Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory
Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory
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DOI：
10.1017/s0022112074001352
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发表时间：
1974-08
影响因子：
3.7
通讯作者：
D. E. Cormack;L. Leal;J. Imberger
中科院分区：
文献类型：
--
作者：
D. E. Cormack;L. Leal;J. Imberger
研究了端壁受热差的小宽高比空腔内的自然对流问题。利用匹配渐近展开式表明，流动由两种不同的形式组成：核心区域的平行流动和靠近腔端部的第二种非平行流动。找到了核心区域在宽高比A的所有阶上都有效的解，同时得到了末端区域的适当渐近展开的前几项。讨论了平行流结构有效性的参数极限。导出了在极限为A→0时有效的平行流解的努塞尔数和单自由参数的渐近表达式。
The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes: a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A → 0, are derived.