Heat Transfer Boundary Conditions

  • Thread starter luca131
  • Start date
  • #1
7
0

Homework Statement


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?


Homework Equations


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.
 

Answers and Replies

Related Threads on Heat Transfer Boundary Conditions

  • Last Post
Replies
0
Views
3K
  • Last Post
Replies
3
Views
2K
Replies
4
Views
4K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
852
Top