Free convection in enclosed spaces

This equation may be modified by the introduction of the Prandtl number to give 

Properties are evaluated at the film temperature, and it is expected that this relation would be primarily applicable to calculations for free convection in gases. However, in the absence of more specific information it may also be used for liquids. We may note that for very low values of the Grashof-Prandtl number product the Nusselt number approaches a value of 2.0. This is the value which would be obtained for pure conduction through an infinite stagnant fluid surrounding the sphere. 

For higher ranges of the Rayleigh numbers the experiments of Amato and Tien [79] with water suggest the following correlation  

The free-convection flow phenomena inside an enclosed space are interesting examples of very complex fluid systems that may yield to analytical, empirical, and numerical solutions. Consider the system shown in Fig. 7-10, where a fluid is contained between two vertical plates separated by the distance 5. As a temperature difference AT,. = T - T is impressed on the fluid, a heat transfer will be experienced with the approximate flow regions shown in Fig. 7-11, according to MacGregor and Emery [18]. In this figure, the Grashof number is calculated as 

At very low Grashof numbers, there are very minute free-convection currents and the heat transfer occurs mainly by conduction across the fluid layer. As the Grashof number is increased, different flow regimes are encountered, as shown, with a progressively increasing heat transfer as expressed through the Nusselt number 

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Cases involving free convection in enclosed spaces are less well defined. The usual method is to determine an effective thermal conductivity kg. Discussion of this approach is given elsewhere (6, 8, 18). 

What is the approximate criterion dividing pure conduction and free convection in an enclosed space between vertical walls ... 

R. Siegel and R. H. Norris, "Tests of free convection in a partially enclosed space between two heated vertical plates", Trans. ASME, Vol. 79, pp. 663-670 (1957). 

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