The study of the effect of periodic boundary condition is of primary interest to understand the maximum temperature of the wall and avoid overheating phenomena. Available computational fluid dynamic studies provide information on the effect of the local heat flux or local temperature. This study aims to understand the temperature and fluid flow distribution inside the cavity under such periodic thermal boundary conditions to avoid overheating phenomena. This study reports the numerical results of the natural convection inside an air-filled cavity with its horizontal walls insulated and its vertical walls at different thermal boundary conditions. The heat flux of the left wall and the temperature of the right wall are varied sinusoidally. The Lattice Boltzmann Method (LBM) is used to solve the governing equations with the related boundary conditions. The maximum temperature of the wall under the heat flux and the maximum stream function inside the cavity are investigated. Also, the effect of oscillation period on the maximum temperature of the left wall is studied. The results show that the maximum temperature of the left wall corresponds to the heat flux wavelength of 0.8. Moreover, the stream function value increases intensively by increasing the Rayleigh number.

中文翻译：

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具有周期性边界条件的腔内自然对流的格子 Boltzmann 模拟

研究周期性边界条件的影响对于了解壁的最高温度和避免过热现象具有重要意义。可用的计算流体动力学研究提供了有关局部热通量或局部温度影响的信息。本研究旨在了解在这种周期性热边界条件下空腔内的温度和流体流动分布，以避免出现过热现象。本研究报告了在不同热边界条件下，水平壁绝缘和垂直壁的充气腔内自然对流的数值结果。左壁的热通量和右壁的温度呈正弦变化。格子玻尔兹曼方法 (LBM) 用于求解具有相关边界条件的控制方程。研究了热流作用下壁面的最高温度和腔内的最大流函数。此外，研究了振荡周期对左壁最高温度的影响。结果表明，左壁最高温度对应的热通量波长为0.8。此外，流函数值随着瑞利数的增加而急剧增加。结果表明，左壁最高温度对应的热通量波长为0.8。此外，流函数值随着瑞利数的增加而急剧增加。结果表明，左壁最高温度对应的热通量波长为0.8。此外，流函数值随着瑞利数的增加而急剧增加。