Abstract Three-dimensional numerical simulations were conducted for the natural convection phenomena which occurs between an inner hot body and its outer enclosure. The physical model considered here is that a body of cubical shape is located at the center of an isothermal cooled spherical enclosure. Therefore, the fluid flow inside the enclosure results from the temperature difference between the cooled spherical enclosure and the heated cube. The governing equations are solved using a second-order accurate finite volume approach on a staggered grid system and multi-grid acceleration. Three different fluids, an air (Pr = 0.71), a water (Pr = 6.2) and the other a dielectric liquid (Pr = 25) are employed encompassing descriptive Rayleigh numbers Ra that range three orders of magnitude from 104 to 107. The conducted benchmark study leads to excellent accordance with previous findings. Detailed three-dimensional flow and thermal structures in the enclosure were analyzed using the distribution of iso-contours of temperature, iso-surfaces of the standard velocity vector and streamtraces for different Rayleigh numbers. The variation of the local and the surface-averaged Nusselt numbers at the inner hot cube wall are also presented to exhibit the overall heat transfer characteristics inside the enclosure. At the end, monomial correlations are presented for the quantification of the heat transfer that emanates from the heated cube and the spherical enclosure in harmony with the various Rayleigh number. It was found that the thermal and flow fields eventually reach steady state for Rayleigh numbers ranging from 104 to 107. Results indicate also that the heat transfer is increasing significantly by increasing Rayleigh numbers and optimal heat transfer rate is obtained for high Rayleigh number set to 107.

中文翻译：

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加热立方体与其球形外壳之间自然对流的数值分析

摘要 对内热体与其外壳之间发生的自然对流现象进行了三维数值模拟。这里考虑的物理模型是立方体位于等温冷却球形外壳的中心。因此，外壳内的流体流动是由冷却的球形外壳和加热的立方体之间的温差引起的。在交错网格系统和多网格加速度上使用二阶精确有限体积方法求解控制方程。采用三种不同的流体，空气 (Pr = 0.71)、水 (Pr = 6.2) 和另一种介电液体 (Pr = 25)，包括描述性瑞利数 Ra，范围从 104 到 107 的三个数量级。所进行的基准研究与先前的研究结果非常吻合。使用温度等值线的分布、标准速度矢量的等值面和不同瑞利数的流迹线，对外壳中详细的三维流动和热结构进行了分析。内部热立方体壁处的局部和表面平均努塞尔数的变化也被呈现出来，以展示外壳内部的整体传热特性。最后，提出了单项式相关性，用于量化从加热的立方体和球形外壳发出的热传递，并与各种瑞利数相协调。结果表明，对于 104 到 107 的瑞利数，热场和流场最终会达到稳态。