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624 CHAPTER 31 1949 Guide In the following example, it will be assumed that the ceiling panel must deliver 70 per cent of its heat or 24,882 Btuh by radiation, since the total calculated heat loss is 35,117. When two plane surfaces of infinite size are parallel to each other and their surfaces are at different temperatures, the exchange of heat between the two is proportional to the difference between the fourth powers of their absolute temperatures. This is also true when one surface is completely surrounded by another surface: for example if one sphere is placed within another sphere, the flow of heat between tne outer sur face of the smaller sphere and the inner surface of the larger sphere is proportional to the fourth power of the absolute temperatures of the two surfaces. In a panel-heated room, the heated panel may be considered to be completely en closed by the remaining surfaces, because all heat radiated by the heated panel is intercepted by those surfaces. Consequently, the flow of heat from the heated ceiling to the room, by radiation, is proportional to the difference between the fourth powers of the absolute temperature of the ceiling and the absolute mean radiant temperature of the remaining surfaces. The rate at which a surface emits heat varies with the temperature of the surface and with other characteristics of the surface. For ordinary heat flow calculations it ' Fig. 9. HeatDelivered to Room by Radiation from Panel is sufficiently accurate to assume that the materials which are commonly used in building construction emit heat at a rate of: TV 0.156 -- j Btuh per square foot where ' '\ ' \ T is the absolute temperature of the surface in Fahrenheit degrees. On this basis the flow of heat from the ceiling to its surrounding surfaces is at the rate of: 480 x 0156 [(i^)4-(loo)] Btuh' In order that this rate may. be equal to 24,582 Btuh, T must be 572 and the ceiling temperature about 112 F. Instead of calculating this temperature it may be taken from Fig. 9, as follows: The ceiling must deliver heat to the room, by radiation, at the rate of 24,582/480 or 51 Btuh per square foot. Find.51 on the left margin and move horizontally to the intersection with a 62 MRT line, and from the point of intersection to the lower mar gin and'read about 112 F. .With a ceiling temperature of 112 F, the MRT of the room will be 480 X 112. + 1,536 X 62; the sum divided by 2,016, or 74 F. If an air temperature of 68 F and an MRT of 74 F should not produce satisfactory Panel Heating and Radiant Heating 625 *, Table 2. Total Heat Emission by Radiation* Boot 08 Mean Radiant Tevtib- ATUKS F Dbg R&diation in Btu per (square foot) (hour) emitted to surroundings with a .tempera ture of absolute zero by bodies at various temperatures and with emissivity factor e e' t e IM 0.95 0.90 0.80 Bodt OB Mean Radiant TeU?ERATOfiB 1 F Dm Radiation in Btu per (square foot) (hour) emitted to surroundings with a temperature of absolute < sero by bodies at various temperatures and with cmisBivity factor e t 1.00 0.95 0.90 0.80 : 30 35 40 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 . 63 64 65 66 67 . 68 69 70 99.7 103.9 108.0 112.5 113.3 114.3 115.2 116.0 116.9 117.9 118.8 119.8 120.6 121.7 122.6 123.5 124.4 125.3 126.3 127.1 128.2 129.1 130.1 131.0 132.1 133.0 134.0 135.0 136.0' 94.7 98.7 102.8 106.9 107.7 108.6 109.5 110.3 111.0 112.0 112.9 113.8 114.6 115.5 116.4 117.4 118.2 119.0 119.9 120.7 121.8 122:6 123.5 124.4 125.5 126.4 127.3 128.3 129.3 89.8 79.7 93.6 83.1 97.2 86.4 101.3 89.0 102.0 90.8 102.9 91.5 103.8 92.3 104.5 92.8 105.3 93.6 106.4 94.4 106.9 95.1 . 107.8 95.9 108.6 96.6 109.4 97.3 110.3 . 98.1 111.3 98.9 112.0 99.6 112.8 100.3 113.8 101.1 114.4- -101.8 115.3 102.6 116.2 103.3 117.1 104.1 117.9 104.8 118.8 105.8 119.7 106.4 120.5 107.2 121.5 108.0 122.3 108.8 71 72 73 74 75 80 85 90 100 110 120 130 140. 150 160 170 180 190 200 210 220 250 300, 350 400 450 500 550 600 137.0 137.9 138.9 140.2 141.6 147.2 152.9 158.5 170.3 182.3 195.6 210.9 224.1 238.0 252.1. 271.6 289.1 307.7 326.5 349.3 373.0 439.5 577.3 743.0 945.8 1181.0 1470.0 1798.0 2181.0 130.1 131.0 132.0 133.1 134.4 140.0 145.2 150.5 161.7 173.2 185.7 200.4 212.9 226.1 239.8 258.0 274:9 292.1 310.2 331.9 354.4 417.6 548.2 705.8 898.5 1121.0 1396.0 1708.0 2072.0 123.3. .109.7 124.0 110.3 124.9 111.0 126.1 112.1 127.4 113.2 132.5 117.9 137.6 122:4 . 142.7 126.9 153.2 136.2 164.2' 146.0 176.1 156.5 189.8 168.8 201.8 179.2 214.4 190.5 226.9 . 201.8 244.5 . 217.2 260.1 231.3 276.9 246.1 293.9 261.3 314.3 279.5 335.7 298.2 395.6 351.6 519.6 461.8 668.6 594.3 850.8 756.5' 1063.0 944.0 1323.0 1176.0 1619.0 1439.0. 1962.0 1745.0 * These factors are calculated from the formula /0.173 X T*\ r " * V 100,000,000/ where gr == total radiation, Btu per (eq ft) (hr) e = emissivity. T = absolute temperature, Fahrenheit degrees. conditions, the-oeilmg temperature can easily be changed as necessary by changing the temperature of the circulating water. Calculations like the preceding may also be made with the aid of Table 2. The rate at which the ceiling must radiate heat exceeds by 51 Btuh per square foot the rate at which the ceiling receives radiant heat from its surroundings. Assuming the emissiv ity of the walls, floor, and ceiling to be 90 per. cent of that of a black body, the heat radiated to the ceiling, from the surfaces wnose MRT is 62 F, is (Table 2) at the rate. . of 115.3 Btuh per square foot; the ceiling must therefore radiate heat at the rate of 115.3 plus 51 or 166.3; its temperature must be (Table 2) between 110 F and 120 F, and, by interpolation, 112 F, as calculated. 7. Select the medium for heating the ceiling panel The medium may be electricity, steam, air, or.water, but usually is air or water,. If air is used it is generally heated in the basement, passed up through hollow inside, walls or through ducts in those walls. allowed to flow between the ceiling and the floor above, and returned to the basement through hollow outside walls or through ducts in those walls. - If the walls and floors are constructed of hollow tile, the cells in the tile, can be placed so that they will form continuous ducts through which tho warm air can flow up the inside walls, then between the ceiling and the floor above, and down the out side walls. In way the walls and ceiling become heating panels.