The two-dimensional time-dependent natural convection heat transfer of non-Newtonian nanofluids is studied numerically between the gap of two horizontal cylinders. The inner and outer cylinders were kept at Ti and To (Ti>To), respectively. The finite volume technique was used in the study. The effects of Ra number (103Ra106), aspect ratio (0.4AR1.2), power law index of the nanofluid (0.6n1.4), horizontal eccentricity (0.2 epsilon H0.8), vertical eccentricity (-0.8 epsilon v+0.8) and rotation of the inner cylinder (0500) on the flow field and heat transfer were investigated. It was found that a very good agreement exists with the present numerical results and the results of the open literature. The results indicate that with increasing the Ra number from 103 to 106 the heat transfer increases by about 80%. The increase in aspect ratio also increases the heat transfer. The results showed that with increasing the power law index from 0.6 to 1.4, the heat transfer decreases by a rate of about 78%. In addition, the time to reach steady-state conditions increases with increasing power law index. Simulations were performed for a power law index of 0.8 to investigate the effect of eccentricity of the inner cylinder, and it was observed that the heat transfer is higher for negative vertical eccentricities, and the time to reach steady conditions shortens with the effect of negative vertical eccentricity and power law index.