Question:
Steel rods, 2 m in length and 60 mm in diameter, are being drawn through an oven that maintains a temperature of 800°C and convection heat transfer coefficient of 128 W/m
2·K. The steel rods (Ï = 7832 kg/m
3, c
p= 434 J/kg·K, k = 63.9 W/m·K, and α = 18.8 × 10
€“6m
2/s) were initially in uniform temperature of 30°C. Using
(a) Table 18€“2
(b) Fig. 18€“15, determine the amount of heat transferred to the steel rod after 133 s of heating.
Transcribed Image Text:
TABLE 18-2 Coefficients used in the one-term approximate solution of transient one- dimensional heat conduction in plane walls, cylinders, and spheres (Bi = hLIk for a plane wall of thickness 2L, and Bi = radius r) hrjk for a cylinder or sphere of Plane Wall Cylinder A1 Sphere A1 Bi A1 λι λι 0.01 0.0998 1.0017 0.1412 1.0025 0.1730 1.0030 0.1995 0.2814 1.0033 1.0050 1.0099 0.02 0.1410 0.1987 0.2445 1.0060 0.04 1.0066 0.3450 1.0120 0.06 0.2425 1.0098 0.3438 1.0148 0.4217 1.0179 0.08 1.0130 1.0197 0.4860 0.2791 0.3960 1.0239 0.1 0.3111 1.0161 0.4417 1.0246 0.5423 1.0298 0.2 0.4328 1.0311 0.6170 1.0483 0.7593 1.0592 0.9208 0.3 0.5218 1.0450 0.7465 1.0712 1.0880 1.0931 0.4 0.5932 1.0580 0.8516 1.0528 1.1164 0.5 0.6533 1.0701 0.9408 1.1143 1.1656 1.1441 0.6 0.7051 1.0814 1.0184 1.1345 1.2644 1.1713 1.3525 1.4320 0.7 0.7506 1.0918 1.0873 1.1539 1.1978 1.1016 1.1107 1.2236 0.8 0.7910 1.1490 1.1724 1.5044 0.9 0.8274 1.2048 1.1902 1.2071 1.2488 1.0 0.8603 1.1191 1.2558 1.5708 1.2732 2.0 1.0769 1.1785 1.5995 1.3384 2.0288 1.4793 3.0 1.1925 1.2102 1.7887 1.4191 2.2889 1.6227 1.7202 4.0 1.2646 1.2287 1.9081 1.4698 2.4556 5.0 1.3138 1.2403 1.9898 1.5029 2.5704 1.7870 1.8338 6.0 1.3496 1.2479 2.0490 1.5253 2.6537 1.2532 7.0 1.3766 2.0937 1.5411 2.7165 1.8673 8.0 1.3978 1.2570 2.1286 1.5526 2.7654 1.8920 9.0 1.4149 1.2598 2.1566 1.5611 2.8044 1.9106 2.8363 10.0 1.4289 1.2620 2.1795 1.5677 1.9249 1.2699 20.0 1.4961 2.2880 1.5919 2.9857 1.9781 30.0 1.5202 1.2717 2.3261 1.5973 3.0372 1.9898 40.0 1.5325 1.2723 2.3455 1.5993 3.0632 1.9942 50.0 1.5400 1.5552 1.2727 2.3572 1.6002 1.6015 3.0788 1.9962 2.3809 3.1102 100.0 1.2731 1.9990 1.2732 1.5708 2.4048 1.6021 3.1416 2.0000 To - To Oo = 1.0 0.7 Sphere 0.5 0.4 0.3 hro Bị 100 0.2 0.1 0.07 0.05 0.04 0.03 0.02 0.01 0.007 0.005 0.004 0.003 0.002 0.001 3 4 5 6 7 8 9 10 T= atlr? 0.5 1.0 1.5 2 2.5 20 30 40 50 100 150 200 250 Too Initially T= T, (a) Midpoint temperature. From M. P. Helsler, "Temperature Charts for Induction and Constant Temperature Heating," Trans. ASME 69, 1947, Fig. 9, p. 231. Reprinted by permission of ASME International. Го T-T Ho To- Omax 1.0 rir, = 0.2. 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.6 0.5 0.5 0.4 0.4 0.3H'ö 0.2 H0.g 0.3 0.2 0.1 0.1 1.0LHI Sphere Sphere 0. 10 5 10-4 10-3 10-2 10 102 103 104 0.01 0.1 1.0 10 100 10 Bi?t = h?at/k? Bi hr. (b) Temperature distribution. (c) Heat transfer. From M. P. Helsler, "Temperature Charts for Induction and Constant Temperature Heating," Trans. ASME 69, 1947, Fig. 12, p. 232. Reprinted by permission of ASME International. From H. Gröber et al.
