SUMMARYIn this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the di erential quadrature (DQ) method. The vorticity-stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 10 4 to 10 6 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of ow and thermal ÿelds. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the ow and thermal patterns.
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