Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures
Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures
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DOI：
10.1090/qam/64563
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发表时间：
1954-10
影响因子：
0.8
通讯作者：
G. Batchelor
中科院分区：
文献类型：
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作者：
G. Batchelor
本文考虑了由浮力作用于长矩形内流体所产生的二维对流运动，该矩形的两个长边为不同温度下的垂直边界，其目的是确定两个垂直边界之间的热传递速率。建立了控制方程，揭示了流动唯一地由Prandtl数<r，Rayleigh数A = g（Tx - T0）（f /（T0））和矩形边长比l/d决定。在用于建筑物的热绝缘的空腔的情况下，这在本文中被特别记住，A通常为约1000 d3（其中d以厘米为单位），并且l/d取约5至200之间的值。问题的实质是确定在A和l/d的任何给定值下，几种不同的流态中的哪一种出现。看来，对于上述实际值，流动并不完全是一种单一类型，并且有必要讨论A和l/d值的几个范围中的每一个的传热。第4节、第5节和第6节分别涉及以非常小的A值、大的l/d值和大的A值为特征的层流状态。在第7节中，建立了这些流动稳定的近似准则，在第8节中，简要地考虑了湍流时的传热表达式。所有这些不同的结果所提供的统一图像将在第9节中讨论。对传热的理论预测与有限的实验数据进行了比较，这些数据主要是由穆尔和赖赫（1930）获得的。理论和实验一致表明，在实际条件下，d < 1 cm时，对流的影响可以忽略不计; d < 2.5 cm时，垂直边界的单位面积传热量随d的增加而减少，d再增加时，单位面积传热量基本保持不变（与Z-1/4成正比）。1.问题的背景。本文的目的是确定在不同温度下，两个平行的垂直边界之间的空气空间中的热传递速率。空气空间由水平边界距离I封闭（通常，与垂直壁之间的距离d相比，I较大），如图1所示。在与草图平面成直角的其余方向上，空气空间被视为延伸到无限远。所有的边界条件将被假定为在后一个方向上是一致的，并且对流
The two-dimensional convective motion generated by buoyancy forces on the fluid in a long rectangle, of which the two long sides are vertical boundaries held at different temperatures, is considered with a view to the determination of the rate of transfer of heat between the two vertical boundaries. The governing equations are set up; they reveal that the flow is determined uniquely by the Prandtl number <r, the Rayleigh number A = g{Tx — T0)(f /(T0kv), and the ratio of the sides of the rectangle l/d. In the case of cavities used for thermal insulation of buildings, which is kept specially in mind throughout the paper, A is usually about 1000 d3 (where d is in centimeters), and l/d takes values between about 5 and 200. The essence of the problem is to determine which of several different flow regimes occurs at any given values of A and l/d. It appears that with the above practical values the flow is not decisively of one single kind, and the discussion of the heat transfer for each of several ranges of values of A and l/d is necessary. Sections 4, 5 and 6 are concerned with laminar flow regimes characterized by very small values of A, large values of l/d, and large values of A, respectively. In Section 7 approximate criteria for these flows to be stable are established, and in Section 8 the expressions for the heat transfer when the flow is turbulent are considered briefly. The unified picture provided by all these different results is considered in Section 9. A comparison of the theoretical predictions about the heat transfer with the limited experimental data, mostly obtained by Mull and Reiher (1930), is made. Theory and experiment agree in suggesting that, under practical conditions, the effect of convection is negligible for d < 1 cm, and that the heat transfer per unit area of vertical boundary decreases as d increases, provided d < 2.5 cm, and remains approximately constant (at a value proportional to Z-1/4) for further increase of d. 1. The background to the problem. The purpose of this paper is to determine the rate at which heat is transferred across the air space between two plane parallel vertical boundaries which are held at different temperatures. The air space is closed by horizontal boundaries distance I apart (I being large compared with the distance d between the vertical walls, in general), as sketched in Fig. 1. In the remaining direction, at right angles to the plane of the sketch, the air space is regarded as extending to infinity. All boundary conditions will be assumed uniform in this latter direction, and the convective