Abstract
This paper examines natural convection in the shallow annular gap between two concentric circular cylinders. Asymptotic solutions are obtained in the limit as the aspect ratio ϵ (defined as the ratio of the enclosure height to the gap width) goes to 0. It is shown that the solution at O( ϵ n ) can only be completely specified by examining the governing equations at O( ϵ n+2 ). Solutions are obtained, and Nusselt number correlations are presented, when the dimensionless radius of the inner cylinder δ is of O(1/ ϵ) and when δ is of O(1). The results indicate that curvature effects profoundly influence the nature of convection in shallow annular enclosures.
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