Mastering Two Group Diffusion Theory: Solving Thermal Flux Problems with Ease

[Raccoonn]

Hello,

Frustration in receiving timely responses from my teaching assistant has lead me to this website. Currently have a homework assignment on multiple group diffusion theory and one of the assigned questions is,

Determine the thermal flux due to an isotropic point source, So fast neutrons/second, in an infinite moderating medium. Use two-group diffusion theory. In particular discuss the solution to this problem from the case in which L1 > L2 and L2 > L1. (Deuderstadt and Hamilton Chapter 7, Problem 8)

I understand the last part qualitatively and that's where my problem starts. Most of this assignment is understanding the idea of multiple-group theory and dealing with group constants in terms of multiplication factors and collapsing, which is covered clearly in our notes and the text. But, solving for thermal flux from two-group diffusion equations, I am at a loss. I can setup the equations but I do not know where to begin, If anyone can help as I said this is my first time even visiting this website and I am not sure if this is out of line. I am just running low on time before work and understand grad students are busy people and emails may take time. In this class up until now we have been working with mostly numerical solutions in homework dealing with point reactor kinetics, step by step processes I can follow and explain quantitatively using results to back qualitative analysis. If anyone has any tips or possible literature they can point me to I would be much appreciative. Once again first time here, came here cause I am a desperate busy student just looking for some timely help, if I am overstepping or if there is a better place for such a post please let me know. Although it's my first time I'll be coming back and would like to make some friends, learning new things is always fun and I have always been interested in the idea of the physics of smell.

 

[hmeier]

Try this,

D₁∇²ø(r)₁-∑_rem1θ(r)₁=δS
D₂∇²ø(r)₂-∑_rem2θ(r)₂=∑_1→2θ(r)₁

where ∑_remi=∑_ai+∑_i→j

Calculate θ(r)₁ that will be something like S/4∏r², and then put it in the second ecuation as the thermal source coming from the fast scattering and clear ø(r)₂, and then see what happens with the different L_i
1: fast
2: thermal

Hernán