Natural Convection in Vertical Annuli: A Numerical Study for Constant Heat Flux on the Inner Wall

A numerical investigation has been conducted to evaluate the effects of diameter ratio and aspect ratio in natural convection of gases within vertical annuli. The inner cylinder is maintained at uniform heat flux and the outer cylinder at constant temperature. The horizontal top and bottom walls are insulated. Detailed results of heat transfer rate, temperature, and velocity fields have been obtained for 1 ≤ κ ≤ 15, 1 ≤ A ≤ 10, and 100 < Ra_L^* < 10⁷. The inner wall temperature is a function of diameter ratio and aspect ratio. The heat transfer results have been compared with those for isothermal heating, and have been found to be higher. The inner diameter is seen to be the appropriate length scale for high Rayleigh number flows and/or high radius ratios, and the radius ratio effect on heat transfer is seen to be insignificant for radius ratios greater than 10. The heat transfer results based on the inner diameter are in very good agreement with published experimental results, although these experiments were conducted for very high aspect ratio. Heat transfer correlations are provided.