Document Dvdwa73rbVbVoxyZv2aODQLGN

278 CHAPTER 12 1952 Guide on the weather side will increase the time lag and decrease the instan taneous maximum rate of heat gain. Two examples are given to show how to estimate, roughly, the instan taneous rate of heat gain through sunlit composite walls or. roofs., Example 8: Estimate the maximum instantaneous design rate of heat gain from a horizontal roof in a location having an industrial type of atmosphere. The roof is made up of black, built-up roofing on the weather side (a = 1, U = 4,thermal resistance = 0.28), 1 in. of insulating board, and 4 in. of concrete with no ceiling. The temperature of the indoor air is 80 F. ^ Solution: The overall coefficient of heat transfer for this construction is: II = 1--------------------------------------------- = 0.22 Btu per (hour) (square foot) (F deg) U 0.25 + 0.28 + 3.03 +.0.33 + 0.61 . If the time lag of the built-up roofing be ignored, the sum of the time lags of the individual layers is, from Table 10, (0.23 + 2.5) or 2.73 hr. Actually, the time lag will be between 0.5 hr and 1.0 hr greater than this, so assume a time lag of 3.5 hr. From Table 10, the homogeneous concrete roof having a time lag of 3.5 hr would have a value of X of about 0.65; use this .value for the composite roof. From Fig. 2, X is approximately 0.65. With values of U and i,,* found from Table 9, as in previous examples, use Equation 5 and find the maximum design instantaneous rate of heat gain as: 1 = 0.22[(103.4 - 80) + 0.65(151 - 103.4)1 = 11.9 Btu per (hr) (sq ft). A The maximum instantaneous rate of heat gain from this roof would occur at about 4:30 p.m.,-sun time. Example 9: Estimate the maximum instantaneous design rate of heat gain on August 1 from a south wall in a location at 40 deg north latitude having a clear at mosphere. The wall consists of 4 in. of face brick (a, = 0.7; = 4.0), 4 in. of common brick, furred, with an air space (thermal resistance = 0.75), and finished on the inside with | in. of plaster on metal lath (thermal resistance -- 0.23); the tem perature of the indoor air is constant at 75 F. Solution: The overall coefficient of heat transfer for this construction i3: I] _ --------------------- ---- = 0.32 Btu per (hr) (sq ft) (F deg). U 0.25 + 0.44 + 0.80 + 0.75 + 0.23 + 0.61 From Table 10, the sum of the time lags for the face brick and the common brick is (2.4 + 2.3) or 4.7 hr. The.actual time lag will be slightly greater than this, and a value of 5.5 hr will be assumed. From Fig. 2, X is approximately 0.45. By interpolation in Table 9, tm = 89.5 F, and +* = 115.4 F. From Equation 5 the maximum instantaneous design .rate of heat gain is: 1 = 0.321(89.5 - 75) + 0.45(115.4 - 89.5)] = 8.4 Btu per (hr) (sqft). A The time of this heat gain is about 6:30 p.m., sun time. Those concerned with a further study of the details of cooling-load estimates in particular relation to periodic heat flow will find much of value and interest in the reports of experiments studies of these problems.8, e 111 l8, 14' 16 PRACTICAL TABLES FOR CALCULATING SOLAR HEAT GAIN THROUGH WALLS AND ROOFS Use of Equivalent Temperature Differentials The preceding paragraphs have explained the principles and methods used in estimating solar heat gain- by use of sol-air temperature. This method is rather tedious and is not convenient for every-day use. Some Cooling Load 279 new practical tables12 have therefore been' `developed using - the basic method reported by Mackey and Wright.11 These new tables utilize equivalent temperature differentials which may be multiplied by the overall heat transmission coefficient U to give directly the total heat transmission, Btu per square foot, from solar radiation and from temperature difference between outside and room air. These tables were prepared from sol-air data, as shown in Table 11, which Table 11. Summer Design Sol-Aib Temperatures Used for Tables 12 and 13 q Mean Sun Time 4 Sol-Air Temperature U Fahrenheit Degrees Any Sur Horn. North face1* ` East South West Ratio*: -j-- Joo 12 Midnight I AM 2 3 4 5 6 7 8 9 10 11 12 Noon 1FM 2 3 4 5 6 7 8 9 10 11 24 Hr Avg tm 0 0.225 0 0.225 0.125 0.225 0.125 0.225 0.125 77 77 .77 77 77 77 77 77 77 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 76 75 75 75 75 75 75 75 75 75 74 74 74 74 74 74 74 74 74 74 74 74 75 80 74 74 74 74 74 76 74 110 93 74 74 74 74 75 91 75 123 100 75 75 75 75 77 106 77 126 103 82 78 77 77 80 119 80 125 104 93 86 80 80 83 129 83 117 100 102 93 83 83 87 137 87 108 96 110 99 89 87 90 142 90 ' 92 92 114 104 98 92 93 144 93 93 93 115 105 110 102 94 140 94 95 94 111 104 124 111 95 132 95 95 95 104 100 135 119 94 120 94 93 107 93 91 96 91 .87 90 87 94 94 99 96 141 120 93 93 95 94 139 118 91 91 91 91 125 111 87 87 88 .87 103 94 85. 85 85 83 83 83 81. 81 81 79 79 79 85 85 85 85. . 85 85 83 83 83 83 83 83 81 81 81 81 81 81 79 79 79 79 79 79 83.1 100.5 83.1 93.0 88.4 89.0 86.2 93.0 88.4 *<* = surface absorptivity, dimensionless: roof <= 0.9; dark walls => 0.9, and light walls = 0.5. fco = unit convective conductance = 4.0 Btu per (hr) (F deg). b values in this column are magnitudes of to, the outdoor air temperature. are approximately the same as data for an industrial atmosphere in Table 9. It is suggested that Tables 12 and 13 be used for general estimating purpose. These analytical procedures, as well as those using Tables 9 and 10 pre sented here, yield generally higher rates of heat gain than reported for Pitts burgh in early A.S.H.V.E. experimental studies. Current authoritative opinion indicates a preference for analytical calculations.