An attempt has been made to study the natural convection around a hollow vertical cylinder numerically which is suspended in motionless power-law fluids in the laminar range. The influence of various non-dimensional pertinent parameters, such as Grashof number (10 ≤ Gr ≤ 105), Prandtl number (0.71 ≤ Pr ≤ 100), and power-law index (0.2 ≤ n ≤ 1.8) on thermofluid characteristics around the hollow cylinder, is predicted computationally. Simulations are performed by varying the cylindrical aspect ratio (L/D) over the range of 1 ≤ L/D ≤ 20. It is reported that the average Nusselt number appreciably grows with the rise of Gr or/and Pr for a constant L/D. Moreover, the rate of rising of Nusselt number (Nu) with Gr or/and Pr strongly depends upon the power-law index (n); i.e., Nu finds a stronger dependence on Gr than that of Pr with a lower value of n (shear-thinning fluids, (n < 1)) and a completely different pattern has been noticed in shear-thickening fluids (n > 1). Furthermore, the average Nu on the outer wall (Nuouter) grows approximately in a linear way with an increase in aspect ratio for a particular Gr, Pr, and n. In contrast, Nuinner drops drastically and almost attains the asymptotic trend at a greater value of aspect ratio for lower Gr or/and Pr. The decreasing pattern of Nuinner is found to be remarkably steep for n < 1 (shear-thinning fluids) in comparison to n > 1 (shear-thickening fluids). Correlations are developed for Nuouter and Nuinner in terms of Gr, Pr, n, and L/D, which operate extremely well within ± 6% of the computational data.