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452 CHAPTER 24 1965 Guide And Data Book Table 26 .... Simplified Thicknesses (l) for Rigid Pipe Insulations Size, la OJ5, in. r. fa.1 - H H l \K - 1M 0.84 1.05 1.32 1.66 : 1.90 0.42 0.52. 0.66 0.83 0.95 1.00 0.88 1.06 0.88 1.00 .2 2H3 3X 4. 2.38 2.88 3.50 4.00 4.50 1.19 ' 1.44 1.75 . 2.00 2.25 ` . 1.03 . 1.03 1.00 1.28- 1.03 4X 5.00 2.50 5 6.56 2.78 6 6.63 3.31 7 7.63 3.81 8 8.63 4.31 9 9.63 4.81 10 10.75 5.37 11 11.75 1 5.87 12 12.75 6.37 14 14.00 7.00 Over 14 up to and including 33 1.28 1.00 0.97 __ __ __ -- -- -- .-- `iX 2 l!56 1.44 1.56 1.63 1.50 2.06 1.94 2.09 1.91 2.31 1.56 2.09 1.84 . 2.34 1.53 2.03 1.78 . ' 2.28 1.53 2.03 1.78 1.50 1.47 1.53 1.53 2.28 2.00 . 2.03 2.03 . 2.03 1.53 . 1.59 1.59 1.56 1:44 1.44 - 2X6 '2.09 ' 2.09 2.06 1.94 1.94 Nosund Thkktttu, laches 2X 3 3X A 4X S 2.88 .2.75 2.63 2.44 2.81 3.38 3.25 3.13 . 2.94 3.31 3.88 3.75 3.63 3.44 3.81 . 4.38 4.25 4.13 3.94 4.38 - 4.94 4.81 4.69; 4.53' 4.91 5.44 5.31 5.19. 5.03 . 5.41 2.59 2.84 . 2.53 2.78 2.53 2.84 2.56 2.53 2.53 2.66 3.09 3.34 3.03 3.34 3.09 3.59 - 3.91 3.59 . 3.84 3.59 4.16 4.41 4.09 : 4.34 4.09 3.34 3.06 - 3:03 3.16 : 3.16 3.84 3;56 3.66- 3!66 3.66 ! 4.47 . 4.19 4.16 , 4.16 , .4.16 4.66 4.91 4.59 4.34 4.72 4:47? . 4.69 ! 4.66 4.66 4.66 5.16 5.53 5.22 4.97 ` 5.22. y.:4.97 5.19 5.22 5.16 5.16 2.66 2.59 2.59-. . 2.56 2.44 .2.44 3:16 3.09 3.09 3.06 2.94 2.94 . .3.66 : 4.16 3159 4.09 3.59 4.09 3.56 , 4.06 .3:44 . 3.94 3.44 3.94 ; 4.66 ; 4.69: 4.59! 4.59! 4.44 4.44' 5.16 5.09 5.09 5.09 4.94 4.94 k = thermal conductivity of insulation at mean temperature, Btu per (hour) (square foot) (Fahrenheit degree per inch thickness). * L -- thickness of insulation, inches. L, " temperature of ambient air, Fahrenheit. . t, ^ temperature of inner surface of insulation, Fahrenheit. f, -- temperature ofouter surface of insulation, Fahrenheit, ti, I* * intermediate surface temperatures of layers of insu lation, Fahrenheit. r, * inner radius of insulation, inches. t, -- outer radius of insulation, inches. - ru fj, *= outer radius of intermediate. layers of insulation, inches. . R, - surface resistance 1/A, (hour) (square foot) (Fahrenheit degree) per Btu. h -- surface conductance coefficient, Btu per (hour) (square foot) (Fahrenheit degree), log, = natural or Naperian logarithm. To calculate the heat flow per square foot of pipe surface, Equation 12 can be used. g, -- q, tJt. (12) where g, " rate of heat transfer per square foot of pipe surface, Btu per (hour) (square foot). For steady, state conditions, the heat flow through each successive material is the same. However, the temperature drop through each material is proportional to its thermal resistance. The terms which appear in the denominators of Equations 10 and 11 represent the resistances to heat flow. The heat transferred is inversely proportional to the sum of the resistances (Ri + fi* + * + &) of the system! The various temperature drops in the1 system are proportional to thpi rtgastann**. i ' - The assumptions used for calculations 'of 'heat loss are usually: -1, " temperature at inner surface of insulation equal to the temperature of fluid in the pipe or container, still air ambient temperature = 80 F. - - . r, = inner radius of insulation " outside radius of iron pipe.., . r, = outer radius of insulation = r, + L. Example IS: Compute the heat loss from a boiler wall if the interior Insulation surface temperature is 1100 F and the ambient still air temperature is 80 F. The wall is insulated with 4X m of mineral fiber block and X in. of mineral fiber insulating and fin fulling cement. fig. 6 .... Heat How Through Cylindrical Surfaces Design; Heat Transmission Coefficients ;453 Solution: Assume that the mean temperature of the mineral fiber block is 700 F, the mean temperature of the insulating cementis 200 F, and R -- 0.'"' From Table 21, ki = 0.64 and ks - 0.80. Then,' ____ 1020 4.5 0.5 ---- +------- + 0.60 0.64 0.80 : 8.26 - 123.5 Btu/(hr) (sq ft) As a check, from Fig. 7, at 123.5 Btu/{hr) (sq ft). R, - 0.55. The mean temperature of the mineral Abies' block is: 1100 - (3.52/8.26) (1020) - -- .1100 - 435 ~ 665 F. . The mean temperature of the cement is: 1100 - (7.35/8.26)(1020) - 1100--908 = 192 F. From Table 21, at 665 F, k, = 0.62, and at 192 F, k*.- 0.80. Recalculating g, with tfaeae adjusted values: 1020 .1020 1 Ts--^5--------- " sS _ I20-3 Btu/<tr) ("1 f- 0.62 + 0.80 + ^ From Fig. 7, at 120.3 Btu/(hr) (sq ft), fi. = 0.55 Toe mean temperature of the mineral fiber block is: 1100 - (3.65/8.48)(1020) - 1100 - 439 - 661 F. The mean temperature of the inmilating cement is: 1100 - (7.62/8.48) (1020) - 1100 - 917 - 183 F. Btu/(hr) (sq ft~-------------------- " Example H: Compute the heat loss per square foot of out surface of insulation if the pipe temperature is 1200 F and the an wt still air temperature is 80 F! The pipe is a nominal 6 L pipe and is insulated with a nominal 3 in. of diatomaceoi ea u the inner layer and a nominal 2 in. of eakitim silicate i me outer layer. --ion.- From Table 26, r. - 331 in. A nominal 3-in. thic olica insulation to fit a nominal 6-in. iron pipe nominal 2-in. thick calcium silicate insulation 1 f a " 3.CO m. diatomaoeouo silica is 2.06 in. thirlr Then rarer, 3.31 ul; r, - 6.34in.; and r, - 8.40in. temperature of the diatomaceoi oen pU 'y'n' the mean temperature of the and R, - 0.50. silicate : From Table 21, k, - 0.68 and k, - 0AO: 8.40 log. ~ 0.68 8.40 log, f = 77.6 Btu/(hr) (sq ft). 5.45 , 2.35 ,, _ 068 + 0.40 + ' From Fig. 7, at 77.6 Btu' (hr) '(sq ft), R, * 0.59. The mean temperature of the diatomaceous silica is: . *' 1200 - (4.00/14.40) (1120) = 1200 - 313 887 F. ' ' Hie mean temperature of the calcium silicate is: 1200 - (10.97/14.40);(1120) - 1200 - 853 - 347 F. From Table 21, it = 0.74 and k* 0.44. Recalculating: * ) . 1120' .1 _ S-_ 545------ 2J5------------------84.1 Btu/(hr) (sqft). !,, . . . V '.. 0.74 4 0.44 + M ' . ' '. _ From Fig. 7, at 84.1 Btu.(hr) (sq ft), R,-- 0.58. ' ' The mean temperature of the calcium silicate is: - . 1200 ~ (10.04/13.30)(1120) - 1200 - 846 = 354 F. From Table 21, ki -- 0.74 and fc -- 0.44. ! 1120 ' ?. = ~m------ ---------------------- - 84.2 Btu/(hr)(sq ft) . AA + +0.58 . 0.74 0.44 - . .5 , .- Since R,, ki, and k* will not change at 84.2 Btu/(hr) (sq ft), the heat loss is 84.2 Btu/(hr) (sq ft). The heat loss per square foot.of the inner surface of-insulation would be: .. - r, / 8.40\ " 84.2 - 214 Btu/(hr)' (sq ft)/ .. REFERENCES = ' 1 F. B. Rowley, A. B. Algren, and J. L. Blackshaw: ASHVE Rbseasch Repobt No. 869---Surface conductances as .affected by air velocity, temperature and character .of surface (ASHVE Transactions, VoL 36, 1930, p. 444). G. V. Parmelee and R. G. Huebscher: Forced Connection Heat Transfer from Flat -Surfaces (ASHVE Research Bul letin No. 3, p. 40, also > published in ASHVE Transactions, Vol 53, 1947, p. 245). : * G. V. Pannelre and W. W. Aubele; ASHVE Reseaech Repobt No. 1399--Heat flow through unshaded glass: Design data for load calculations (ASHV13 Transactions, VoL 56, 1950, p. 371). * M. 8. Kersten: Thermal Properties of Soils (University of Minnesota, Engineering Experiment Station Bulletin No. 28, June 1949). * F. A. Joy: Improving attic space insulating values (ASHAE TBANBAcnoita, VoL 64, 1958, p. 251). * F. C. Houghten, 8. L Taimuty, Gul Gutberlet, and C. J. Brown: ASHVE Research Report No. 1213--Heat loss through basement walls and floors (ASHVE Transactions, VoL 48, 1942. p. 369). * R. S. Dili, W. C. Robinson, and H. E. Robinson: Measure- meats of Heat Losses from Slab Floors (National Bureau of Standards, Building Materials and Structures Report BMS 103). 1 G. V. Parmelee: Heat Transmission through Glass (ASHVE Research Bulletin No. 1, July 1947). * Clifford Strack: Handbook of Air Conditioning, Heating and Ventilating (The Industrial Press, New York, 1959, p. 4-107 and 170). BIBLIOGRAPHY ASHVE Research Reports: No. 852--F. B. Rowley, A. B. Algren, and J. L. Biackshaw: Effects of air velocities on surface coefficients (ASHVE Tbansactions, VoL 36, 1930, p. 123). No. 895--F. C. Houghten and Paul McDermott: Wind veloci ties gradients near a surface and their effect on film conduct ance (ASHVE Transactions, VoL 37, 1931, p. 301).