Gas at a temperature of 250°C with a convective coefficient 75 W/m2·K flows through a packed bed of aluminum (2024) spheres that is used as a thermal energy storage system. If the initial temperature of the spheres is 25°C and the diameter of each sphere is 75-mm, find the time, in seconds, required to for a sphere to reach 85% of the maximum possible thermal energy as well as the surface temperature and the centerline temperature at this time, both in °C. Evaluate the properties of the aluminum (2024) at 500 K.

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Explanation:

Airflow t

T¥, h D

Ts

w

Heater

h

(q•, k ) L

(a) Under conditions for which a uniform surface temperature Ts is maintained around the circum- ference of the heater and the temperature Too and convection coefficient h of the airflow are known, obtain an expression for the rate of heat transfer per unit length to the air. Evaluate the

heat rate for Ts = 300°C, D = 20 mm, an alu- minum sleeve (ks = 240 W/m · K), w = 40 mm, N = 16, t = 4 mm, L = 20 mm, Too = 50°C, and h = 500 W/m2 · K.

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