Heat conduction in a nuclear fuel rod assembly (Fig. 10B.3) considers a long cylindrical nuclear fuel rod,

Question:

Heat conduction in a nuclear fuel rod assembly (Fig. 10B.3) considers a long cylindrical nuclear fuel rod, surrounded by an annular layer of aluminum cladding. Within the fuel rod heat is produced by fission; this heat source depends on position approximately as

Here S_n0 and b are known constants, and r is the radial coordinate measured from the axis of the cylindrical fuel rod. Calculate the maximum temperature in the fuel rod if the outer surface of the cladding is in contact with a liquid coolant at temperature T_L. The heat transfer coefficient at the cladding-coolant interface is h_L, and the thermal conductivities of the fuel rod and cladding are k_s and k_C.