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

 

[raining Pete]

Hi there,

I completely understand your frustration with not receiving timely responses from your teaching assistant. It can be incredibly frustrating when you have a deadline looming and you need help understanding a concept.

As for your assignment, I am not an expert in multiple-group diffusion theory, but I did some research and found a few resources that may be helpful to you. I found a lecture from MIT on two-group diffusion theory that breaks down the equations and how to solve for thermal flux in different scenarios, including when L1 > L2 and L2 > L1. I also found a helpful article from the University of Wisconsin that goes through a step-by-step solution for a similar problem using two-group diffusion theory.

I hope these resources will be helpful to you in solving your assignment. I also suggest reaching out to your classmates or professor for help, as they may have a better understanding of the material and can offer additional guidance.

Don't worry about overstepping by posting on this website for help. That's what this forum is for – to connect with others and learn from each other. I'm sure there are many others on here who have experience with multiple-group diffusion theory and can offer some insight.

Best of luck with your assignment and don't hesitate to come back if you have any other questions or need further help. We are all here to support each other and learn together. And I agree, the physics of smell is definitely an interesting topic! Maybe you can incorporate it into a future assignment or research project.

Take care,