Document 0gJY630E3KKXErD0Ybbd8ZdBm

100____________________ CHAPTER 5 1948 Guide - D = diameter of pipe or circular duct or height of vertical wall, inches. (Effect of diameter or height becomes constant at 24 in.). Xav - average of wall surface and surrounding air temperature, Fahrenheit degrees absolute. h ~tf = temperature excess .between wall surface and surrounding air, Fahrenheit degrees. Fop-horizontal cylinders, the value of C = 1.016 has been well estab lished by various investigations. : For vertical plates, the value of C = 1.394 has been fairly well established. Suggested values 2 of C for hori zontal plates warmer than the surrounding air are 1.79 when facing upward and 0.89 when facing downward. Table 2. Heat Transmission bv Free Convection for Large Vertical Surfaces Expressed in Btu per (square fool) (hour) Temperature Difference between Body and Surrounding Still Air at 80 F . The heat transmission by free convection from.vertical walls 24 in. or more .in height is given in Table 2 as calculated from Equation 2a for an ambient air temperature of 80 F. The values, in Table 2 are . not changed appreciably by a considerable change in air temperature for a given temperature excess. For instance, a change in air temperature from 80 to 40 F will increase the heat transmission given in Table 2 by only 1.3 per cent. Table 2 can also be used for calculating the free convection rate of transmission for various commercial shapes such as pipes and ducts. These calculations are simplified by the use of the factors in Tables 3 and 4.. Table 3 gives factors by which the values in Table. 2 must be multiplied. to obtain the free convective transfer from various shapes whose characteristic dimensions are 24 in. or over, and Table 4 gives the factors to be used in conjunction with the factors in Table 3 for obtaining the free convection from Table 2 for pipes and ducts whose characteristic dimensions are less than 24 in. For example, the free convection transfer from a 3 in. O.D. horizontal cylinder for a temperature difference of 40 deg = 25.0 X 0.73 X 1.52 = 27.7 Btu per (square foot) (hour). ; Problems in either forced convection or natural convection may be solved by the simple first-power equation if the convection coefficient is expressed as a unit conductance: Qc ". he A (!i -- It) (2b) Fundamentals of Heat Transfer 101 where ?c = heat transmission by convection, Btu per hour, A i surface area, square feet. <.-/ = temperature difference between the surface and the fluid Fahrenheit degrees. he = unit conductance, from Table 5, Btu per (square foot) (hour) (Fahrenheit degree temperature difference.) Table 3. Free Convection Factors for Various Shapes Shapes Horizontal plates warmer than air facing upward--------------------- Factor 0.73 .0.88 1.00 1.28 0.64 0.64 1.28 Table 4. Free Convection Factors for Various Diameter Pipes or Various Height Plates Actual O.D., or height, in____ 1 2 3 4 5 6 7 . 8 Factor. .. . .. 1.88 1.64 1.52 1.43 1.37 1.32 1.28 1.25 Actual O.D., or height, in------- 9 10 12 14 16 18 20 22 Factor 1.22 1.19 1.15 Lll 1.09 1.06 1.04 1.02 Thermal Radiation Equation The relation shown in. Equation 3 is usually applicable to systems in which radiant exchange takes place between the surfaces of solids, as sche- qt = oAtFAFB (X,* - 7V) (3) matically shown in Fig. 3. Gaseous and luminous radiation are not con sidered in this discussion. Equation 3 states that the net radiation per unit transfer area of surface 1, qr/A Btu per (hour) (square'foot), which sees surface 2 through a non-absorbing medium, is proportional to the difference of the fourth powers of the absolute , surface temperatures (7V -- 7V). The proportionality factor (<j FaFe) may be conveniently separated into three parts: . . ,. :. a = the Stefan-Boltzmann radiation constant.. .... ;; = 1730 X 10"11 Btu per (hour) (square foot) (Fahrenheit degree absolute tempera ture to the fourth power). Fa = the configuration factor which is dimensionless and 1. This factor accounts for the shape and relative position of the two surfaces. The value of Fa = 1 may be used in the cases of large parallel planes, long concentric . cylinders or smaller bodies in large enclosures. Fs = the emissivity factor which is also dimensionless and . 1. This factor accounts for the absorption and emission characteristics of the surfaces for the radiation which exists. Individual emissivities (e) should be.taken from Table .6 and applied, for either radiation or" absorption, as follows:............ a. For a'small body in a large enclosure, use the emissivity of the small body only: FE=? et'.. . . v-' "