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only answer 4,5!

PROBLEM 2 Heat Conduction In nuclear power plants, heat transfer is a key factor for nuclear reactors design. The schematic of a nuclear reactor is shown below. The tubular thorium rod is working as the fuel with a uniform heat generation rate of 108 W/m3. The fuel rod is surrounded by a graphite shell which is cooled by water Assume the inside surface of the thorium rod is well insulated. Thermal conductivities are invariant with temperature for all materials. (30 pts) Coolant 1-8mm 600 K Graphite 3-14 mm T1 Thorium (d) kt-57 Wm K T2 1. 2. 3. 4. Determine the temperature T2 at the outer surface of the thorium rod. (6 pts) Derive a general solution for the temperature distribution in the tubular thorium rod. (6 pts) Using the boundary conditions provided, solve the temperature distribution in part 2. (6 pts) To prevent melting of the fuel rod and the graphite layer, T1 and T2 must be kept below 1000 K Discuss whether these conditions are achieved. (6 pts) 5. For the conditions specified in this problem, discuss whether there exists a graphite layer thickness that maximizes the heat transfer for the fuel rod to the cooling water. (6 pts)

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