RÉSUMÉ

Axisymmetric numerical simulations have been conducted to analyse steady-state convection of power law fluids in square cross-sectional cylindrical annular space with differentially heated vertical walls for nominal Rayleigh number range 10³ ≤ Ra ≤ 10⁶, nominal Prandtl number range 10² ≤ Pr ≤ 10⁴, and power law exponent range 0.6 ≤ n ≤ 1.8 for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions. It has been shown that the mean Nusselt number based on the inner periphery Nu_i increases with decreasing (increasing) power law exponent (nominal Rayleigh number) due to strengthening of thermal advection. However, Nu_i has been found to be insensitive to the change in nominal Prandtl number. It has been demonstrated that Nu_i decreases with increasing internal cylinder radius (normalized by its height r_i /L) before approaching the mean Nusselt number for a square enclosure in the limit at r_i /L → ∞. By contrast, the mean Nusselt number normalized by the corresponding Nusselt number for pure conductive transport (i.e., Nu_i /Nu_cond) increases with increasing r_i /L. It has been found that Nu_i assumes smaller values for the CWHF boundary condition than in the CWT boundary condition for the same set of values of nominal Rayleigh and Prandtl numbers, and power law exponent for large values of Ra. Detailed physical explanations have been provided for the observed behavior, and correlations for Nut have been proposed based on scaling arguments, which satisfactorily capture the mean Nusselt number obtained from these steady-state simulations.