Natural convection in the annulus between concentric horizontal circular and square cylinders

Abstract

Numerical solutions are presented for natural convection heat transfer between a heated horizontal cylinder placed concentrically inside a square enclosure. Three different aspect ratios (R/L 0.1, 0.2, and 0.3), and four different Rayleigh numbers (Ra = 10, 10, 10, and 10), are considered. The governing elliptic conservation equations are solved in a boundary-fitted coordinate system using a control volumebased numerical procedure. Results are displayed in the form of streamlines, isotherms, maximum stream function estimates, and local and average normalized Nusselt number values. At constant enclosure aspect ratio, the total heat transfer increases with increasing Rayleigh number. For constant Rayleigh number values, convection contribution to the total heat transfer decreases with increasing values of R/L. For convection-dominated flows, the average Nusselt number correlation is expressed as Nu = 0.92Ra(R/ L)*. Generated results are in good agreement with previously published experimental and numerical data.