From solutions: T1 =932 K and T2 = 956 K

A high-temperature, gas-cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (k=57W/m.K) is encased in graphite (k=3W/m.K) and gaseous helium flows through an annular coolant channel as shown in figure below. Consider conditions for which the helium temperature is T=600K and the convection coefficient at the outer surface of the graphite is h=2000W/m2K. If thermal energy is uniformly generated in the fuel element at a rate of 108W/m3, what are the temperatures T1 and T2 at the inner and outer surfaces, respectively, of the fuel element, assuming adiabatic surface at r/. If the melting points of thorium and graphite are 2000K and 2300K respectively, do you think the prescribed operating condition will be acceptable