Abstract
The solution for steady two-dimensional natural convection between two horizontal concentric cylinders, each of which is maintained at a different uniform temperature, is obtained through the first three terms in power series of Rayleigh number. Effects of viscous and compressional heating are neglected, and all fluid properties except the specific weight are treated as constant. The range of Rayleigh number for which the solution is reliable is derived. The streamline configuration obtained for gases and non-metallic liquids is shown to agree with photographic evidence. The influence of Prandtl number is slight for these fluids, but the Prandtl number effect is significant for liquid metals (very small Prandtl numbers), a multicellular streamline configuration being shown for mercury. The conditions under which this multicellular flow occurs are delineated. Velocity and temperature distributions are illustrated and discussed. Both local and overall heat transfer rates are represented by appropriate Nusselt numbers. The influence of Prandtl number on the overall heat transfer is a higher-order effect, entering solely in fourth and higher powers of Rayleigh number.
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