Consider a one dimensional slab of Width W of a homogeneously distributed multiplying medium (.e….
Consider a one dimensional slab of Width W of a homogeneously distributed multiplying medium (.e. fissile material). Width W 10 11 2 3 Multiplying Media UL, I, and b AXW14 NO Assume the steady-state one-speed neutron diffusion equation applies to this arbitrary region or composition “m”. -D 1. Assuming an arbitrary N-node numerical discretization as shown above, derive the finite-difference equation for an arbitrary intemal node i 2. Derive the finite-difference equation for the teft- most node (x=0) assuming the following symmetry boundary condition applies do D = 0 dx 3. Assume that the following boundary condition applies to the right-most node (x=W) L = 0 4. Using the average matenal constants provided below, write a short program in Fortran or C++ to solve this problem for an arbitrary set of N nodes and arbitrary width w 5. Benchmark Calculate the critical dimension of this slab analytically and compare to the numerical results of your computer program 6. (Bonus 20% to total grade) Add a reflector of arbitrary thickness R to this problem and contrast your results to those encountered under Item 5. You can use the properties of hydrogen
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