This research attempts to investigate the effects of concentration and radius ratio on convective heat transfer and entropy generation of a non-Newtonian hybrid nanofluid flowing through a concentric an- nulus. The nanofluid is prepared by suspending tetramethylammonium hydroxide (TMAH) coated Fe 3 O 4 (magnetite) nanoparticles and gum arabic (GA) coated carbon nanotubes (CNTs) in water. Variable ther- mal conductivity and viscosity are used in simulations. The convective heat transfer coefficient of inner and outer walls, and total entropy generation augment with increasing Fe 3 O 4 and CNT concentrations. Increasing radius ratio from 0.2 to 0.8, at CNT concentration of 1.1% and Fe 3 O 4 concentration of 0.7%, de- creases the heat transfer coefficient of inner wall by 85.05%, while increases that of outer wall by 35.49%. Models of convective heat transfer coefficient of both walls and total entropy generation are developed using neural network. Genetic algorithm is used with compromise programming to achieve optimal cases with maximum heat transfer and minimum entropy generation. In this method, the objective functions are mixed and the problem transforms into a single-objective optimization. Finally, applying the nanofluid with high concentrations is recommended for all conditions except the cases in which importance of en- tropy generation is considered much greater than that of heat transfer.