A high temperature, gas cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (Ka=57 W/m*K) is encased in graphite (Kb= 3 W/m*K) and gaseous helium flows through an annular coolant channel. Consider conditions for which the helium temperature is T=600k and the convection coefficient at the outer surface of the graphite is h= 2000 W/m^2*K. If thermal energy is uniformly generated in the fuel elemnt at a rate of q=10^8 W/m^3 what are the temperaturesT1 and T2 at the inner and outer surfaces, respectively, of the fuel element?
1/r d/dr (r dT/dr)+q/k=0
The Attempt at a Solution
Not really sure how to derive this formula. The boundary conditions I have chosen was
at r=0 dT/dr=0 because the max temperature should be in the center. My second boundary condition is the T(r0)= Ts. If someone could help derive this formula that would be great been trying to derive the temperature profile for sometime now.
If someone could so me a crude derivation of the temperature profile that would be great.