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Homework 3 solutions

# Homework 3 solutions - Homework 3 due Wednesday September...

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Homework 3 – due Wednesday, September 8 th 1. Thermal conditions in a gas-cooled nuclear reactor with a tubular thorium fuel rod and a concentric graphite sheath constitute a composite cylindrical wall. A thorium fuel element ( k = 57 W/m-K) is encased in graphite ( k = 3 W/m-K) and helium flows through an annular coolant channel around the system. If the helium temperature T = 600 K with an h = 2000 W/m 2 -K: (20 pts) (a) Draw the thermal circuit. (b) Calculate the temperature at the inner and outer surfaces of the fuel element for a generation rate of q(dot) = 10 8 W/m 3 (c) Compute and plot the temperature distributions in the thorium and graphite for three different generation rates in the range 10 8 q(dot) ≤ 5 X 10 8 . (Use separate plots for the different materials). What is the maximum allowable value for q(dot)? (d) Discuss anything unusual in this problem because of the situation involved. r 1 (from the center to the inner surface of the fuel element): 8 mm r 2 (from the center to the outer surface of the fuel element): 11 mm r 3 (from the center to the outer surface of the graphite): 14 mm

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