• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2744-2749
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• 2008

Numerical calculations are carried out for the natural convection induced by temperature difference between a cold outer square cylinder and a hot inner circular cylinder for Rayleigh number of $Ra=10^7$. This study investigates the effect of the inner cylinder location on the heat transfer and fluid flow. The location of inner circular cylinder ($\delta$) is changed vertically along the center-line of square enclosure. The natural convection bifurcates from unsteady to steady state according to $\delta$. Two critical positions of ${\delta}_{C,L}$ and ${\delta}_{C,U}$ as a lower bound and an upper bound are ${\delta}_{C,L}=0.05$ and ${\delta}_{C,U}=0.18$, respectively. Within the defined bounds, the thermal and flow fields are steady state. When the inner cylinder locates at ${\delta}{\geq}{\delta}_{C,U}$, the space between the upper surface of inner cylinder and the top surface of the enclosure forms a relatively shallow layer where the natural convection characterized as the pure Rayleigh-Benard convection forms alternately the upwelling and downwelling plums, as a result that a series of cells known as Benard cells is derived.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.12
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• pp.975-982
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• 2014

This study evaluates the effect of a heated circular cylinder's size on three-dimensional natural convection in a cubical enclosure. The Rayleigh number was varied between $10^3$ and $10^5$, and the Prandtl number was maintained at 0.7. In this study, the radius of the circular cylinder was changed by 0.1 L within a range of 0.1-0.4 L. The thermal and fluid flow characteristics were regarded to be independent of time in the range of the Rayleigh number and cylinder radius considered in this study. The surface-averaged Nusselt numbers of the cylinder and the enclosure were found to increase with the increase in the radius of the cylinder. The effect of the cylinder's size on natural convection in the enclosure was analyzed across the thermal and flow fields, and the distributions of the Nusselt numbers.