A heated 6-mm-thick Pyroceram plate ( = 2600 kg/m 3 , c p = 808 J/kg

A heated 6-mm-thick Pyroceram plate (ρ = 2600 kg/m³, c_p = 808 J/kg · K, k = 3.98 W/m · K, and a = 1.89 × 10^–6 m²/s) is being cooled in a room with air temperature of 25°C and convection heat transfer coefficient of 13.3 W/m² · K. The heated Pyroceram plate had an initial temperature of 500°C, and is allowed to cool for 286 seconds. If the mass of the Pyroceram plate is 10 kg, determine the heat transfer from the Pyroceram plate during the cooling process using

(a) Table 4–2

(b) Figure 4–17.

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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) Bi λ₁ A₁ 0.01 0.0998 1.0017 0.02 0.1410 1.0033 0.04 0.1987 0.06 0.2425 0.08 0.2791 1.0130 0.1 0.3111 1.0161 0.2 0.4328 1.0311 0.3 0.5218 1.0450 0.4 0.5932 1.0580 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 Plane Wall 6.0 7.0 8.0 9.0 10.0 20.0 30.0 40.0 50.0 100.0 00 1.0066 1.0098 Cylinder A₁ A₁ 0.1412 1.0025 0.1995 0.2814 1.0099 0.3438 0.3960 0.4417 0.6533 1.0701 0.9408 0.7051 1.0814 1.0184 0.7506 1.0918 0.7910 1.1016 0.8274 1.1107 1.0873 1.1490 1.2048 0.8603 1.1191 1.2558 1.0769 1.1785 1.5995 1.1925 1.2102 1.7887 1.2646 1.2287 1.9081 1.3138 1.2403 1.9898 1.3496 1.2479 2.0490 1.3766 1.2532 2.0937 0.6170 0.7465 0.8516 1.0931 1.1143 1.0592 1.0880 1.1164 1.1441 1.1713 1.1978 1.2236 1.2488 1.2071 1.5708 1.2732 1.3384 2.0288 1.4793 1.4191 2.2889 1.6227 1.4698 2.4556 1.7202 1.5029 2.5704 1.7870 1.5253 2.6537 1.8338 1.5411 2.7165 1.8673 1.3978 1.2570 2.1286 1.5526 2.7654 1.4149 1.2598 1.5611 2.8044 1.4289 1.2620 1.5677 2.8363 1.4961 1.2699 2.2880 1.5919 2.9857 1.5202 1.2717 2.3261 1.5973 1.2723 2.3455 1.5993 1.6002 3.0788 1.6015 3.1102 1.6021 3.1416 2.1566 2.1795 Sphere A₁ 0.1730 1.0050 0.2445 0.3450 1.0148 0.4217 1.5325 1.5400 1.2727 2.3572 1.5552 1.2731 2.3809 1.5708 1.2732 2.4048 1.0197 0.4860 1.0246 0.5423 1.0483 0.7593 1.0712 0.9208 1.0528 1.1656 1.1345 1.2644 1.1539 1.3525 1.1724 1.4320 1.1902 1.5044 A₁ 1.0030 1.0060 1.0120 1.0179 1.0239 1.0298 3.0372 3.0632 1.8920 1.9106 1.9249 1.9781 1.9898 1.9942 1.9962 1.9990 2.0000