Annuli finned

The total surfece area, A, in the annulus is the sum of the extended surface area and the hare pipe surfeces not covered hy fins. See Table 10-40. The fm efficiency, rj, Cf or E, from Figure 10-154 is corrected for the percent surlace that is finned. The corrected value, is the effective surfece efficiency. 

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. 

Emulsion Models To simulate the core-annulus strueture, the cross section in emulsion models is divided into an inner dilute core region where particles are transported upwards, and a denser annular region where partieles descend along the wall, as in Fig. 26, but without the clusters. The thickness of the solid layer along the vertical heat transfer surfaces is often approximated as uniform. However, for membrane wall heat transfer surfaces, the annulus layer tends to be thicker at the fin than at the tube crest (Grace, 1990 Golriz 1992). 

Based on numerous calculations with various fin height and thickness parameters, a height of 10 mm and a fin width of 5 mm appeared to be the best compromise between pressure drop and heat transfer. The remaining parameter of fin spacing or total number of fins in the annulus remains to be determined. This parameter was varied over an appropriate range of values, and the calculated results for resultant thermal conductance and fractional pressure drop are presented in Fig. 4.50. The thermal conductance represents the heat load dissipated by the finned annulus per degree of temperature difference between the fin root and the fluid at the inner diameter. 

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