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476 Chapter 25 ` ' 1945 Guide ----3.--The-film-coeffitient-of-heat~transfer-between-the intemal surface 'of the coil andthe fluid flowing within the coil, usually given in Btu per (hour) (square foot internal surface) (degreeFahrenheit mean temperature difference). These three individual coefficients acting in series result in an overall coefficient of heat transfer in accordance with the basic laws. For a bare pipe coil the overall coefficient of heat transfer, whether for heating or for cooling (dry), can be expressed by a simplified basic formula as follows: V= 1-------------------- ------------------------ _R_ 4. A 4. J_ hr_ k * fea- (2> where V = overall coefficient of heat transfer, Btu per (hour) (square foot external surface) (degree Fahrenheit mean temperature difference between air and fluid within the coil). hi -- film coefficient of heat transfer between the internal surface of the coil and the fluid flowing within the coil, Btu per (hour) (square foot internal surface) (degree Fahrenheit mean temperature difference between that surface and the average fluid temperature). Aa = film coefficient.of heat transfer between air and the external surface of the coil, Btu per (hour) (square foot external surface) (degree Fahrenheit mean tem-. perature difference between the mass of air and the external surface). ' k " conductivity of material from which the bare pipe is constructed, Btu per (hour) (square foot) (degree Fahrenheit per inch thickness). L = thickness of- tube wall, inches. R = ratio between external and internal surface of the bare tube, usually varying from 1.03 to 1.15 for the tube used in typical heating or cooling coils. This ratio R is inserted in the formula in order to place internal fluid coefficient of heat transfer on the basis of external surface. Frequently, when pipe or tube walls are thin and of material having high conductivity (as is the case in construction of typical heating and cooling coils) the term L/k in Equa tion 2 becomes negligible and.is generally disregarded. (The effect of the term L/k in typical bare pipe heating or cooling coils seldom exceeds 1 to 2 per cent of the overall coefficient). Thus, in its simplest form, for bare pipe: R. 1 IT + at (3) For finned coils the formula1 for the overall coefficient of heat transfer can be conveniently written: A+ .i. Ar T)fAa <4> in which the term rjf, called the fin efficiency, is introduced to allow for the resistance to-heat flow encountered in the fins. The term R, in this case, is the ratio of total external surface to internal surface. For typical designs of finned coils for heating or cooling, this ratio varies from 10 to 30. Term R is again introduced to place the internal surface coefficient of heat transfer on a basis of external surface. In the discussions which follow, coefficients h, and will be considered separately, and also various ways of combining them will be outlined. External Film Coefficient While -formulae have been developed expressing the film coefficient Aa for air passing parallel to a plane surface, they cannot be used directly '`Rational Development and Rating of Extended Air Cooling Surface, by H.' B. Pownall (Refrigerating Engineering, October. 1935. p. 211). Heat Transfer Surface Coils 477 for fins on tubes because of air turbulence and because of the temperature gradient prevalent from the edge of a fin to its center. It is therefore necessary to make tests to evaluate the. combined term T),fca. The term, ijffea, will be written merely h& in this discussion as there is no necessity for separately evaluating rj and because values of Aa are usually applied only to the particular coils for which tests are made. Transfer of heat from a fluid to a solid is accomplished by the con tacting. of the molecules of the fluid with the solid. When a molecule strikes a solid, its energy level equalizes with the energy level of the solid. The total amount of heat exchanged between the molecules of a fluid and a solid is determined by the number of contacts per unit of surface per. unit of time, and by the energy change of the fluid.2 The energy change, in the case of air, is measured by the temperature change times the specific heat of the air. The number of contacts is measured by a percentage of the weight of air flowing per unit of time. In the case where water vapor is mixed with air, and the water vapor is cooled but not condensed, the amount of heat transferred is increased by the energy change of the vapor particles. The additional energy is measured by the temperature change, by the specific heat of the water vapor, and by the weight of vapor contacting the surface per unit of time. In a mixture of air and vapor there is a definite ratio between the weight of the vapor and of the air per cubic foot of the mixture. Therefore, as the temperature`of the mixture is lowered, the amount of heat lost by the vapor always bears a definite ratio to the amount of heat lost by. theair. The amount of energy involved in the temperature change of the vapor is small, however, and it is usually included with that of the air by using a value of 0.245 for the specific heat of humid air. . Dehumidification of air by a cooling coil occurs whenever the surface temperature of any part of the coil is below the dew-point temperature of the air. Enough molecules of water vapor are condensed on the coil to create a state of equilibrium between the vapor pressure of the moisture on the coil surface and the vapor pressure of the moisture in that part of the air stream which is in immediate contact with the coil surface. Because of the good contact between the condensed film of water and the ' coil surface, the water film attains a temperature approaching that of the coil surface. Therefore, those particles of air which actually contact the water film leave the film.with a dew-point temperature equal to the outer surface film temperature. However, many air particles, with their attendant water vapor particles, never contact the coil surface, but are by-passed between the fins. These air particles have the same dew-point temperature when they leave the coil as they had when they entered, but after leaving the coil they mix with the air. particles which did contact the surface, producing a mixture of air which has a dew-point tempera-. ture that lies between the original dew-point temperature and the film surface temperature. This process explains why air seldom leaves a coil in a saturated condition. The foregoing contact-mixture concept of heat transfer has been found by several independent investigators to be consistent with experimental data. The concept has been used successfully in analyzing the per formance of evaporative condensers, cpoling towers, condensers and evaporators. A relation3 has been found between heat transfer and Graphical Method of Determining Finned Coil Capacities -Described, by E. P. Wells (Heating, Piping na Atr Conditioning, December, 1936, p. 666). ... *he Contact-Mixture Analogy Applied to Heat Transfer with Mixtures of Air and Water Vapor, by W. H. Carrier (AS.M.E. Transactions, January, 1937, Vol. 59, No. 1, p. 49).