Abstract Natural convective flow and heat transfer around a locally heated circular cylinder kept in a rectangular enclosure are investigated. At first, a problem valid for a rectangular domain is formulated and then an analytical coordinate transformation is introduced to map the rectangular domain to the physical domain considered here. Based on the coordinate transformation, a set of governing equations is obtained which is further simulated by imposing appropriate conditions on the walls of the cavity and the inner solid bodies. Numerical solutions are validated through comparison of the present results with the available published data. It is found that streamlines and isotherms are greatly influenced by the width (w) and breadth (b) of the heat source and the Rayleigh number ( Ra\mathit{Ra}). The Nusselt number ( Nu\mathit{Nu}) is computed at the surface of the inner and outer cylinders, revealing that it grows considerably when controlling parameters w, b, and Ra\mathit{Ra} are increased. The strength and number of the vortices generated within the velocity field heavily depend on the size and location of the outer cylinder. The span-wise local Nusselt number variation shows some sharp rises compared to the neighboring values in Nu i {\mathit{Nu}_{i}} and Nu o {\mathit{Nu}_{o}}, which is due to the large temperature gradient at those points.

中文翻译：

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放置在矩形外壳中的局部加热圆柱体周围的自然对流

摘要 研究了保持在矩形外壳中的局部加热圆柱体周围的自然对流和传热。首先，提出一个对矩形域有效的问题，然后引入解析坐标变换将矩形域映射到这里考虑的物理域。在坐标变换的基础上，得到了一组控制方程，通过在腔壁和内部实体上施加适当的条件进一步模拟。通过将当前结果与可用的已发布数据进行比较来验证数值解。发现流线和等温线受热源的宽度（w）和宽度（b）以及瑞利数（Ra\mathit{Ra}）的影响很大。Nusselt 数 (Nu\mathit{Nu}) 在内外圆柱表面计算，表明当控制参数 w、b 和 Ra\mathit{Ra} 增加时，它显着增加。速度场内产生的漩涡的强度和数量在很大程度上取决于外圆柱体的大小和位置。与 Nu i {\mathit{Nu}_{i}} 和 Nu o {\mathit{Nu}_{o}} 中的相邻值相比，跨度局部 Nusselt 数变化显示出一些急剧上升，这是由于这些点的大温度梯度。