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MMLU-Pro / 12015 / 0.228 era thick circumferential fins with a radial depth of 2.54 cm are welded…

Problem

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question

0.228 era thick circumferential fins with a radial depth of 2.54 cm are welded to a 15.24 cm dia. steel barrel. The fins arespaced at a distance of 0.456 cm apart. The barrel wall temperatureis 393°K, and the ambient air temperature is 293°K.Determine the rate at which heat is rejected from the finnedbarrel. Also, find the rate of heat rejection, assuming thatthe barrel is not finned. The convective heat transfer coefficientis 284 W/m^2 °K, and the thermal conductivity of steelmay be taken as 48 W/m-°K. Table 1: Selected values of the modified Bessel functions of the first and secondkinds,orderszero and one. x I_o(x) I_1(x) (2/\pi)K_o(x) (2/ \pi)K_1(x) 0.0 1.000 0.0000 + \infty + \infty 02 1.0100 0.1005 1.1158 3.0405 0.4 1.0404 0.2040 0.70953 1.3906 0.6 1.0920 03137 0.49498 0.32941 0.8 1.1665 0.4329 0.35991 0.54862 1.0 1.2661 0.5652 0.26803 0.38318 1.2 1.3937 0.7147 0.20276 0.27667 1.4 1.5534 0.8861 0.15512 0.20425 1.6 1.7500 1.0848 0.11966 0.15319 1.8 1.9896 1.3172 0.92903 × 10^-1 0.11626 2.0 2.2796 1.5906 0.72507 0.89041 × 10^-1 2.2 2.6291 1.9141 0.56830 0.68689 2.4 3.0493 2.2981 0.44702 0.53301 2.6 3.5533 2.7554 0.35268 0.41561 2.8 4.1573 3.3011 0.27896 0.32539 3.0 4.8808 3.9534 0.22116 0.25564 3.2 5.7472 4.7343 0.17568 0.20144 3.4 6.7848 5.6701 0.13979 0.15915 3.6 8.0277 6.7028 0.11141 0.12602 3.8 9.5169 8.1404 0.8891 × 10^-2 0.9999 × 10^-3 4.0 11.3019 9.7595 0.7105 0.7947 4.2 13.4425 11.7056 0.5684 0.6327 4.4 16.0104 14.0462 0.4551 0.5044 4.6 19.0926 16.8626 0.3648 0.4027 4.8 22.7937 20.2528 0.2927 0.3218 5.0 27.2399 24.3356 0.2350 0.2575 5.2 32.5836 29.2543 0.1888 0.2062 5.4 39.0088 35.1821 0.1518 0.1653 5.6 46.7376 42.3283 0.1221 0.1326 5.8 56.0381 50.9462 0.9832 × 10-3 0.1064 6.0 67.2344 61.3419 0.7920 0.8556 × 10^-3 6.2 80.7179 73.8859 0.6382 0.6879 6.4 96.9616 89.0261 0.5146 0.5534 6.6 116.537 107.305 0.4151 0.4455 6.8 140.136 129.378 0.3350 0.3588 7.0 168.593 156.039 0.2704 0.2891 7.2 202.921 188.250 0.2184 0.2331 7.4 244.341 227.175 0.1764 0.1880

category

engineering

options

  1. 435 W, 90 W
  2. 450 W, 100 W
  3. 430 W, 110 W
  4. 385 W, 85 W
  5. 410 W, 105 W
  6. 414 W, 92.8 W
  7. 400 W, 80 W
  8. 420 W, 95 W
  9. 390 W, 75 W
  10. 450 W, 120 W

src

stemez-HeatTransfer

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Source and history

upstream_id / Original problem ID
12015
task_id
bd879b04-ed83-5c18-8b87-6dda0ed98fd3
task_key
default--test--12015
task_revision_id
1
config / split
default / test

Official source

initial import