Question

# In this problem, consider a homogeneous slab of length a = 25 cm with nuclear data given by: E, =strength Q = 2.0 × 10³ neutrons per cc per second

is placed in the central region of the slab extending between x = 10 cm and x = 15 cm. The boundary conditions on both sides of the slab are extrapolated endpoint:1.5 cm-1, E, = 2.2 cm-1, µo = 0. A source of \phi\left(-\frac{\tilde{a}}{2}\right)=\phi\left(\frac{\tilde{a}}{2}\right)=0 Solve this diffusion equation using the Green's function for finite slab geometries to find ø(x). [Plot the flux solution as a function of position for several choices of N, the number of terms you keep in the series expanşion: 1, 3, 5, 7) 2. Use the code you wrote in Part I to solve this problem numerically with a spatial mesh of 500 cells of length 0.05 cm. Plot the numerical solution on the same graph as the analytic solution(N = 7) and comment on the agreement between the two plots. [Compute the maximum relative error in the numerical solution compared to the analytic solution.] Run a Monte Carlo neutron transport simulation and compare the transport results with the diffusion results. Use the same spatial grid for the transport and diffusion solutions. In what regions of the slab do the diffusion results differ most from the transport results? [Make sure and use a large number of particle histories in the MC simulation to ensure the statisical error is small - 107 should suffice. ]

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