The current work aims to perform the hydrothermal and entropy generation (EG) characteristics in a naturally cooled eccentric horizontal annulus filledwith non-Newtonian water-magnetite/CNT nanofluid (NF). The wall temperature of both cylinders is constant and the temperature of the outer cylinder is lower than that of the inner cylinder. The impacts of vertical eccentricity, nanoadditive concentration (𝜑) and Rayleigh number (𝑅𝑎) on the first and second-laws performance features of the annulus are investigated numerically. It was found the average Nusselt number (𝑁𝑢), the global thermal EG (TEG) and the global frictional EG (FEG) augment with boosting both the 𝑅𝑎 and 𝜑. In addition, it was depicted that the negative eccentricity is desirable and undesirable from the perspective of the first and second-laws of thermodynamics. Moreover, the outcomes revealed that the first-law/second-law performance of the aqueous magnetite/CNT NF is better/weaker than that of the aqueous magnetite NF. Furthermore, for all the examined cases, the TEG rates are much higher than the FEG rates, and as a result, the pattern of total EG changes follows the TEG. Among all the studied cases, the minimum total EG was 4 W/K, which belonged to the case of 𝜑𝑀 = 0.9%, 𝜑𝐶𝑁𝑇 = 0%, 𝑅𝑎 = 103 and 𝑒 = 0.001.
