Document 99Mp4QzEYzxv00p1rqydoJ8Rq

272 CHAPTER 12 1951 Guide air temperature U is the temperature of the outdoor-air, which, in the absence of all radiation exchanges, would give the same rate of heat entry into the surface as would exist with the actual combination of incident solar radiation, radiant energy exchange with the sky and other outdoor sur roundings, and convective heat exchange with the outdoor air. The sol-air temperature is developed as follows: 1. The basic heat balance equation which includes the factors listed, gives the rate of heat entryinto the weather side of a sunlit building surface, and is written: = OD7D + ah + f'o(o - It) + lRs - *lRl, Btu per (hr)(sq ft) (2) where a = absorptivity (dimensionless) of weather side of wall or roof for incident solar radiation. Subscripts D and d refer respectively to direct and diffuse. I = incident solar radiation, Btu per (hour)(square foot). Subscripts D and d refer respectively to direct and diffuse. t, = outside air temperature, Fahrenheit degrees. (i. = temperature of weather surface of wall or roof, Fahrenheit degrees. /TO -- unit convective conductance of weather surface, Btu per (hour) (square foot) (Fahrenheit degree). R, - low temperature radiant energy falling on surface from outdoor surround ings, Btu per (hour) (square foot of receiving surface). ti, = emissivity of surface at temperature fa, (also equals absorptivity for R,), dimensionless. Ri. = low temperature radiant energy emitted by a black body at temperature II, Btu per (hour) (square foot). 2. The sol-air temperature is defined as: qplp odld -f- eij(Ra ~ Rl) f. = f. + (3) 3, The instantaneous rate of heat entry into the weather surface of the wall or roof becomes: (1) _ 'l) (4) The term cl(R, - Rl) is difficult to evaluate, since tL, on which Rl depends, cannot be found until U and the thermal properties of the struc ture are known. However, tL may be estimated from experimental ob servations of surface temperatures of walls and roofs which appear in the literature8,9 on periodic heat flow. Rl can then be found from Chapter 5, Table 5, and eL can be found from Table 3 of the same chapter. The term R* represents the low temperature radiant energy from outdoor surroundings which falls on the surface in question (cl is the fraction absorbed). In the case of horizontal surfaces, all of this energy comes from the atmosphere of which water vapor is the principal radiating com ponent. For horizontal surfaces, Brunt's10 correlation of a long series of observations shows Ra to be dependent upon the dew-point temperature. For the commonly used design dew-point 67 F, his empirical equation Cooling toad 27, - Table 9.- .Design Sol-Aib Tbmpebatubbs fob 40 Nobth Latitude and 18 D Declination, Nobth (August 1) fob Cleab and Industbial Atmosphebes u,Sol-Aib Temperature, Fahrenheit Dbgbbbs -----------ANTb Clear Atmospheres Industrial Atmospheres WSon Time Sub face Hob. N E S Hob. N E S W 0.0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 Zero 12 77 77 77' 77 77 76 76 76 76 76 2 76 76 76 76 76 75 75 75 75 75 4 7A 74 ` 74 74 74 74 75 76 74 74 74 85 85 112 76 76 102 83 132 79 78 119 81 137 86 81 9 80 136 85 134 99 85 83 149 88 124 110 88 87 160 92 111 119 92 90 165 96 96 124 96 1 pjn. 93 166 98 98 125 117 2 04 160 . 99 99 121 135 77 77 77 77 77 75 76 76 76 76 76 76 76 76 76 75 75 75 75. 75 74 74 74 74 74 74 75 75 74 74 82 80 95 77 76 65 81 113 80 79 110 82 120 86 82 123 85 120 96 86 135. 88 115 105 90 145 62 108 113 65 150 95 98 117 68 151 98 101 119 114 146 99 101 116 126 95 151 100 100 114 149 138 100 101 111 135 94 136 . 98 98 103 154 127 99 99 103 137 93 120 101 96 97 150 113 99 97 68 131 91 102 102 93 93 129 99 97 93 66 112 7 87 87 88 87 87 89 87 88 87 92 88 85 85 85 85 85 85 85 85 85 85 85 83 83 83 83 83 83 83 83 83 83 83 10 81 81 81 81 81 81 81 81 81 81 81 u 79 79 79 79 76 79 79 79 79 79 79 24 hravg tm 83.1 109.1 88.5 95.8 92.2 ' 95.8 103.4 86.0 92.9 91.2 62.9 a = surface absorptivity, dimensionless. faro ts UI1it surface conductance, radiation and convection combined, Btu per (hr) (sq ft) (F deg). b Values in this column are magnitudes of <0, the outdoor dry-bulb temperature. gives Re as 82 percent of the hemispherical radiation emitted by a black surface radiating at a temperature equal to that of the outdoor dry-bulb temperature. For vertical surfaces, R, varies, since part of the energy is received from the ground, the temperature of which is influenced by solar radiation. -Few data for vertical surfaces are available. Because of the lack of data regarding R, and the difficulty of evaluating (l(R, -- Rl), present practice in calculating sol-air temperatures is to compensate for the term by increasing /,, . This is a rough approxima tion, since, during a considerable part of the night, outdoor surface tem peratures are at or close to the ambient air temperatures, yet the radiation loss is of appreciable magnitude! Example 6: If to = 90 F, a, = 0.7, /, = 200 Btu per (hr)(sq.ft), fee = 3.0, find the sol-air temperature for a roof when the dew-point temperature is 67 F. Solution. Previous experience indicates that the roof temperature under these conditions will be about 120 F. ei, equals 0.9. Using the tabular data of Table 4, Chapter 5, to determine R, and Rl: - 90 + 0,7 (200) + 0-9 (0-82 X 159 - 196) =m Q p 3 Example 8: Find tr if compensation for -- Rl) is made by replacing fco with foe, the surface conductance for radiation and convection combined, equal to 4.0. ,Solution. J,, = 90 + 'LIS) = 125.0 F. 4 "' '