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190 CHAPTER 13 Table 9.... Total Equivalent Temperature Differentials for Calculating Heat Gain Through Sunlit and Shaded Roofs Description of Boot Contnidm* 1960 Guide 1* Woodb or 1' Wood* + V or 2* insulation 2* Concrete or 2* Concrete + l' or V insulation or 2T Wood* 2* Gypsum or 2* Gypsum + ' insulation 1' Wood* or 2* Wood* or + 49 rock wool 2* Concrete or in furred ceiling 2* Gypsum 4* Concrete with 2' insulation 6' Concrete 6r Concrete + V insulation Light construction roof with 1' water Heavy construction roof with 1' water Any roof with 6' water Light construction Heavy construction Light construction Medium construction Heavy construction tigtrf CauIndiM Booft--Exposed to Sun 12 38 54 62 50 26 10 4 0 a CoMlnidion Booh -Cxpotod to Son 6 30 48 58 50 . 32 14 6 2 0 20 40 52 54 42 20 10 6 0 20 38 50 52 40 22 12 Hoary Comfroifion Roof*- Exposed to Sod 6 4 6 24 38 46 44 32 18 12 6 6 20 34 42 44 34 20 > i Corerod rritft Water Exposed to Son lC0t14O 4 16 22 18 14 10 2 -2 -4 10 14 16 14 10 0 0 6 10 10 8 4 0 o 0 toft rift Boot Sproyx fxpowd fa Suet 0 4 12 18 16 14 10 2 -2 -2 2 8 12 14 12 10 o 6 Booh m Shade -4 0 6 12 14 12 8 2 0 -4 -2 2 8 12 12 10 6 2 -2 -2 0 4 8 10 10 8 4 -j { 1 i \ < ' j \ 1 \ i f 1 f ( } f Notes for Table 9 Total beat waasmisirop Icon aefar) Explanation: ...________________ between outericr and roam air. Bta / l,per (hi) (sq ft) of tool j Eapnleat tecaperatura l , ] differential boa abovej J 1. Sotaro. Calculated by Mackey and Wrijht method (tee referencelist) eadadiostedaftexstadyiat AHBAE oripnal testdate. Estimated lor about Aofust I in 40 dee north latitude- (For sol-air temperatures used ia calculation* aee Table 8.) Far typical ***-:r" day wbere the naxunnm ootdoor temperature iitlF and minimum temperature at night i apprmimately7S F (daily rane of temperature, 20 F) mean 21 hr temperature 84 Flora room temperature of 80 F. All roof* bare been r'ip^H a dark color which abeorbe SO percent of aotai radiation, and reflect* only 10 percent. 2. Applicative. Tbcae Talus* may be uaed for all normal air oanditioninfmtiraatea; usually -wfthpot correction, ia latitude 0 dec to 60 dec north or eoatb when the feed t calculated for the betteet weather. Not* 6 explains bow to adjust the temperature differential Ice other room and outdoor temperatura*. A Poakoi Roof*. If tbe tool i* peaked and the heat cals ia primarily doe to aolar radiation, tta* for the area of the roof, the area protected eft a horiaontal plane. t- Attica U tbe Offline is insulated and if a fan is uaed in tbe attic for positive veatflatioa, the total temperature differential for a roerf exposed to tbe sun may be decreased 26 percent. . 8. Cometiom. For toapoiatiav difference rotea awMoer mcrimic itoign temperature erinrts room u differentfrom It dog. If the outdoor rirsifn temperature minus room temperature ia different bom the beae of !5 dec, correctas foflowe: When the difference a creater (or tesa) thaA IS de* add the excess to (or subtract tto defideacy from) tbe above differentials. Ft outdoor daily rca* of tewperatws ether than to dog. M the daily ranee of temperature is less than 20 deg, add 1 de* for every f dec lover daily raace; U the daily range is greater than 20 dec, subtree* l deg for every 1 dec higher drily ranee. Farexample, tbe daily ranee is Miami, Florida ia 12 deg or 8 deg lem than 20 deg, there to*, tbe correction is -H deg at efl hour* of the day. Cooling Load 191 Notes for Table 9.... Total Equivalent Temperature Differentials for Calculating Heat Gain Through Sunlit and Shaded Roofs (Concluded) liifU Colon. Creditalmald not be taken tor light eolorad tool* except wbere the permsaesra of tbe light color is established by experience, aa in rural areas or where tto* is little smoke. When tbe estetfca surface of roof exposed to tbe aoa is e light color. Bach as white or aluminum (which absorb approximately 66 percent end re flect 60 percent of theseder radiation) add to the temperature differential for roof ia shade 53 percent of the difference between tbe roof in sun and roof in shade. When the roof exposed to the son s a medinm color such as tight grey, bine or green, or bright red, add 80 percent of this difference. Far tolar fnmnmWrm ia krfr'fwto otkrr (tea ft) dot north, and is ether aontht. The table values of temperature differentials will be approximately oorraet to a roof in tbe loflowing month*-. Nobxb Uirwi Sooth Latttcos (dec) Mofttba Latitude (dec) Months 0 AD months 0 10 AQ moatta 10 to AD months except Nov, Dee, tea 80 Her. Apr, May, June, July, Auc, Sept 30 46 April, May. June, July, Aug 40 60 May, Juae, July SO AH months All months All months except May, June, July Sept, Oct, Nov, Dee, Jan. Feb, M*x Oct, Nov, Dee, Jaa, Feb Nov, Dec, Jaa For ottor montba, tbe total temperature differential (<*) may be approximated by the use of the following formula: shn t, = temperature differential for tbe same roof is shade far dashed time of day; obtained from Table 9. Jr -- maximum solar transmisrioa through glass, Bta per (hr) (sq ft) to flat skylight in Aug., 40 deg north latitude (Koto: this ia maximum value irrespective of time). 1, -- same aa ft except use the maximum value for flat skylight, to mostth, and latitude desired for t, . t, -- temperature differential for partiostarroof exposed to eon for tbe desired time of day from Table 9. (Koto that this mo h*t odjeolnoot onty for ooiar radiation and that thorn met h values will be obtained if tbe overall heat .transmission co efficient is calculated using 1.2 as the inside film conductance for summer. Hie roof coefficients of transmission for summer shown, in Table 11 are based on surface conductances fa, of 4.0 for an outside roof surface and 1.20 for an inside ceiling surface. Hie outside conductance 4.0 is used for summer because it corresponds to a wind velocity of approximately 7.5 mph averaged for rough and smooth surfaces, and is more repre sentative of summer wind velocities. Also, the lower wind velocity should be used in order to be on the safe side in determining the sol-air temperature. The inside conductance 1.20 is used because the convective portion of the film con ductance for downward heat flow from a horizontal surface is appreciably less than the winter conductance for heat flowing upward. Since there is little difference in toaQ transmission coefficients for summer, based on the conductances of 4.0 and 1.65, and the winter coefficients, based on 6.0 and 1.65, it is recom mended that the overall coefficient V, for trolls, be taken directly from the tables in Chapter 9 in which they are based on an outside film conductance of 6.0, corresponding to a 15 mph wind velocity. Advantages of Equivalent Temperature Differential Method Hie advantages of the equivalent temperature differential method of determining the total heat transmission are given in following paragraphs, and are apparent from Examples 5 to 7. 1. .The total sensible heat flow is obtained by multiplying the overall beat transmission coefficient U, and the equivalent temperature differential indicated in Tables 9 and 10. 2. The temperature differentials listed for a few representa tive types of construction may be used on all classes of walls and roofs, even though tbe overall heat transmission coefficient is different, provided the structure has thermal and physical properties similar to one of those listed in Tables 9 and 10. 3. Adjustments can be made, according to instructions given in the footnotes, for room and outdoor conditions differ ent from those on which the tables are based- Examples of Use of Equivalent Temperature Tables Example 6: Given: A roof is constructed of 6 in. of stone concrete with 2 in. of insulating board and tar felt roofing % in. thick, and is exposed to the sun. The location is the central part of the United States. Find the rate of heat flow into building at 2:00 p.m. during July for an outdoor design temperature 95 F, and an indoor temperature 80 F. Solution: From Table 9 in 2 p.m. column for 6-in. concrete lus 2-ia. insulation find the total equivalent temperature ifferential 34 deg. Tbe overall heat transmission coefficient for summer is taken from Table 11 and is found to be 0.13. The heat-flow rate equals 34 X 0.13 -- 4.42 Btu per (hr) (sq ft). Example 6: For the conditions of Example 5, find the rate of heat flow into building at 2:00 p.m. during July for design temperatures of 105 F (outdoor) and 78 F (indoor). Daily range of temperature 30 deg, i.e., outdoor temperature minimum of 75 F which occurs at 4:00 or 5:00 a.m.; this being 30 deg less than the maximum. Solution: Make correction in equivalent temperature differ ential in accordance with Note 5 in Table 9 as follows: The correction for 27-deg design temperature difference is (27 - 15) ~ +12. The correction for 30-deg daily range is ^ ~ --^ -- --5. Net total correction is +12 -- 5 -- +7. The heat-flow rate at 2:00 p.m. is (34 + 7) X 0.13 ** 5.32 Btu per (hr) (sq ft). A method of determining heat-flow rates, when structure is not given in Tables 9 or 10, is illustrated in Example 7. Example 7: A 4-in. stone concrete roof covered with an average depth of 4 in. of cinder concrete (k =* 4.9), on which is placed a 9^-ia. thick felt roof with }-in. pitch and slag.