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184 CHAPTER 13 1959 Guide Table 11.... Summer Coefficients of Heat Transmission U of Rat Roofs Covered with BuilMJp Roofing* Ww per Ua*frt Uepjare food if deg difference between (he air an (he (we rides) Insulation on Top of Dedr (Covered With Suitt Up Rooting) Tjrp* of ftoof Deck (Ceding not dmm) Flat metal roof deck Precast cement tile TTucfcnew of Roof Deck (indieil No Ceding-- Underride of Roof Exposed Furred Ceding with Air Space. Me*al lath and Plaster No insulaHon bmdoting board4 thickness, in. M 1 iH 2 No Insulation Insulating board4 thickness, in. mH 1 2 4 Ply Felt Roof Ditto + H " Slag 4 Ply Felt Roof m 0.73 0.35 0.23 0.17 0.13 0.40 0.25 0.18 0.14 0.12 0.54 0.30 0.20 0.16 0.13 0.34 0.22 0.16 0.13 0.11 0.67 0.33 0.22 0.17 0.13 0.38 0.24 0.18 0.14 0.12 Concrete -~a 1I Gvpsum and wood Gberb -------v --------\ mDitto +Hin. Slag 4 Ply Felt Roof 2 4 6 Ditto 2 4 + H in. Slag 6 4 Ply Felt Roof 2H 3M Ditto 2K + M in. Slag 3tf 0.50 0.65 0.59 0.54 0.49 0.46 0.42 0.28 0.20 0.15 0.12 0.33 0.31 0.30 0.22 0.21 0.20 0.16 0.16 0.16 0.13 0.13 0.13 0.28 0.27 0.28 0.20 0.19 0.19 0.15 0.15 0.14 0.12 0.12 0.12 0.32 0.37 0.36 0.33 0.31 0.30 0.29 0.21 0.17 0.13 0.11 0.24 0.23 0.22 0.18 0.17 0.17 0.14 0.13 0.13 0.12 0.12 0.11 0.21 0.21 0.20 0.16 0.16 0.16 0.13 0.13 0.13 0.11 0.11 0.10 0.34 0.2S 0.29 0.25 0.23 0.17 0.13 0.12 0.20 0.15 0.12 0.11 0.20 0.16 0.13 0.11 0.18 0.14 0.12 0.10 0.25 0.21 0.22 0.19 0.18 0.14 0.12 0.097 0.16 0.13 0.11 0.094 0.16 0.13 0.11 0.093 0.15 0.13 0.10 0.090 Wood ------- ^y """ ' 4 Ply Felt Roof 1 iH 2 3 Ditto + H d- Slag 1 lH 2 3 0:43 0.33 0.29 0.22 ' n 9R n vf. 0.20 0.10 0.19 0.17 0.16 0.13 0.15 0.13 0.13 0.11 0.12 0.11 0.11 0.09 0.35 0.29 0.26 0.20 0.23 0.20 0.19 0.15 0.17 0.15 0.14 0.12 0.14 0.12 0.12 0.10 0.11 0.10 0.10 0.09 0.29 0.24 0.22 0.17 0.25 0.21 0.20 0.16 0.20 0.18 0.16 0.13 0.15 0.14 0.13 0.12 0.13 0.12 0.11 0.10 0.11 0.0970.094 0.085 0.18 0.17 0.15 0.13 0.14 0.13 0.13 0.11 0.12 0.11 0.10 0.09 0.10 0.093 0.090 0.081 * Tbe summer coefficients ere considered temporary, end have been <--l/fl>d with en outdoor wind velocity of 8 mph. Foe summer an inside surface cooductaaca of 1-8 bas been used instead of tbe refuiar 1-88 Talus. In aQ of these rools s 4 ply felt roof has bees assumed H in- **!<*, conductivity -- 1.33. Pitch and slat bars been assumedas anadditional thickness of H in. which has been assigned thermal conductivity " ID. In both esses thermal conductivity refer* to one tad thiok- * tOH percent fyi'--1"-. 13H percent wood fiber. Thickness indicatsd indudea H in. xypsum board. This it s poured roof. * Nominal thickness of wood b specified, but actual thiekness wss used in calculations. 4 If oerkboard insatationa used, thecoefficient 17 may be decreased 10 percent. surface, is exposed to the sun. The location is the central part of the United States. Design temperatures are: outdoor 95 F; daily range 20 deg; indoor temperature 80 F. Find the heatflow rate at 2:00 p.m. for a day in July. Solution: For the purpose of selecting the equivalent tempera ture differential, this construction is assumed to be equal approximately to an uninsulated 6-in. concrete roof, for which the equivalent temperature is found to be 38 deg in the 2:00 pjn. column of Table 9. Calculate the overall heat transmission coefficient U (see Equation 3 of Chapter 9) of the roof as follows: 1 4 4 0.375 0.60 1 1.2 + 12 + 4.9 + 1.33 + 1.00 + 4.0 The heat-flow rate is then 38 X 0.33 equals 12.5 Btu per (hr) (sq ft). TABLES FOR CALCULATING SOLAR HEAT GAIN THROUGH GLASS AREAS Basic Principles In order to set forth the principles involved in calculating heat flow through glass areas, the general instantaneous heat balance relation will be presented. It will be shown sche matically in Tig. 2. The net heat gain for the indoor space is the result of several contributing factors. - The following observations concerning the behavior of Cooling Load glass with respect to radiant energy will lead to a better understanding of the heat bn.lanre relation. 1. Glass transmits, in varying degrees, radiation having wavelengths between 0.29 ana 4.75 microns. The percentage . of each wavelength transmitted is dependent upon tbe chem ical and physical characteristics of the glass, and upon the angle of incidence of the radiant energy. Of the energy not transmitted, part is absorbed and part reflected. 2. Glass is opaque to radiant energy emitted from sources below 450 F. 3. Because of the above principles, it is convenient to group radiant energy into two classifications, solar radiant energy and low temperature radiant energy. The complete heat balance for a glass section can be ex pressed for a unit tinu* interval as follows: Rg.2. ... Instantaneous Heat Balance for a Glass or Glass Block Section Total heat flow, "I _ r Transmitted, "j Cthrough glass sectioni.j Lsolar radiation J Heat flow by convective*! [ Jand radiative exchanges at | the indoor surface (2a) The second term of the right, aide of Equation 2a ean algo be expressed by a heat balance equation as follows: Heat flow by convective-) J"Absorbed-] [and radiative exchanges I = I solar I at the indoor surface J |_radiationJ PRadiative exchanges be I -tween outer surface of glass Land outdoor surroundings J (2b) Convective exchanges "1- I-Heat storage-) [ J [.glassbetween outer surface of J I within the I glass and outdoor air sectionj Equations 2a and 2b can be combined and expressed in symbolic terms by Equation 2c. Tabular values of the two bracketed terms of Equation 2a are presented later in thin section for various types of glass for specific design conditions. (?/-4) = [td!d + rj/d + [d/d + oul* + **22, -- where - /. (I,. - I.) - 51 (2c) is/A) " instantaneous rate of heat flow, Btu per (hour) (square foot). To |T4 = transmittance of glass for direct and diffuse solar radiation, respectively. 185 Id incident direct and diffuse solar radiation, respec tively, Btu ner (hrmr) (square foot), ao , ad -- absorptance of glass for direct and diffuse solar radiation, respectively. * -- emissivity of glass at temperature t$, . R, = low temperature radiant 'energy falling on glass from outdoor surroundings, Btu per (hour) (square foot). R, -- low temperature radiant energy emitted by a sur face with emissivity equal to 1.0 at temperature If* . / 19 outdoor. convective conductance, Btu per (hour) (square foot) (Fahrenheit degree). I** " temperature of outdoor surface of glass, Fahrenheit. I* = temperature of outdoor air, Fahrenheit. S -- rate at which glass stores energy, Btu per (hour) (square foot). Transmissivity and absorptivity vary with both wave length of the incident radiation and incident angle. Normal incidence transmittance values for some commonly used types and combination are given in Table 14.. Some varia tion in these values can be expected in practice due to vari ations in 'manufacture and in solar energy distribution. However, a change in transmissivity causes a compensating change in absorptivity. Generally, the total heat flow is not greatly altered. Transmittance data for a number of types of glass and various patterns of 8>in. glam block are given in ASHAE research papers.1**1 " " " **>u As stated earlier in this chapter, present data as to the value of R, are inadequate, so for the present it is suggested that fc be increased to include radiation, and the term iffmRt -- <*Rf* be disregarded. It is not practicable to give values of S in this chapter. However, for ordinary glass, the value of 5 is mrud! Fig. 3 is a graphical solution, for single gloss, of Equation 2b. Only absorbed solar radiation is considered, although low temperature radiation exchange and heat storage can be added algebraically to atIt if such data are available. The small thermal resistance of the glass has been neglected. The heat-flow rates are for 80 F indoor temperature, an in- Rg. 3 .... Convection and Radiation Heat Row for Vertical Single Glass