Nuclear Reactor Analysis Problem 5.34

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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?
 
Attachments
  • Handwritten derivation on lined paper of one-group neutron diffusion for a bare reactor: diffusion equation, extrapolated boundary condition, k-infinity relation, material buckling equations, and the extrapolated radius a expressed with arctangent and square root terms.
    20200228_191742.jpg
    41.4 KB · Views: 306

Discussion

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:
 
Attachments
  • Handwritten notes on lined paper deriving a formula for a with a-hat = pi times the square root of L squared over (k-infinity minus 1), minus the square root of 4/3 L squared, followed by a substituted value of a = 293.81 cm for k-infinity = 1.2 and L = 50 cm, and questions about k-infinity of vacuum.
    20200302_110527.jpg
    52 KB · Views: 270
  • Handwritten notes on lined paper: extrapolation distance d = 57.7 cm, a = 293.51 cm, with â = 351.24 cm; a sketch of four flux humps in a row labelled a; text on slab thickness and criticality in a vacuum; part b starts with k_eff = 1.
    20200302_110534.jpg
    44.9 KB · Views: 321

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