ANALYSIS OF NATURAL CONVECTION IN THE SPACE BETWEEN CONCENTRIC VERTICAL CYLINDERS OF DIFFERENT HEIGHT AND DIAMETER

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Abstract
Numerical finite-difference solutions were carried out for natural convection in the enclosed space between two concentric vertical cylinders, with each cylinder being maintained at a different uniform temperature. In the Investigated configurations, the Inner cylinder was of lesser height than the outer cylinder. For the computations, the height of each cylinder was set equal to its diameter. The investigated parameters Included the ratio of the inner-cylinder diameter to the outer-cylinder diameter, the vertical position of the inner cylinder, and the Rayleigh number of the inner cylinder: the Prandtl number was fixed at 0.7 for all cases. The presentation of results encompassed streamline and isotherm maps, velocity profiles, per-surface and overall heat transfer rates and Nusselt numbers, and local Nusselt numbers. It was found that as the natural convection grows stronger with Increasing Rayleigh number, the most vigorous motions tend to be concentrated in the upper portion of the enclosure, with an accompanying bottom-to-top stratification. At a given Rayleigh number, the natural convection is stronger for smaller diameter ratios. In the presence of vigorous natural convection, the overall inner-cylinder Nusselt number corresponding to a given Rayleigh number is nearly Independent of the geometric parameters (diameter ratio, inner-cylinder elevation) in the investigated range. On the other hand, the local Nusselt number distributions are more responsive to the geometry of the configuration.