非均匀内部热源驱动对流的温度和热通量界

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中文摘要：通过理论分析和数值模拟研究了两个水平等温壁面之间受非均匀内部热源驱动的对流，以探索温度和数值热通量的界。具体而言，通过将温度分解为定常的背景温度剖面和脉动温度两部分，解析地推导出了加权平均温度<QT>的严格下界。作为首个考虑非均匀内部热源的解析界，它能与已有的用于均匀内部加热对流的界兼容。更具物理意义的是，通过使用下壁面平均热通量(qb)作为中间变量，我们得到了一个解析关系用于构建<QT>和平均竖直热通量<wT>的不等关系。它揭示了<QT>的下界和<wT>的上界之间的内在关联，即这两个界本质上是等价的，它提供了一种简单的方法将一个界转化为另一个。此外，我们通过一系列全面的数值模拟，对解析界进行了广泛的测试验证。

外文标题：Temperature and heat flux bounds of convection driven by non-uniform internal heating

外文摘要：Convection driven by a spatially non-uniform internal heat source between two horizontal isothermal walls is studied by theoret-ical analysis and numerical simulation,in order to explore the bounds of the temperature and the vertical heat flux.Specifically,the rigorous lower bound of the weighted average temperature<QT>is derived analytically,by decomposing the temperature field into a background profile and a fluctuation part.This bound obtained for the first time to consider non-uniform heat sources is found to be compatible with the existing bound obtained in uniform internal heat convection.Of physical importance,an analyt-ical relationship is derived as an inequality connecting<QT>and the average vertical heat flux<wT>,by employing the average heat flux on the bottom wall(qb)as an intermediary variable.It clarifies the intrinsic relation between the lower bound of<QT>and the upper bound of<wT>,namely,these two bounds are essentially equivalent providing an easy way to obtain one from another.Furthermore,the analytical bounds are extensively demonstrated through a comprehensive series of direct numerical simulations.

外文关键词：

Internally heated convectionNonuniform internal heat sourceAnalytical boundsBackground method

作者：

陈良兵、高安康、廖紫默、万振华、刘难生

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作者单位：

Department of Modern Mechanics,University of Science and Technology of China,Hefei 230026,China

关键词：

Internally heated convection Nonuniform internal heat source Analytical bounds Background method

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaFundamental Research Funds for the Central Universities

项目编号：

922522029215230112293000122930021230232012388101

出版年：

2024

DOI：

10.1007/s10409-024-23630-x

力学学报(英文版)

CSTPCD

影响因子：0.363

ISSN：0567-7718

年,卷(期)：2024.40(8)