Open Cavity Problems

The first section presents some fundamental ideas that are frequently referred to in the remainder of the chapter. The next three sections deal with the major topics in natural convection. The first of these addresses problems of heat exchange between a body and an extensive quiescent ambient fluid, such as that depicted in Fig. 4.1a. Open cavity problems, such as natural convection in fin arrays or through cooling slots (Fig. 4.1fe), are considered next. The last major section deals with natural convection in enclosures, such as in the annulus between cylinders (Fig. 4.1c). The remaining sections present results for special topics including transient convection, natural convection with internal heat generation, mixed convection, and natural convection in porous media. 

In open cavity problems, buoyancy generated by heat exchange with the enclosure walls drives flow through the cavity (Fig. 4.20a). Either the wall temperature or the heat flux can be specified on the cavity walls, and cavities may take a variety of forms (Fig. 4.20). The fluid temperature far from the cavity is assumed constant at T. The cooling of electronic equipment and the augmentation of heat transfer using finned surfaces are two important areas where open cavity problems arise. 

FIGURE 4.23 Flow configurations and nomenclature for various open cavity problems. 

The concept of surrounding the surfaces by a layer of stationary fluid, called the conduction layer, is useful for the present enclosure problem as well as for the external and open cavity problems. Unless the conduction layer thickness is greater than the cavity dimensions, a central region is produced (Fig. 4.26a and b), which experience has shown takes up a nearly uniform temperature this region can therefore be modeled as isothermal. Once the thicknesses of the conduction layers have been specified, finding the heat transfer and the temperature Tcr of this central region is a relatively straightforward heat conduction problem. 

Weld line With moldings that include openings (holes), problems can develop. In the process of filling a cavity the flowing melt is obstructed by the core, splits its stream, and surrounds the core. The split stream then... 

RM is a simple, basic, four-step process that uses a thin-walled mold with good heat-transfer characteristics. Its closed mold requires an entrance for insertion of plastic and, most important, the capability to be opened so that solidified products can be removed. These requirements are no problem. Liquid or dry-powder plastic equal to the weight of the final product is put into the mold cavity(s), which rotates simultaneously about two axes located perpendicular to each other (Fig. 8-68). These two rotation speeds can be varied to permit more... 

Munitions filled with HD drained more slowly and with more difficulty than expected, and the unexpected frothing of agent created serious maintenance and production problems. Freezing the munitions before opening the agent cavity to the atmosphere minimized the frothing. 

Snorting the drug can also be dangerous. The delicate tissues that line the nasal cavities and air passages can be damaged by direct contact with MPH because the tablets contain hydrocholoride salt of methylphenidate, which yields dilute hydrochloric acid when it comes into contact with moisture within the nose. While this is not a problem in the stomach (because hydrochloric acid is one of the stomach acids used to digest foods), the acid can bum the delicate epithelial nasal tissues. This can result in open sores, nose bleeds, and with chronic use can lead to deterioration of the nasal cartilage. 

Thus, another approach consists in selecting some boundary conditions and properties. It is obvious that all exact correlation functions must satisfy and incorporate them in the closure expressions at the outset, so that the resulting correlations and properties are consistent with these criteria. These criteria have to include the class of Zero-Separation Theorems (ZSTs) [71,72] on the cavity function v(r), the indirect correlation function y(r) and the bridge function B(r) at zero separation (r = 0). As will be seen, this concept is necessary to treat various problems for open systems, such as phase equilibria. For example, the calculation of the excess chemical potential fi(iex is much more difficult to achieve than the calculation of usual thermodynamic properties since one of the constraints it has to satisfy is the Gibbs-Duhem relation... 

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