Nuclear Reactor Analysis Problem 5.34

[Tanman77]

Homework Statement:

Here is problem 5.34 from Nuclear Reactor Analysis: Two infinite slabs, each of thickness a in the x direction, are separated by an inner region of thickness 2a and are bounded by vacuum on their outer surfaces. The slab material is of composition to give k∞=1.2 and thermal diffusion length of 50cm. Determine the thickness a for criticality when: (a) inner region is vacuum and (b) inner region is a medium with k∞=1 and same D and L as the outer slabs.

Relevant Equations:

See attached photo.

I'm aware that geometric buckling is equal to material buckling when k =1, any pointers on how to set up the boundary conditions for this problem?

 

[Abhishek11235]

Show your work otherwise no one will help you!

 

[Tanman77]

Show your work otherwise no one will help you!

I gave some relevant equations in the attached picture, I am merely asking how i should set up boundary conditions for this problem.

 

[Tanman77]

Here is further progress: