1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Heat Transfer Boundary Conditions

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations
    1/r d/dr (r dT/dr)+q/k=0

    3. 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.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted