Calculate the diffusion coefficient d of light water at

Question

1. Calculate the diffusion coefficient (D) of (light) water at thermal neutron energy (i.e., 0.025eV). Present your answer in cm.

2. Consider a bare slab reactor with a source located at x=0, such that S(x)=Sδ(x). It has a graphite medium and has a boundary at x=± a, after which is a vacuum. Assume steady state and no leakage along y and z directions.

(a) Write the neutron diffusion equation applicable to the given reactor condition. List assumptions/conditions necessary to reduce the equation.

(b) Specify both the boundary condition(s) and the source condition(s) to solve the equation.

(c) The differential equation in the form of,

d²Ψ/dx² - λ² Ψ = 0

has a general solution given by

Ψ = C1e^-λx + C2e^λx .

Solve the diffusion  equation and show that the solution is given by (show all the detailed steps):

Φ = (SL/2D)[sinh (a + d - |x|/L)/cosh (a + d)/L] where d=extrapolated distance

Hint: Use the identities given by: sinhx = (e^x - e^-x )/2 and cosh x = (e^x + e^-x )/2