The initial rod temperature is T₁ = 17 °C and the centre of the rod needs to be heated to T₁ = 438 °C from the surroundi

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The Initial Rod Temperature Is T 17 C And The Centre Of The Rod Needs To Be Heated To T 438 C From The Surroundi 1 (1.04 MiB) Viewed 43 times

The initial rod temperature is T₁ = 17 °C and the centre of the rod needs to be heated to T₁ = 438 °C from the surrounding hot air temperature of Tair = 571 °C. If we assume the Biot number is equal to 4.0, determine the Fourier number. The table below can assist in the calculations. The zeroth- and first-order Bessel functions of the first kind 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 ro) n Jo(n) J₁(n) 0.0 1.0000 0.0000 Plane Wall Sphere 0.1 0.9975 0.0499 Cylinder A₁ Bi λ₁ A₁ A₁ A₁ A₁ 0.2 0.9900 0.0995 0.01 0.0998 0.3 0.9776 0.1483 1.0017 0.1410 1.0033 0.1412 1.0025 0.1995 0.2814 1.0099 0.3450 0.1730 1.0030 1.0050 0.2445 1.0060 0.02 0.4 0.9604 0.1960 0.04 0.1987 1.0066 1.0120 0.2425 0.3438 1.0148 0.9385 0.5 0.4217 0.2423 1.0179 0.06 1.0098 0.08 0.2791 1.0130 0.6 0.9120 0.2867 1.0239 0.4860 1.0197 1.0246 0.5423 1.0298 0.1 0.3111 0.3960 0.4417 0.6170 1.0483 1.0161 0.7 0.8812 0.3290 0.2 0.4328 1.0311 0.8 0.8463 0.3688 0.3 1.0880 0.9 0.8075 0.4059 0.4 1.1164 1.0 0.7652 0.4400 0.5 1.1 0.7196 0.4709 0.6 1.2 0.6711 0.4983 0.7 1.3 0.6201 0.5220 0.8 1.4 0.5669 0.5419 0.9 1.0 1.5 0.5118 0.5579 2.0 1.6 0.4554 0.5699 3.0 1.7 0.3980 0.5778 4.0 0.7593 1.0592 0.5218 0.7465 1.0712 1.0450 0.9208 0.5932 1.0580 0.8516 1.0931 1.0528 0.6533 1.0701 0.9408 1.1143 1.1656 1.1441 0.7051 1.0814 1.0184 1.1345 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 1.0769 1.1785 1.5995 1.3384 2.0288 1.4793 1.1925 1.2102 1.7887 1.4191 2.2889 1.6227 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 1.8338 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 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 1.9990 1.5708 1.2732 2.4048 2.0000 1.8 0.3400 0.5815 5.0 1.9 0.2818 0.5812 6.0 7.0 2.0 0.2239 0.5767 8.0 2.1 0.1666 0.5683 9.0 2.2 0.1104 0.5560 10.0 1.4289 1.2620 2.3 0.0555 0.5399 20.0 2.4 0.0025 0.5202 -0.0968 0.4708 30.0 40.0 50.0 100.0 0.4097 2.6 2.8 -0.1850 3.0 3.2 -0.2601 0.3391 1.6021 3.1416 -0.3202 0.2613