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Bumek [7]
3 years ago
7

4–72 A person puts a few apples into the freezer at 215°C to cool them quickly for guests who are about to arrive. Initially, th

e apples are at a uniform temperature of 20°C, and the heat transfer coefficient on the surfaces is 8 W/m2·K. Treating the apples as 9-cm-diameter spheres and taking their properties to be r 5 840 kg/m3, cp 5 3.81 kJ/kg·K, k 5 0.418 W/m·K, and a 5 1.3 3 1027 m2/s, determine the center and surface temperatures of the apples in 1 h. Also, determine the amount of heat transfer from each apple. Solve this problem using analytical one-term approximation method (not the Heisler charts).

Physics
1 answer:
KiRa [710]3 years ago
4 0

Complete and Clear Question:

A person puts a few apples into the freezer at -15°C to cool them quickly for guests who are about to arrive. Initially, the apples are at a uniform temperature of 20°C, and the heat transfer coefficient on the surfaces is 8 W/m2·K. Treating the apples as 9-cm-diameter spheres and taking their properties to be \rho = 840 kg/m3,  c_{p} = 3.81 kJ/kg·K, k = 0.418 W/m·K, and \alpha = 1.3 * 10^{-7} m^{2} /s, determine the center and surface temperatures of the apples in 1 h. Also, determine the amount of heat transfer from each apple. Solve this problem using analytical one-term approximation method (not the Heisler charts).

Answer:

Temperature at the center of the apple, T(t) = 11.215°C

Temperature at the surface of the apple, T(r,t) = 2.68°C

Amount of heat transfer from each apple, Q = 21.47 kJ

Explanation:

For clarity and easiness of expression, the calculations are handwritten and attached as a file. Check the attached files for the complete calculation.

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