Nuclear Reactor Analysis Problem 5.34

Tanman77
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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?
 

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Show your work otherwise no one will help you!
 
Abhishek11235 said:
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.
 
Here is further progress:
 

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