Extended surfaces efficiency

For an extended surface exchanger, the overall extended surface efficiency ti is considered uniform and constant. 

In an extended surface heat exchanger, heat transfer takes place from both the fins (r /< 100 percent) and the primary surface (%= 100 percent). In that case, the total heat transfer rate is evaluated through a concept of total surface effectiveness or extended surface efficiency T 0 defined as... 

Subsequently, determine the fin efficiency r and the extended surface efficiency tip ... 

Fin efficiency is defined as the ratio of the mean temperature difference from surface to fluid divided by the temperature difference from fin to fluid at the base or root of the fin. Graphs of fin efficiency for extended surfaces of various types are given by Gardner [Tmn.s. Am. Soc. Mech. Eng., 67,621 (1945)]. 

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 combustion gases flow across the tube banks in the convection section and the correlations for cross-flow in tube banks can be used to estimate the heat transfer coefficient. The gas side coefficient will be low, and where extended surfaces are used an allowance must be made for the fin efficiency. Procedures are given in the tube vendors literature, and in handbooks, see Section 12.14, and Bergman (1978b). 

Mercury represents a serious environmental risk, and the study of removal of mercury from wastewater has received considerable attention in recent years. Mercury concentration was usually reduced by deposition on a cathode with high surface area. Removal of mercury is studied using extended surface electrolysis which reduces the level of mercury to below acceptable concentrations of 0.01 ppm in wastes by employing a Swiss roll cell with a cadmium-coated, stainless-steel cathode. An industrial cell with a fluidized bed electrode has also been studied. Graphite, as an efficient porous electrode, has been used to remove traces of mercuric ions form aqueous electrolyte solutions. In order to apply the electrochemical method for some effluents, it is necessary to use sodium hypochlorite to convert elemental mercury and less soluble mercury compounds to water-soluble mercuric-chloride complex ions. 

Extended surfaces are used to augment heat transfer from the base area. To compare and evaluate these extended surfaces, two performance factors are used fin efficiency and fin effectiveness. In the... 

The fin efficiency is found from mathematically derived relations, in which the film heat-transfer coefficient is assnmed to be constant over the entire fin and temperature gradients across the thickness of the fin have been neglected (see Kraus, Extended Surfaces, Spartan Books, Baltimore, 1963). The efficiency cnrves for some common fin configurations are given in Figs. ll-30a and ll-30h. 

K. A. Gardner. Efficiency of Extended Surfaces." Trans. ASME 67 (1945), pp. 621-31. Reprinted by permission of ASME International. 

Using extended surfaces is addressed in several later sections on specific types and applications of heat exchangers. This section analyzes the efficiency of these surfaces, which is a problem of heat conduction, with the additional consideration of heat transfer to or from the surrounding fluid by convection. 

Hie denominator of Eq. (2.140) denotes the heat transfer from an area of the wall equivalent to the base area of the extended surface the heat transfer to be evaluated in the numerator and denominator is based on the same temperature difference, Tq — Tqo. Since the temperature of a wall and the heat transfer coefficient between the wall and the ambient are somewhat changed when an extended surface is attached to the wall, the effectiveness defined by Eq. (2.140) is quite approximate. The error involved in this approximation depends on the length of and the space between the extended surfaces. Since the changes in the wall temperature and the heat transfer coefficient affect both the numerator and the denominator of Eq. (2.141), the efficiency defined by this equation is more realistic and is often preferred in practice. Furthermore, rather than using it only for one type of extended surface, this efficiency may be better utilized in the comparison of different extended surfaces. The particular value of the latter efficiency for Ex. 2 10 is... 

In Fig. 2.37 this efficiency is compared with the efficiency of four different fins with variable cross section. Note that cost and manufacturing convenience may be more important factors than a 5-10% more efficient fin. For this reason, the efficiency of extended surfaces will not be further elaborated (for a detailed treatment see Ref 7). 

Fin efficiencies for other types of extended surface are available. Figure... 

T 0 Overall surface efficiency of total heat transfer area on one side of the extended... 

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