative aspects with parameters such as mean Nusselt number, surface Nusselt number, heat transfer enhancement ratio, and entropy generation. Heat transfer rate increases with an increase in flow rate and volume fraction for both steady and unsteady flow. Heat transfer enhancement in steady flow ranges from 1.10 to 1.35. For unsteady flow (Re = 150 & Re = 300), nanofluid's heat transfer enhancement ratio is higher than water in the range of 1.10–1.8. This is attributed to the early separation of flow and the presence of large recirculatory regions. With the increase in Re, the entropy generation decreases for circular and square cylinders. Compared to nanofluid, the entropy generation is higher for water.