Boundary Layer Regime for Laminar Free Convection between Horizontal Circular Cylinders

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Abstract
The steady, buoyancy-driven, laminar motion induced in the annulus of two horizontal, concentric, circular cylinders by a difference in the boundary temperatures is studied analytically in the large Rayleigh number limit. The flowfield is divided into five physically distinct regions: (1) an inner free convection boundary layer near the inner cylinder, (2) an outer free convection boundary layer near the outer cylinder, (3) a vertical plume above the inner cylinder, (4) a stagnant region below the inner cylinder, and (5) a core region surrounded by the other four regions. Zeroth-order solutions which account for the coupling of those five regions are obtained in the high Prandtl number limit using a boundary-layer approximation and integral methods. Comparisons of the calculated heat transfer and temperature fields with experiment and numerical finite-difference results are favorable.

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