Natural convective heat transfer from an isothermal vertical cylinder with a square cross-section which has an exposed horizontal top surface has been numerically studied. The exposed upper surface is maintained at the same temperature as the vertical walls of the cylinder. The cylinder is mounted on a flat horizontal adiabatic base plate. The interest in this situation stems from the fact that it is an approximate model of some electrical component cooling situations. The flow has been assumed to be steady and laminar and it has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. The solution has been obtained by numerically solving the three-dimensional governing equations, these equations being written in terms of dimensionless variables. The numerical solution has been obtained using a commercial finite element method based code, FIDAP. The solution has the following parameters: the Rayleigh number, Ra, based on the height of the heated cylinder, h, and the overall temperature difference T_w - T_f, the dimensionless size of the square cross-section of the cylinder surface, W = w/h, w being the size of the cross-section, and the Prandtl number, Pr. Because of the applications that motivated this study, results have only been obtained for Pr = 0.7. A wide range of the other governing parameters has been considered. The conditions under which the heat transfer from the exposed upper surface can be neglected compared to that from the vertical side walls in the evaluation of the mean Nusselt number for the entire cylinder have been explored.
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机译：对具有正方形横截面的等温垂直圆柱体的自然对流传热进行了数值研究，该圆柱体的横截面为方形，且表面暴露在外。裸露的上表面保持与圆柱体垂直壁相同的温度。圆柱体安装在平坦的水平绝热基板上。对这种情况的兴趣源于以下事实：它是某些电气组件冷却情况的近似模型。假定流动是稳定的和层流的，并且假定流体性质是恒定的，除了密度随温度的变化会引起浮力，这已经通过使用Boussinesq方法进行了处理。该解决方案是通过对三维控制方程进行数值求解而获得的，这些方程是根据无量纲变量编写的。使用基于商业有限元方法的代码FIDAP获得了数值解。该解决方案具有以下参数：基于加热圆柱体的高度h和总温差T_w-T_f的瑞利数Ra，圆柱体表面正方形横截面的无量纲尺寸，W = w / h，w是横截面的大小，Prandtl数Pr。由于推动了这项研究的应用，仅在Pr = 0.7时获得了结果。已经考虑了广泛的其他控制参数。在评估整个气缸的平均努塞尔数时，已经探索了与从垂直侧壁传热相比可以忽略从暴露的上表面传热的条件。
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