The entropy generation due to mixed convective heat transfer of nanofluids past a rotating circular cylinder placed in a uniform cross stream is investigated via streamline upwind Petrov–Galerkin based finite element method. Nanosized copper (Cu) particles suspended in water are used with Prandtl number (Pr) = 6.9. The computations are carried out at a representative Reynolds number (Re) of 100. The dimensionless cylinder rotation rate, α, is varied between 0 and 2. The range of nanoparticle volume fractions (ϕ) considered is 0 ≤ ϕ ≤ 5%. Effect of aiding buoyancy is brought about by considering two fixed values of the Richardson number (Ri) as 0.5 and 1.0. A new model for predicting the effective viscosity and thermal conductivity of dilute suspensions of nanoscale colloidal particles is presented. The model addresses the details of the agglomeration–deagglomeration in tune with the pertinent variations in the effective particulate dimensions, volume fractions, as well as the aggregate structure of the particulate system. The total entropy generation is found to decrease sharply with cylinder rotation rates and nanoparticle volume fractions. Increase in nanoparticle agglomeration shows decrease in heat transfer irreversibility. The Bejan number falls sharply with increase in α and ϕ.