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72 Chapter 3 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- ffr = oAiFaFe (TV - 7Y) (3) matically shown inrFig. 3. Gaseous and luminous radiation are not consid ered in this discussion. Equation 3 states that the net radiation current per unit transfer area of surface 1, qr/A Btu per hour per square foot, which sees surface 2 through a non-absorbing medium, is proportional to the ' Fig. 3. Radiation Between Surfaces difference of the fourth powers of the absolute surface temperatures (Ti* -- 7V). The proportionality factor (a FAFE) may be conveniently separated into three parts: o = the Stefan-Boltzmann radiation constant. = 1730 X 10-u Btu per hour per square foot per degree Fahrenheit absolute temperature to the fourth power. Fa = the configuration, factor 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. (For other values see References.) Fk = the emissivity factor 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: Fk = i. b. For rectangles or disks, either parallel or perpendicular and with a common side, use the product of the emissivities: FH = si X e,. c. For large parallel planes, long concentric cylinders or large enclosed bodies, use both emissivities in'the equation: The radiation under black-body conditions, or for an emissivity of 1.0, is given in Table 76 for cold surfaces as low as --39 F to warmer surfaces as high as 139 F. The emissivities of a number of surfaces ordinarily encountered in engineering practice are shown in Table 6. For radiation table at higher temperatures, and further discussion of radiation calcu lations, see Chapter 45. `Heat Insulation in Air Conditioning, by R. H. Heilman (Industrial and Engineering Chemistry, Vol. 28, July 1936, p. 782). Fundamentals of Heat Transfer \ 73 Combined Convection and Radiation __It should be noted that the previous equations and tables give the heat transfer by convectioiTand by radiation-computed separately--In. many practical cases it is desirable to treat convection and radiation as a single combined process, using a first-power equation: Ore - hrc A (Ij -- /j) (4) where grc is the total heat flow due to radiation and convection, in Btu per hour. Values of hrc, the surface or film conductance for. combined Table 6. Radiation Factors or Emissivities, e. For the determination offactor Fs in Equation 3 Class Surfaces Fraction of Black-Body Radiation At 50-100 F At 1000 F Solar Radiation 1 A small hole in a large box, sphere, furnace, or enclosure 0.97 to 0.99 0.97 to 0.99 0.97 to 0.99 2 Black non-metallic surfaces such as asphalt, carbon, slate, paint, paper______ ____________ 0.90 to 0.98 0.90 to 0.98 0.85 to 0.98 3 Red brick and tile, concrete and stone, rusty steel and iron, dark paints (red, brown, green, etc.)..,,..._____ __________ 0.85 to 0.95 0.75 to 0.90 0.65 to 0.80 4 Yellow and buff brick and stone, firebrick, fire clay................ . 0.85 to 0.95 0.70 to 6.85 0.50 to 0.70 5 White or light-cream brick, tile, paint or paper, plaster, white wash............................................... 0.85 to 0.95 0.60 to 0.75 0.3 to 0.5 . 6, Window glass. .............................. 0.90 to 0.95 Transparent 7 Bright aluminum paint; gilt or bronze paint...... ........................... 0.4 to 0.6 0.3 to 0 5 8 Dull brass, copper, or alumi num; galvanized steel; pol ished iron...................................... 0.2 to 0.3 0.3 to 0.5, 0.4 to 0.65. '9 Polished brass, copper, monel metal... 0.02 to 0.05 0.05 to 0.15 0.3 to 0.5 10 Highly polished aluminum, tin plate, nickel, chromium............. 0.02 to 0.04 0.05 to 0.10 0.10 to 0.40 radiation and convection, are given in Chapter 4, Table 1 and Fig. 1. Complete tables for the combined heat transfer of steam and hot water radiators, pipes, coverings, etc., will be found in the appropriate chapters. When dealing with the effect of operating temperatures upon the com bined heat transfer of a given piece of equipment (as for instance a steam radiator), another form of equation is frequently used: qrc = B A (h - t,) (5) Values of n in this equation usually range from 1.3 to 1.5 (see Chapter 13). I he chief advantage of this equation is the convenience of representing