The Galerkin finite element method was used to analyze the natural convection heat transfer in an irregular enclosure made by two isothermal concentric horizontal cylinders: the inner square cylinder and the outer circular cylinder. Two different aspect ratios, A/R = 0.2 and 0.4, are considered for two possible symmetric attitudes of the inner square cylinder. For the case of aspect ratio 0.4, experimental verification has also been made by obtaining field temperature measurement and streamline visualization. It is found that there is no boundary layer separation past the sharp edges of the inner cylinder in the range of Rayleigh numbers less than 105, although this phenomenon plays a negative role in the local and overall heat transfer. Above the upper horizontal surface of the inner square cylinder, a well-defined symmetric plume is found despite its low flow speed and temperature gradient. For the geometry of stand-on-edge position of the inner cylinder, vortex cores exist in the enclosure in quadruple for Ra≤5.0×104 and A/R = 0.4, and in double for other cases including A/R = 0.2.

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