01 POWER ISLAND / 01 CCPP / V. Ganapathy-Industrial Boilers and HRSG-Design (2003)
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FIGURE 8.20 Square (top) and triangular (bottom) pitch for boiler=exchanger tubes.
Copyright © 2003 Marcel Dekker, Inc.
Example
If 500 tubes of 2 in. diameter are located in a fire tube boiler shell at a triangular pitch of 3 in., the bundle diameter would be
D ¼ 1:05 3 5000:5 ¼ 70:5 in:
If the pitch were square, the bundle diameter would be
D ¼ 1:128 3 5000:5 ¼ 75:7 in:
Sometimes tubes have to be located within a given sector of a circle. In such cases, it is helpful to know the area of a sector of a circle given its height and diameter. Table 8.38 gives the factor C, which when multiplied by D2 gives the sector area.
Example
Find the area of a sector of height 10 in. and diameter 24 in.
Solution. For h=D ¼ 10=24 ¼ 0:4167; C from Table 8.38 ¼ 0.309. Hence,
Area ¼ C D2 ¼ 0:309 24 24 ¼ 178 in:2
8.51
Q:
How is the thickness of insulation for a flat or curved surface determined? Determine the thickness of insulation to limit the casing surface temperature of a pipe operating from 800 F to 200 F, when
Ambient temperature ta ¼ 80 F
Thermal conductivity of insulation Km at average temperature of 500 F ¼ 0.35 Btu in.=ft2 h F
Pipe outer diameter d ¼ 12 in.
Wind velocity V ¼ 264 ft=min (3 mph) Emissivity of casing ¼ 0.15 (oxidized)
Copyright © 2003 Marcel Dekker, Inc.
TABLE 8.38 C Factors for Finding Area of Sector of a Circle (Area ¼ CD2)
h=D |
C |
h=D |
C |
h=D |
C |
h=D |
C |
h=D |
C |
|
|
|
|
|
|
|
|
|
|
|
|
0.050 |
0.01468 |
0.100 |
0.04087 |
0.150 |
0.07387 |
0.200 |
0.11182 |
0.001 |
0.00004 |
0.051 |
0.01512 |
0.101 |
0.04148 |
0.151 |
0.07459 |
0.201 |
0.11262 |
0.002 |
0.00012 |
0.052 |
0.01556 |
0.102 |
0.04208 |
0.152 |
0.07531 |
0.202 |
0.11343 |
0.003 |
0.00022 |
0.053 |
0.01601 |
0.103 |
0.04269 |
0.153 |
0.07603 |
0.203 |
0.11423 |
0.004 |
0.00034 |
0.054 |
0.01646 |
0.104 |
0.04330 |
0.154 |
0.07675 |
0.204 |
0.11504 |
0.005 |
0.00047 |
0.055 |
0.01691 |
0.105 |
0.04391 |
0.155 |
0.07747 |
0.205 |
0.11584 |
0.006 |
0.00062 |
0.056 |
0.01737 |
0.106 |
0.04452 |
0.156 |
0.07819 |
0.206 |
0.11665 |
0.007 |
0.00078 |
0.057 |
0.01783 |
0.107 |
0.04514 |
0.157 |
0.07892 |
0.207 |
0.11746 |
0.008 |
0.00095 |
0.058 |
0.01830 |
0.108 |
0.04578 |
0.158 |
0.07965 |
0.208 |
0.11827 |
0.009 |
0.00113 |
0.059 |
0.01877 |
0.109 |
0.04638 |
0.159 |
0.08038 |
0.209 |
0.11908 |
0.010 |
0.00133 |
0.060 |
0.01924 |
0.110 |
0.04701 |
0.160 |
0.08111 |
0.210 |
0.11990 |
0.011 |
0.00153 |
0.061 |
0.01972 |
0.111 |
0.04763 |
0.161 |
0.08185 |
0.211 |
0.12071 |
0.012 |
0.00175 |
0.062 |
0.02020 |
0.112 |
0.04826 |
0.162 |
0.08258 |
0.212 |
0.12153 |
0.013 |
0.00197 |
0.063 |
0.02068 |
0.113 |
0.04889 |
0.163 |
0.08332 |
0.213 |
0.12235 |
0.014 |
0.00220 |
0.064 |
0.02117 |
0.114 |
0.04953 |
0.164 |
0.08406 |
0.214 |
0.12317 |
0.015 |
0.00244 |
0.065 |
0.02166 |
0.115 |
0.05016 |
0.165 |
0.08480 |
0.215 |
0.02399 |
0.016 |
0.00268 |
0.066 |
0.02215 |
0.116 |
0.05080 |
0.166 |
0.08554 |
0.216 |
0.12481 |
0.017 |
0.00294 |
0.067 |
0.02265 |
0.117 |
0.05145 |
0.167 |
0.08629 |
0.217 |
0.12563 |
0.018 |
0.00320 |
0.068 |
0.02315 |
0.118 |
0.05209 |
0.168 |
0.08704 |
0.218 |
0.12646 |
0.019 |
0.00347 |
0.069 |
0.02366 |
0.119 |
0.05274 |
0.169 |
0.08779 |
0.219 |
0.12729 |
0.020 |
0.00375 |
0.070 |
0.02417 |
0.120 |
0.05338 |
0.170 |
0.08854 |
0.220 |
0.12811 |
0.021 |
0.00403 |
0.071 |
0.02468 |
0.121 |
0.05404 |
0.171 |
0.08929 |
0.221 |
0.12894 |
0.022 |
0.00432 |
0.072 |
0.02520 |
0.122 |
0.05469 |
0.172 |
0.09004 |
0.222 |
0.12977 |
0.023 |
0.00462 |
0.073 |
0.02571 |
0.123 |
0.05535 |
0.173 |
0.09080 |
0.223 |
0.13060 |
0.024 |
0.00492 |
0.074 |
0.02624 |
0.124 |
0.05600 |
0.174 |
0.09155 |
0.224 |
0.13144 |
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(continued ) |
Copyright © 2003 Marcel Dekker, Inc.
TABLE 8.38 (continued )
h=D |
C |
h=D |
C |
h=D |
C |
h=D |
C |
h=D |
C |
|
|
|
|
|
|
|
|
|
|
0.025 |
0.00523 |
0.075 |
0.02676 |
0.125 |
0.05666 |
0.175 |
0.09231 |
0.225 |
0.13277 |
0.026 |
0.00555 |
0.076 |
0.02729 |
0.126 |
0.05733 |
0.176 |
0.09307 |
0.226 |
0.13311 |
0.027 |
0.00587 |
0.077 |
0.02782 |
0.127 |
0.05799 |
0.177 |
0.09384 |
0.227 |
0.13395 |
0.028 |
0.00619 |
0.078 |
0.02836 |
0.128 |
0.05866 |
0.178 |
0.09460 |
0.228 |
0.13478 |
0.029 |
0.00653 |
0.079 |
0.02889 |
0.129 |
0.05933 |
0.179 |
0.09537 |
0.229 |
0.13562 |
0.030 |
0.00687 |
0.080 |
0.02943 |
0.130 |
0.06000 |
0.180 |
0.09613 |
0.230 |
0.13646 |
0.031 |
0.00721 |
0.081 |
0.02998 |
0.131 |
0.06067 |
0.181 |
0.09690 |
0.231 |
0.13731 |
0.032 |
0.00756 |
0.082 |
0.03053 |
0.132 |
0.06135 |
0.182 |
0.09767 |
0.232 |
0.13815 |
0.033 |
0.00791 |
0.083 |
0.03108 |
0.133 |
0.06203 |
0.183 |
0.09845 |
0.233 |
0.13900 |
0.034 |
0.00827 |
0.084 |
0.03163 |
0.134 |
0.06271 |
0.184 |
0.09922 |
0.234 |
0.13984 |
0.035 |
0.00864 |
0.085 |
0.03219 |
0.135 |
0.06339 |
0.185 |
0.10000 |
0.235 |
0.14069 |
0.036 |
0.00901 |
0.086 |
0.03275 |
0.136 |
0.06407 |
0.186 |
0.10077 |
0.236 |
0.14154 |
0.037 |
0.00938 |
0.087 |
0.03331 |
0.137 |
0.06476 |
0.187 |
0.10155 |
0.237 |
0.14239 |
0.038 |
0.00976 |
0.088 |
0.03387 |
0.138 |
0.06545 |
0.188 |
0.10233 |
0.238 |
0.14324 |
0.039 |
0.01015 |
0.089 |
0.03444 |
0.139 |
0.06614 |
0.189 |
0.10312 |
0.239 |
0.14409 |
0.040 |
0.01054 |
0.090 |
0.03501 |
0.140 |
0.06683 |
0.190 |
0.10390 |
0.240 |
0.14494 |
0.041 |
0.01093 |
0.091 |
0.03559 |
0.141 |
0.06753 |
0.191 |
0.10469 |
0.241 |
0.14580 |
0.042 |
0.01133 |
0.092 |
0.03616 |
0.142 |
0.06822 |
0.192 |
0.10547 |
0.292 |
0.14666 |
0.043 |
0.01173 |
0.093 |
0.03674 |
0.143 |
0.06892 |
0.193 |
0.10626 |
0.243 |
0.14751 |
0.044 |
0.01214 |
0.094 |
0.03732 |
0.144 |
0.06963 |
0.194 |
0.10705 |
0.244 |
0.14837 |
0.045 |
0.01255 |
0.095 |
0.03791 |
0.145 |
0.07033 |
0.195 |
0.10784 |
0.245 |
0.14923 |
0.046 |
0.01297 |
0.096 |
0.03850 |
0.146 |
0.07103 |
0.196 |
0.10864 |
0.246 |
0.15009 |
0.047 |
0.01339 |
0.097 |
0.03909 |
0.147 |
0.07174 |
0.197 |
0.10943 |
0.247 |
0.15095 |
0.048 |
0.01382 |
0.098 |
0.03968 |
0.148 |
0.07245 |
0.198 |
0.11023 |
0.248 |
0.15182 |
0.049 |
0.01425 |
0.099 |
0.04028 |
0.149 |
0.07316 |
0.199 |
0.11102 |
0.249 |
0.15268 |
0.250 |
0.15355 |
0.300 |
0.19817 |
0.350 |
0.24498 |
0.400 |
0.29337 |
0.450 |
0.34278 |
Copyright © 2003 Marcel Dekker, Inc.
0.251 |
0.15441 |
0.301 |
0.19908 |
0.351 |
0.24593 |
0.401 |
0.29435 |
0.451 |
0.34378 |
0.252 |
0.15528 |
0.302 |
0.20000 |
0.352 |
0.24689 |
0.402 |
0.29533 |
0.452 |
0.34477 |
0.253 |
0.15615 |
0.303 |
0.20092 |
0.353 |
0.24784 |
0.403 |
0.29631 |
0.453 |
0.34577 |
0.254 |
0.15702 |
0.304 |
0.20184 |
0.354 |
0.24880 |
0.404 |
0.29729 |
0.454 |
0.34676 |
0.255 |
0.15789 |
0.305 |
0.20276 |
0.355 |
0.24976 |
0.405 |
0.29827 |
0.455 |
0.34776 |
0.256 |
0.15876 |
0.306 |
0.20368 |
0.356 |
0.25071 |
0.406 |
0.29926 |
0.456 |
0.34876 |
0.257 |
0.15964 |
0.307 |
0.20460 |
0.357 |
0.25167 |
0.407 |
0.30024 |
0.457 |
0.34975 |
0.258 |
0.16501 |
0.308 |
0.20553 |
0.358 |
0.25263 |
0.408 |
0.30122 |
0.458 |
0.35075 |
0.259 |
0.16139 |
0.309 |
0.20645 |
0.359 |
0.25359 |
0.409 |
0.30220 |
0.459 |
0.35175 |
0.260 |
0.16226 |
0.310 |
0.20738 |
0.360 |
0.25455 |
0.410 |
0.30319 |
0.460 |
0.35274 |
0.261 |
0.16314 |
0.311 |
0.20830 |
0.361 |
0.25551 |
0.411 |
0.30417 |
0.461 |
0.35374 |
0.262 |
0.16402 |
0.312 |
0.20923 |
0.362 |
0.25647 |
0.412 |
0.30516 |
0.462 |
0.35474 |
0.263 |
0.16490 |
0.313 |
0.21015 |
0.363 |
0.25743 |
0.413 |
0.30614 |
0.463 |
0.35573 |
0.264 |
0.16578 |
0.314 |
0.21108 |
0.364 |
0.25839 |
0.414 |
0.30712 |
0.464 |
0.35673 |
0.265 |
0.16666 |
0.315 |
0.21201 |
0.365 |
0.25936 |
0.415 |
0.30811 |
0.465 |
0.35773 |
0.266 |
0.16755 |
0.316 |
0.21294 |
0.366 |
0.26032 |
0.416 |
0.30910 |
0.466 |
0.35873 |
0.267 |
0.16843 |
0.317 |
0.21387 |
0.367 |
0.26128 |
0.417 |
0.31008 |
0.467 |
0.35972 |
0.268 |
0.16932 |
0.318 |
0.21480 |
0.368 |
0.26225 |
0.418 |
0.31107 |
0.468 |
0.36072 |
0.269 |
0.17020 |
0.319 |
0.21573 |
0.369 |
0.26321 |
0.419 |
0.31205 |
0.469 |
0.36172 |
0.270 |
0.17109 |
0.320 |
0.21667 |
0.370 |
0.26418 |
0.420 |
0.31304 |
0.470 |
0.36272 |
0.271 |
0.17198 |
0.321 |
0.21760 |
0.371 |
0.26514 |
0.421 |
0.31403 |
0.471 |
0.36372 |
0.272 |
0.17287 |
0.322 |
0.21853 |
0.372 |
0.26611 |
0.422 |
0.31502 |
0.472 |
0.36471 |
0.273 |
0.17376 |
0.323 |
0.21947 |
0.373 |
0.26708 |
0.423 |
0.31600 |
0.473 |
0.36571 |
0.274 |
0.17465 |
0.324 |
0.22040 |
0.374 |
0.26805 |
0.424 |
0.31699 |
0.474 |
0.36671 |
0.275 |
0.17554 |
0.325 |
0.22134 |
0.375 |
0.26901 |
0.425 |
0.31798 |
0.475 |
0.36771 |
0.276 |
0.17644 |
0.326 |
0.22228 |
0.376 |
0.26998 |
0.426 |
0.31897 |
0.476 |
0.36871 |
0.277 |
0.17733 |
0.327 |
0.22322 |
0.377 |
0.27095 |
0.427 |
0.31996 |
0.477 |
0.36971 |
0.278 |
0.17823 |
0.328 |
0.22415 |
0.378 |
0.27192 |
0.428 |
0.32095 |
0.478 |
0.37071 |
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(continued ) |
Copyright © 2003 Marcel Dekker, Inc.
TABLE 8.38 (continued )
h=D |
C |
h=D |
C |
h=D |
C |
h=D |
C |
h=D |
C |
|
|
|
|
|
|
|
|
|
|
0.279 |
0.17912 |
0.329 |
0.22509 |
0.379 |
0.27289 |
0.429 |
0.32194 |
0.479 |
0.37171 |
0.280 |
0.18002 |
0.330 |
0.22603 |
0.380 |
0.27386 |
0.430 |
0.32293 |
0.480 |
0.37270 |
0.281 |
0.18092 |
0.331 |
0.22697 |
0.381 |
0.27483 |
0.431 |
0.32392 |
0.481 |
0.37370 |
0.282 |
0.18182 |
0.332 |
0.22792 |
0.382 |
0.27580 |
0.432 |
0.32491 |
0.482 |
0.37470 |
0.283 |
0.18272 |
0.333 |
0.22886 |
0.383 |
0.27678 |
0.433 |
0.32590 |
0.483 |
0.37570 |
0.284 |
0.18362 |
0.334 |
0.22980 |
0.384 |
0.27775 |
0.434 |
0.32689 |
0.484 |
0.37670 |
0.285 |
0.18452 |
0.335 |
0.23074 |
0.385 |
0.27872 |
0.435 |
0.32788 |
0.485 |
0.37770 |
0.286 |
0.18542 |
0.336 |
0.23169 |
0.386 |
0.27969 |
0.436 |
0.32887 |
0.486 |
0.37870 |
0.287 |
0.18633 |
0.337 |
0.23263 |
0.387 |
0.28067 |
0.437 |
0.32987 |
0.487 |
0.37970 |
0.288 |
0.18723 |
0.338 |
0.23358 |
0.388 |
0.28164 |
0.438 |
0.33086 |
0.488 |
0.38070 |
0.289 |
0.18814 |
0.339 |
0.23453 |
0.389 |
0.28262 |
0.439 |
0.33185 |
0.489 |
0.38170 |
0.290 |
0.18905 |
0.340 |
0.23547 |
0.390 |
0.28359 |
0.440 |
0.33284 |
0.490 |
0.38270 |
0.291 |
0.18996 |
0.341 |
0.23642 |
0.391 |
0.28457 |
0.441 |
0.33384 |
0.491 |
0.38370 |
0.292 |
0.19086 |
0.342 |
0.23737 |
0.392 |
0.28554 |
0.442 |
0.33483 |
0.492 |
0.38470 |
0.293 |
0.19177 |
0.343 |
0.23832 |
0.393 |
0.28652 |
0.443 |
0.33582 |
0.493 |
0.38570 |
0.294 |
0.19268 |
0.344 |
0.23927 |
0.394 |
0.28750 |
0.444 |
0.33682 |
0.494 |
0.38670 |
0.295 |
0.19360 |
0.345 |
0.24022 |
0.395 |
0.28848 |
0.445 |
0.33781 |
0.495 |
0.38770 |
0.296 |
0.19451 |
0.346 |
0.24117 |
0.396 |
0.28945 |
0.446 |
0.33880 |
0.496 |
0.38870 |
0.297 |
0.19542 |
0.347 |
0.24212 |
0.397 |
0.29043 |
0.447 |
0.33980 |
0.497 |
0.38970 |
0.298 |
0.19634 |
0.348 |
0.24307 |
0.398 |
0.29141 |
0.448 |
0.34079 |
0.498 |
0.39070 |
0.299 |
0.19725 |
0.349 |
0.24403 |
0.399 |
0.29239 |
0.449 |
0.34179 |
0.499 |
0.38170 |
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|
|
|
|
|
0.500 |
0.39270 |
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Copyright © 2003 Marcel Dekker, Inc.
A:
The heat loss q from the surface is given by [7]
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¼ |
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e" |
þ100 |
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|
100 |
|
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# |
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||||||
q |
|
0:174 |
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ts |
459:6 |
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4 |
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ta þ 459:6 |
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4 |
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þ |
0:296 |
t |
t |
aÞ |
1:25 |
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V þ 68:9 |
|
1=2 |
ð |
110 |
Þ |
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ð s |
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68:9 |
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e may be taken as 0.9 for oxidized steel, 0.05 for polished aluminum, and 0.15 for oxidized aluminum. Also,
q |
¼ |
Kmðt tsÞ |
¼ |
|
Kmðt tsÞ |
ð |
111 |
Þ |
|
½ðd þ 2LÞ=2& ln½ðd þ 2LÞ=d& |
Le |
||||||||
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|
where t is the hot face temperature, F, and Le is the equivalent thickness of insulation for a curved surface such as a pipe or tube.
L |
e ¼ |
d þ 2L |
ln |
d þ 2L |
ð |
112 |
Þ |
|
2 |
d |
|||||||
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Substituting ts ¼ 200, ta ¼ 80, V ¼ 264, and e ¼ 0.15 into Eq. (110), we have
q ¼ 0:173 0:15 ð6:64 5:44Þ þ 0:296
ð660 540Þ1:25 264 þ 69 0:5 69
¼ 285 Btu=ft2 h
From Eq. (111),
Le ¼ 0:35 800 200 ¼ 0:74 in:
285
We can solve for L given Le and d by using Eq. (112) and trial and error, or we can use Table 8.39. It can be shown that L ¼ 0.75 in. The next standard thickness available will be chosen. A trial-and-error method as discussed next will be needed to solve for the surface temperature ts. (Note that L is the actual thickness of insulation.)
8.52
Q:
Determine the surface temperature of insulation in Q8.51 when 1.0 in. thick insulation is used on the pipe. Other data are as given earlier.
Copyright © 2003 Marcel Dekker, Inc.
TABLE 8.39 Equivalent Thickness of Insulation,a Le
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Thickness of insulation L (in.) |
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Tube diam. d (in.) |
0.5 |
1 |
1.5 |
2.0 |
3.0 |
4.0 |
5.0 |
6.0 |
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1 |
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0.69 |
1.65 |
2.77 |
4.0 |
6.80 |
9.90 |
13.2 |
16.7 |
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2 |
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0.61 |
1.39 |
2.29 |
3.30 |
5.50 |
8.05 |
10.75 |
13.62 |
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3 |
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0.57 |
1.28 |
2.08 |
2.97 |
4.94 |
7.15 |
9.53 |
12.07 |
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4 |
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0.56 |
1.22 |
1.96 |
2.77 |
4.55 |
6.60 |
8.76 |
11.10 |
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5 |
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0.55 |
1.18 |
1.88 |
2.65 |
4.34 |
6.21 |
8.24 |
10.40 |
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6 |
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0.54 |
1.15 |
1.82 |
2.55 |
4.16 |
5.93 |
7.85 |
9.80 |
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8 |
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0.53 |
1.12 |
1.75 |
2.43 |
3.92 |
5.55 |
7.50 |
9.15 |
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10 |
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0.52 |
1.09 |
1.70 |
2.35 |
3.76 |
5.29 |
6.93 |
8.57 |
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12 |
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0.52 |
1.08 |
1.67 |
2.30 |
3.65 |
5.11 |
6.65 |
8.31 |
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16 |
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0.52 |
1.06 |
1.63 |
2.23 |
3.50 |
4.86 |
6.31 |
7.83 |
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20 |
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0.51 |
1.05 |
1.61 |
2.19 |
3.41 |
4.70 |
6.10 |
7.52 |
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e ¼ |
2 |
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d |
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¼ |
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¼ |
e ¼ |
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aL |
d þ |
2L |
ln |
d þ 2L |
. For example, for d |
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3 and L |
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1.5, L |
2.08. |
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A:
Calculate the equivalent thickness Le. From Eq. (112),
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12 þ 2 |
ln |
14 |
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1:08 in: |
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e ¼ |
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12 ¼ |
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2 |
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Assume that |
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the |
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trial t |
150 F. Let K |
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at a mean temperature of |
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¼ |
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s ¼ |
2 |
m |
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(800 |
150)=2 |
475 F be |
0.34 Btu in.=ft h F. From Eq. (110), |
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q ¼ 0:173 0:15 ð6:14 5:44Þ þ 0:296
ð610 540Þ1:25 264 þ 69 0:5 69
¼ 145 Btu=ft2 h
From Eq. (111),
q ¼ 0:34 800 150 ¼ 205 Btu=ft2 h 1:08
Because these two values of q do not agree, we must go for another trial. Try ts ¼ 170 F. Then, from Eq. (110),
q ¼ 200 Btu=ft2 h
Copyright © 2003 Marcel Dekker, Inc.
and from Eq. (111),
q ¼ 198 Btu=ft2 h
These two are quite close. Hence the final surface temperature is 170 F, and the heat loss is about 200 Btu=ft2 h.
8.53
Q:
A horizontal flat surface is at 10 F. The ambient dry bulb temperature is 80 F, and the relative humidity is 80%. Determine the thickness of fibrous insulation that will prevent condensation of water vapor on the surface. Use Km ¼ 0.28 Btu=ft h F. The wind velocity is zero. Use a surface emissivity of 0.9 for the casing.
A:
The surface temperature must be above the dew point of water to prevent condensation of water vapor. Q5.10 shows how the dew point can be calculated. The saturated vapor pressure at 80 F, from the steam tables in the Appendix, is 0.51 psia. At 80% relative humidity, the vapor pressure will be 0.8 0.51 ¼ 0.408 psia. From the steam tables, this corresponds to a saturation temperature of 73 F, which is also the dew point. Hence we must design the insulation so the casing temperature is above 73 F.
From Eq. (110),
q¼ 0:173 0:9 ð5:44 5:334Þ
þ0:296 ð80 73Þ1:25 ¼ 10:1 Btu=ft2 h
Also, from Eq. (111),
q ¼ ðtd tsÞ KLm ¼ ð73 10Þ 0:L28
(In this case of a flat surface, Le ¼ L.)
Note that the heat flow is from the atmosphere to the surface. td and ts are the dew point and surface temperature, F. Solving for L, we get L ¼ 1.75 in.
Hence, by using the next standard insulation thickness available, we can ensure that the casing is above the dew point. To obtain the exact casing temperature with the standard thickness of insulation, a trial-and-error procedure as discussed in Q8.52 may be used. But this is not really necessary, because we have provided a safe design thickness.
Copyright © 2003 Marcel Dekker, Inc.
8.54a
Q:
A 112 in. schedule 40 pipe 1000 ft long carries hot water at 300 F. What is the heat loss from its surface if it is not insulated (case 1) or if it has 1 in., 2 in., and 3 in. thick insulation (case 2)?
The thermal conductivity of insulation may be assumed to be 0.25 Btu in.=ft2 h F. The ambient temperature is 80 F, and the wind velocity is zero.
A:
Case 1. Equation (110) can be used to determine the heat loss. For the bare pipe surface, assume that e is 0.90. Then
q¼ 0:173 0:9 ð7:64 5:44Þ
þ0:296 ð300 80Þ1:25 ¼ 638 Btu=ft2 h
Case 2. Determination of the surface temperature given the insulation thickness involves a trial-and-error procedure as discussed in Q8.52 and will be done in detail for the 1 in. case.
Various surface temperatures are assumed, and q is computed from Eqs. (110) and (111). Let us use a e value of 0.15. The following table gives the results of the calculations.
ts |
q from Eq. (110) |
q from Eq. (111) |
110 |
26 |
34 |
120 |
37 |
32 |
140 |
61 |
28 |
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We can draw a graph of ts versus q with these values and obtain the correct ts. However, we see from the table, by interpolation, that at ts ¼ 115 F, q, from both equations, is about 33 Btu=ft2 h.
Total heat loss ¼ 3:14 312:9 1000 33
¼ 33;675 Btu=h
Similarly, we may solve for q when the thicknesses are 2 and 3 in. It can be shown that at L ¼ 2 in., q ¼ 15 Btu=ft2 h, and at L ¼ 3 in., q ¼ 9 Btu=ft2 h. Also, when L ¼ 2 in., ts ¼ 98 F and total heat loss ¼ 23,157 Btu=h. When L ¼ 3 in., ts ¼ 92 F and total loss ¼ 18,604 Btu=h.
Copyright © 2003 Marcel Dekker, Inc.