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首页> 外文期刊>Journal of Heat Transfer >Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating
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Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure Due to Uniform and Nonuniform Bottom Heating

机译：均匀和不均匀底部加热引起的三角形外壳自然对流流动的有限元模拟

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摘要

A penalty finite element analysis with biquadratic elements has been carried out to investigate natural convection flows within an isosceles triangular enclosure with an aspect ratio of 0.5. Two cases of thermal boundary conditions are considered with uniform and nonuniform heating of bottom wall. The numerical solution of the problem is illustrated for Rayleigh numbers (Ra), 10~3 ≤ Ra ≤ 10~5 and Prandtl numbers (Pr), 0.026 ≤ Pr ≤ 1000. In general, the intensity of circulation is found to be larger for nonuniform heating at a specific Pr and Ra. Multiple circulation cells are found to occur at the central and corner regimes of the bottom wall for a small Prandtl number regime (Pr =0.026-0.07). As a result, the oscillatory distribution of the local Nusselt number or heat transfer rate is seen. In contrast, the intensity of primary circulation is found to be stronger, and secondary circulation is completely absent for a high Prandtl number regime (Pr=0.7-1000). Based on overall heat transfer rates, it is found that the average Nusselt number for the bottom wall is 2~(1/2) times that of the inclined wall, which is well, matched in two cases, verifying the thermal equilibrium of the system. The correlations are proposed for the -average Nusselt number in terms of the Rayleigh number for a convection dominant region with higher Prandtl numbers (Pr=0.7 and 10).
机译：进行了用二次二次元进行惩罚的有限元分析，以研究纵横比为0.5的等腰三角形围护结构内的自然对流。考虑两种情况的热边界条件，即底壁受热均匀和不均匀。对该问题的数值解进行了说明，其中瑞利数（Ra）为10〜3≤Ra≤10〜5，普朗特数（Pr）为0.026≤Pr≤1000。通常，发现循环强度较大在特定的Pr和Ra下加热不均匀。对于小的Prandtl数形式（Pr ＝ 0.026-0.07），发现在底壁的中央和拐角区域出现多个循环细胞。结果，可以看到局部努塞尔数或传热速率的振荡分布。相反，对于高普朗特数方案（Pr = 0.7-1000），发现一次循环的强度较强，而完全没有二次循环。根据总传热速率，发现底壁的平均努塞尔数是倾斜壁的平均努氏数的2〜（1/2）倍，这在两种情况下很好地匹配，从而验证了系统的热平衡。对于具有较高普朗特数（Pr ＝ 0.7和10）的对流占优势区域，根据瑞利数建议对平均努塞尔特数进行相关。

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