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HEATING VENTILATING AIR CONDITIONING GUIDE 1942 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 for 40 F = 25.0 X 0.73 X 1.52 = 27.7 Btu per square foot'per hour. The increased rate of heat transfer due to forced convection can be calculated from Equation 2b: Sfc = 1 + 0.225 V (2b) where qic = heat transfer by forced convection, Btu per square foot per hour per degree Fahrenheit temperature difference. V =s velocity of air, feet per second. This equation is approximately correct for large surfaces exposed to air currents at temperatures of approximately 70 to 80 F. Fig. 3. Radiation between Surfaces Thermal Radiation Equation ^ = <tFaFe (7V --F,')_ (3) . This relation, which is sometimes applicable to systems in which radiant exchange takes between the surfaces of solids, states that the net radiation current per unit transfer area of surface 1, (dq)/(d.Ai), Btu per. hour per 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 -- TV). The proportionality factor (<j T'aT'e) may be conveniently separated into three parts: a = the Stefan-Boltzmann radiation constant. = 1730 X 10-u Btu per hour per square foot per degree Fahrenheit absolute temperature to the fourth power. 1 Fa = the angle factor is dimensionless and ^ 1. This factor accounts for the relative geometry of the two surfaces, and is called the shape factor. Fe = 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. The radiation conditions described are schematically, shown- in Fig. 3. Gaseous and luminous radiation will not be discussed here. 72 CHAPTER 3. FUNDAMENTALS OF HEAT TRANSFER Table 5. Heat Transmission bv Radiation for Black-Body Conditions3 Expressed in Btu per square foot per hour Temp. Dbg F -30 -20 -10 0. 0 59.3 65.2 71.4 78.0 -1 58.7 64.7 70.8 77.4 -2 58.2 64.1 70.1 76.7 -3 57.7 63.5 69.5 76.0 -4 57.2 62.9 68.9 75.4 0 +1 +2 +3 +4 0 78.0 78.7 79.4 80.1 10 85.0 85.7 86.5 97.2 20 92.4 93.3 94.0 94.8 30 100 101 102 103 40 109 110 111 112 50 118 119 120 121 60 127 128 129 130 70 137 138 139 140 80 148 149 150 151 90 159 160 161 162 100 170 171 173 174 110 183 184 185 187 120 196 197 199 200 130 211 212 214 215 80.8 88.0 95.6 104 112 122 131 142 152 163 175 188 201 217 -5 56.7 62.3 68.3 74.7 +5 81.5 88.7 96.4 105 113 123 132 143 153 164 176 189 203 218 -6 56.2 61.7 67.7 74.0 +6 82.2 89.4 97.2 105 114 123 133 144 154 166 178 191 204 220 -7 55.7 61.1 67.1 73.4 +7 82.9 90.2 98.0 106 115 124 134 145 155 167 179 192 206 221 -8 55.2 60.5 66.4 72.7 +8 83.6 90.9 98.8 107 116 125 135 146 156 168 180 193 207 222 -9 54.7 59.9 65.8 72.1 +9 84.3 91.7 99.6 108 117 126 136 147 157 169 182 195 209 224 *Example: Radiation from walls of room at 32 F to surface at -- 25 F for effective emissivity of 0.95 * (102 -- 62.3) 0.95 = 37.7 Btu per square foot per hour. The radiation under black-body conditions, or for an emissivity of 1.0, is given in Table 5 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 9s. In many problems involving heat transfer by the mechanisms of radia tion and convection in parallel (simultaneous heat transfer by the two mechanisms to:the same surface),-it is algebraically convenient to employ a first power radiation rate equation of a form similar to Equation 2 for convection, namely: Ja, ~ hl ~ ^ (3a) where hT is the unit radiation conductance. Comparison of this equation with Equation 3 yields the relation: . Ar = o FAFE ~ pj 0 FaFe (4 Favc) (3b) where Fave (F, + T,) 2 This unit conductance (hr) is to be used with caution for its behavior is July 1936. p. 782). 73