The current research aims to investigate energy efficiency and flow characteristics of a non-Newtonian nanofluid containing TiO2 nanoparticles in a chaotic geometry. For this purpose, hydrothermal features of the nanofluid are assessed in the C-shaped channel and compared with the straight channel. Heat transfer and pressure drop in the C-shaped channel are higher than those in the straight channel. This finding is due to intense mixing in the C-shaped channel resulting from chaotic perturbations, such that the velocity and temperature profiles in the C-shaped channel are more uniform than those in the straight one. Convective heat transfer coefficient in chaotic channel has a periodic trend in which it increases in regions where boundary layer is disturbed while decreases in regions where boundary layer is allowed to grow. In comparison with base fluid, applying the nanofluid in both channels presents better cooling along with higher pressure drop. At low Reynolds numbers, development of chaotic advection causes more increment in heat transfer rate in comparison with pumping power and therefore, the value for Figure of Merit (FoM) becomes greater than 1. Simultaneous use of nanofluids and chaotic advection can result in not only greater energy efficiency, but also preventing sedimentation of nanoparticles