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首页> 外文期刊>International Journal of Heat and Mass Transfer >The onset of convection in porous layers with multiple horizontal partitions
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The onset of convection in porous layers with multiple horizontal partitions

机译：具有多个水平隔板的多孔层中对流的开始

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摘要

In this paper we investigate the onset of convection in a horizontally partitioned porous layer which is heated from below. Identical sublayers are separated by thin impermeable barriers. A linear stability analysis is performed, and dispersion relations are obtained directly and explicitly for two- and threelayer configurations. A systematic numerical procedure is devised to compute the dispersion relation for an arbitrary number of sublayers, but from this it is possible to guess the correct analytical form of the dispersion relation for general cases.Neutral stability curves are found to organise themselves into natural groups of N members when there are N sublayers. When the disturbance wavenumber, k, is large, each member of any group lies within an O(k~(-1)) distance of all other members, but within an 0(1) distance of other groups. When the number of sublayers is large, the system tends towards one with a critical Darcy-Rayleigh number of 12 and a critical wavenumber of zero; this is the well-known property of a single porous layer with constant heat flux boundary conditions. An asymptotic analysis is performed in order explore these two apparently disparate configurations. Finally, another asymptotic analysis is used to determine the critical Rayleigh number and its associated wavenumber when the number of sublayers is large.
机译：在本文中，我们研究了从下方加热的水平分隔的多孔层中对流的开始。相同的子层由薄的不可渗透的屏障隔开。进行线性稳定性分析，并直接和明确地获得两层和三层结构的色散关系。设计了系统的数值程序来计算任意数量的子层的色散关系，但由此可以猜测一般情况下色散关系的正确解析形式。发现中性稳定性曲线将其自身组织为自然的有N个子层时的N个成员。当干扰波数k大时，任何一组的每个成员都位于所有其他成员的O（k〜（-1））距离之内，但在其他组的0（1）距离之内。当子层数很大时，系统趋向于一个，其达西-瑞利临界值为12，波数为零。这是具有恒定热通量边界条件的单个多孔层的众所周知的特性。为了探究这两个明显不同的配置，进行了渐近分析。最后，当子层数较大时，使用另一种渐近分析来确定临界瑞利数及其相关波数。

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