In an annealing process, a 50-mm-thick stainless steel plate (ρ = 8238 kg/m³, c_p= 468 J/kg·K, k = 13.4 W/m·K, and α = 3.48 × 10^€“6m²/s) was reheated in a furnace from an initial uniform temperature of 230°C. The ambient temperature inside the furnace is at a uniform temperature of 1000°C and has a convection heat transfer coefficient of 215 W/m²·K. If the entire stainless steel plate is to be heated to at least 600°C, determine the time that the plate should be heated in the furnace using

(a) Table 18€“2

(b) the Heisler chart (Figure 18€“14).

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 Sphere A1 Bi A1 λι λι 1.0017 1.0030 0.01 0.0998 0.1412 1.0025 0.1730 0.02 0.1410 1.0033 0.2445 0.1995 1.0050 1.0060 1.0066 1.0099 0.04 0.1987 0.2814 0.3450 1.0120 0.4217 0.06 0.2425 1.0098 0.3438 1.0148 1.0179 0.08 0.2791 1.0130 0.3960 1.0197 0.4860 1.0239 0.5423 0.1 0.3111 1.0161 0.4417 1.0246 1.0298 0.4328 0.5218 0.2 1.0311 0.6170 1.0483 0.7593 1.0592 0.3 1.0450 1.0580 0.7465 1.0712 0.9208 1.0880 0.8516 0.4 0.5932 1.0931 1.0528 1.1164 1.1656 0.5 0.6533 1.0701 0.9408 1.1143 1.1441 0.6 0.7051 1.0814 1.0184 1.1345 1.2644 1.1713 0.7 0.7506 1.0918 1.0873 1.1539 1.3525 1.1978 0.8 0.7910 1.1016 1.1490 1.1724 1.4320 1.2236 0.9 1.1902 0.8274 1.1107 1.2048 1.5044 1.2488 1.0 0.8603 1.1191 1.2558 1.2071 1.5708 1.2732 2.0288 2.0 1.0769 1.1785 1.5995 1.3384 1.4793 1.2102 3.0 1.1925 1.7887 1.4191 2.2889 1.6227 4.0 1.2646 1.2287 1.9081 1.4698 2.4556 1.7202 5.0 1.3138 1.2403 1.9898 1.5029 2.5704 1.7870 6.0 1.3496 1.2479 2.0490 1.5253 2.6537 1.8338 7.0 1.3766 1.2532 2.0937 1.5411 2.7165 1.8673 8.0 1.3978 1.2570 2.1286 1.5526 2.7654 1.8920 1.2598 9.0 1.4149 2.1566 1.5611 2.8044 1.9106 1.9249 10.0 1.4289 1.2620 2.1795 1.5677 2.8363 20.0 1.4961 1.2699 2.2880 1.5919 2.9857 1.9781 1.9898 30.0 1.5202 1.2717 2.3261 1.5973 3.0372 40.0 1.5325 1.2723 2.3455 1.5993 3.0632 1.9942 2.3572 50.0 1.5400 1.2727 1.6002 3.0788 1.9962 100.0 1.5552 1.2731 2.3809 1.6015 3.1102 1.9990 1.6021 1.5708 1.2732 2.4048 3.1416 2.0000 Cylinder 1.0 0.7 0.5 0.4 hro 0.3 0.2 16 80 70 0.1 0.07 0.05 0.04 0.03 0.02 0.01 0.007 0.005 0.004 0.003 0.002 250 350 100 120 140 150 26 30 50 70 14 18 22 0.001 2 3 4 6 8 10 T= at/r? e60 50 40