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28 March, 11:59

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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  1. 28 March, 12:24
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    See explanation

    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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