Document bBV5QQ5e8roQy53dvQJNB5Roo

66 CHAPTER 4 1965 Guide And: Data Book Assuming that the heat transfer coefficients for' the finned surface and prime'surface1 are equal, a surface efficiency, <*, can be derived for use in'Equation 21. - : 1. - ^ d - *> ' ' (20) q-*M(tr-U) (21) where A is the total surface area, equal to the sum of the finned and prime areas. .. The temperature distribution and fin efficiencies for various fin shapes have' been derived' by Harper and Brown,71 Schmidt,T* Gardner,1* and others.' A survey of optimum'fin riimenginng is given by Jakob.14 Figs. 15 to 18 present the curves and equations of Gardner for annular fins, straight fins; and spines:'For'constant thickness'square fins, it is-recom mended that the`efficiency of a constant thickness anrmlar fin of the same area be used.**More accurate* results, par ticularly in the case'of rectangular fins'of large aspcct'ratio, can be obtained by, dividing the fin into circular sectors as described by Carrier and Anderson.11 Various methods-are used to fabricate finned surface.-In some cases fins are extruded from the prime surface--for example, the short fins found on the tubes in flooded evapora tors or water-cooled condensers. In other.cases the fins are fabricated separately, sometimes of a different material, and bonded to the prime surface. Metallurgical bonds are achieved by furnace bracing, dip-brazing, or soldering. Mechanical bonds are obtained by tension winding fins around tubes (spiral fins) or expanding the tubes into the'fins (plate fin). Metallurgical bonding, if properly done, leaves negligible thermal resistance at the joint. It is not always economical, however. The thermal resistance of a mechanical bond may or may not be negligible depending upon the application,-the care taken in the manufacture and the materials and tem peratures involved. For plate fin coils having'expanded tubes,- tests by Dart" showed that substantial losses in per formance can be obtained with fins having cracked collars. jlui'iwawgta Hea Transfer 67 An the other hand, negligible thermal resistance was found in coils with continuous collars and properly expanded tubes. Finned-Tube Heat Transfer The heat transfer coefficients for finned coils follow the ^;e equations of convection, condensation and evaporation. However, the particular arrangement of the fins used appears to affect to some extent the values of constants and the ex ponential powers in the equations. It is generally necessary to refer to test data for the exact coefficients. For natural convection finned coils (sometimes called gravity coils) approximate coefficients can be obtained by the coil to be made up of tubular and vertical fin surfaces at different temperatures, and then applying the natural convection equations to each. This is made difficult by the fact that the natural convection coefficient depends upon the temperature difference, which varies at different points of the fin. ' With natural convection, fins generally need a high fin efficiency, (80 to 95 percent) for optimum heat transfer. A low fin efficiency reduces the temperature near the tip. This not ooly reduces the At near the tip, but also cuts down the coefficient, h, which in natural convection depends onAt. likewise, the coefficient of heat-transfer decreases as the number of fins per inch increases, due to the increased inter ference of convection currents from the adjacent fins-and reduced free-flow passage. Two to four fins per inch are common. In general, high coefficients result from large tem perature differences and small flow restriction. Very little published information is available for heat transfer rates in natural convection finned' coils. Chaddock and Edwards** measured coefficients for a number of circular fin-on-tube arrangements. Using the fin spacing, 6, as the char acteristic length they were able to correlate their data in the form Nnu = fiNarNprS/Dt), where D, is the fin diameter. Data for free convection mid radiation from wire and tube heat exchangers is given in References 85,86, and 87.. . Forced convection finned coils are used extensively in a aide variety of equipment. The fin efficiency for optimum perform ance is smaller than for gravity coils, since the forcedrcon- vection coefficient is almost independent of the temperature difference between the surface and the fluid. However,, very low fin efficiencies should be avoided, since the inefficient surface gives high ratio of pressure drop to heat transfer. An efficiency of 70 to 90 percent is often used. As the number of fins per inch of tube length is increased to obtain a large surface area for heat transfer, the coefficient generally increases somewhat. This is due to larger. air velocity between the fins for the same face velocity, and also due to reduced equivalent diameter. However, a point is reached when the boundary layer formed-on one fin surface (Kg. 2) begins to interfere .with the boundary layer formed on the adjacent fin surface. The interference of boundary layers results in a decrease of the-heat transfer coefficient which may offset the advantage,gained from larger surface area. , The selection of the number of fins per inch for forced con vection finned coils usually depends upon economic and prac tical considerations, such as fouling, frost formation, con densate drainage, cost, weight, and volume..For conventional coils, it is generally not desirable to exceed 13,to-14 fins.pqr inch. Forced-air coils are.seldom designed with less than kit bus per inch, except in the case of units where other factors, uch as frost formation, necessitate fewer per inch. A number of means have been used to,obtain higher coeffi cients with a'given air velocity and surface. The most common consists of creating air turbulence to increase the heat transfer coefficient; although this is:usual)y accompanied by higher pressure drop'. Some of the conventional means of causing air turbulence are: (1) staggered tubes instead of in-line tubes for multiple-'row * coils, (2) artificial-additional tubes,' or collars or fingers made.by suitably forming the fin materials, (3) corrugated fins instead of plane fins, and (4)< louvered or interrupted-fins.' *.*. - Heat transfer data for various types of finned coils willbe found in' the following 'references:- London and Kays,** Shepherd** for one-row plate fin coils; Ghai** for straight fins; Katz*1 for-disk and spiral.fins;`Jameson" for circular fins; Gunter** for pressure drop with various types of surface; and Rhling** onft Hiark*4 for fina insndft tnlv>a:- . i. Some of the data of Shepherd for one-rowcoils is shown in Fig. 19.-The thermal resistances plotted in Fig. 19 include the temperature drop through the fina, and are based on one square foot.of total.external surface area. In the absence of'exaet data,-'dimensionless heat transfer and pressure drop correlations, given by Kern** for circular .fins, double pipe longitudinal finned-surface exchangers,.and longitudinal fin* ingidp tubes of shell-and-tube exchangers may .be used. ; .. -> . < . Finned surfaces for rrmHpnging or boiling are used in water -cooled shell-and-tube .units having circular fin outside the H J