Entropy generation is squarely linked with irreversibility, and consequently with exergy destruction within a thermal system. This study concerns with the temperature distribution, and local and volumetric averaged entropy generation rates within a cylindrical system with two solid co-rotating inner and outer parts and the middle nanofluid flow part. Temperature-dependent thermal conductivities for solid materials are included within the modeling. To obtain the temperature formula within all three sections, a combined analytical–numerical solution technique is applied. An exact analytical solution is also obtained, when constant thermal conductivities for solid materials are assumed. The resultant data from the analytical–numerical solution technique is verified against the investigated exact solution. Thereafter, the velocity and temperature fields from the combined analytical–numerical solution technique are incorporated into the entropy generation formulations to obtain the local and volumetric averaged entropy generation rates. Using abovementioned procedure, the effects of thermophysical parameters such as nanoparticles volume concentration, Brinkman number, thermal conductivity parameter ratios, outer temperature boundary condition, internal heat generation rates and velocity ratios on the temperature field, and entropy generation rates are investigated.