35-cm-diameter cylindrical shaft made of stainless steel (k 14.9 W/m . C, p=7900 kg/m, Cp=477 J/kg C, and a= 3.95x 106 m/s) comes out of an oven at a uniform temperature of 400C. The shaft is then allowed to cool slowly in a chamber at 160C with an average convection heat transfer coefficient of h 60 W/m C. Drive the non- dimensional temperature equation and determine the temperature at the center of the shaft 20 min after the start of the cooling process. 20 M TABLE 4-1 Coefficients used in the one-term approximate solution of transient one- dimensional heat conduction in plane walls, cylinders, and spheres (Bi-hl/k for a plane wall of thickness 2L, and Bi-hr/k for a cylinder or sphere of radius r.) TABLE 4-2 The zeroth- and first-order Bessel functions of the first kind JE ( 0.0 1.0000 0.0000 Plane Wall Cylinder Sphere 0.1 0.9975 0.0499 Bi A A 0.01 0.0998 1.0017 A 0.1412 A 0.02 0.1410 1.0033 0.1995 0.04 0.1987 1.0066 0.06 0.2425 1.0098 0.2814 0.3438 A 1.0025 0.1730 1.0050 0.2445 1.0060 1.0099 0.3450 1.0120 1.0148 0.4217 1.0179 A 0.2 0.9900 0.0995 0.3 0.9776 1.0030 0.1483 0.4 0.9604 0.1960 0.5 0.08 0.6 0.2791 1.0130 0.3960 1.0197 0.4860 1.0239 0.7 0.1 0.3111 1.0161 0.4417 1.0246 0.5423 1.0298 0.8 0.2 0.4328 1.0311 0.6170 0.3 0.5218 1.0450 0.7465 0.4 0.5932 1.0580 0.8516 0.5 0.6533 1.0701 0.9408 1.1143 0.6 0.7 0.8 0.9 1.0 2.0 1.0769 1.1785 1.5995 1.3384 0.7593 1.0592 0.9208 1.0880 1.0528 1.1164 1.1656 1.1441 0.7051 1.0814 1.2644 1.1713 0.7506 1.0918 1.0873 1.1539 1.3525 1.1978 0.7910 1.1016 1.1490 1.1724 1.4320 1.2236 0.8274 1.1107 1.2048 1.1902 1.5044 1.2488 0.8603 1.1191 1.2558 1.2071 1.5708 1.2732 2.0288 1.4793 1.0483 0.9 56989 0.9385 0.2423 0.9120 0.2867 0.8812 0.3290 0.8463 0.3688 0.8075 0.4059 1.0712 1.0931 1.0 1.1 1.0184 1.1345 1.2 1.3 1.4 11234 0.7652 0.4400 0.7196 0.4709 0.6711 0.4983 0.6201 0.5220 0.5669 0.5419 1.5 1.6 3.0 1.1925 1.2102 1.7887 1.4191 2.2889 1.6227 1.7 4.0 5.0 6.0 7.0 8.0 9.0 10.0 20.0 30.0 40.0 50.0 100.0 1.2646 1.2287 1.9081 1.4698 2.4556 1.7202 1.3138 1.2403 1.9898 1.5029 2.5704 1.7870 1.3496 1.2479 2.0490 1.5253 2.6537 1.83381 1.3766 1.2532 2.0937 1.5411 2.7165 1.8673 1.3978 1.2570 2.1286 1.5526 2.7654 1.8920 1.4149 1.2598 2.1566 1.5611 2.8044 1.9106 1.4289 1.2620 2.1795 1.5677 2.8363 1.9249 1.4961 1.2699 2.2880 1.5919 2.9857 1.9781 1.5202 1.2717 2.3261 1.5973 3.0372 1.9898 1.5325 1.2723 2.3455 1.5993. 3.0632 1.9942 1.5400 1.2727 2.3572 1.6002 3.0788 1.9962 1.5552 1.2731 2.3809 1.6015 3.1102 1.5708 1.2732 2.4048 1.6021 3.1416 1.8 1.9 56989 0.5118 0.5579 0.4554 0.5699 0.3980 0.5778 0.3400 0.5815 0.2818 0.5812 ~NN 01234 22 2.0 0.2239 0.5767 2.1 0.1666 0.5683 2.2 0.1104 0.5560 2.3 0.0555 0.5399 2.4 0.0025 0.5202 1.9990 2.0000 2233 2.6 2.8 3.0 3.2 6882 -0.0968 -0.4708 -0.1850 -0.4097 -0.2601 -0.3391 -0.3202 -0.2613