Two core regions with reflector

[EricaS]

Hello there

I'm working on this problem:
Solve numerically for the eigenvalue and neutron flux distribution in a slab reactor consisting of two adjacent core regions each of thickness 50 cm, with a 25-cm-thick reflector on each side. The nuclear parameters of the two core regions are (D = 0.65 cm,∑a = 0.12 cm−1, and ν∑f = 0.125 cm−1) and (D = 0.75 cm, ∑a = 0.10 cm−1, and ν∑f = 0.12 cm−1), and the parameters of the reflector are (D = 1.15 cm, ∑a = 0.01 cm−1, and ν∑f = 0.0 cm−1).
Solve this problem analytically and compare the answers.

Am I correct in saying that the boundary conditions are:
1. Flux at the center of the core region (between the two cores) is equal.
2. Flux at the core-reflector interface is equal.
3. Gradient of the flux at the core-reflector interface is equal.
4. Flux at the extrapolated boundary of the reflector is zero.

Have I correctly specified all the boundary conditions?
Or am I missing some?

Any help would be appreciated.

Thanks!

 

[Astronuc]

3. Gradient of the flux at the core-reflector interface is equal.

The current at the interface is equal, i.e., what leaves one volume must be entering the other volume across the common interface.

In a slab reactor, there is some plane between the surfaces where the current (or gradient in the flux) is zero, and the flux must be finite.

Fluxes in adjacent volumes to not have to be equal at the interface, but the currents must be equal.

 

[rpp]

If I understand the problem description, you have 4 regions.
Since this is a 2nd order differential equation, you need 2 boundary conditions (BC) per region, for a total of 8 BC.

You pointed out flux continuity between the regions. This gives you three BC.
You also pointed out the flux at the extrapolated distances. This give you two more BC.

What you are missing is the continuity of current between the regions. This will give you the final three BC.
You said "gradient", but it is actually the continuity of neutron current.
You have to include the different diffusion coefficients in each region.