In this problem, consider a homogeneous slab of length a = 50 cm with nuclear data given by: E.īo = 0.87. The boundary conditions on the slab are extrapolated endpoint= 0.7 cm-1, Es1.3 cm-1, vEf = 1.47 cm-1conditions: \phi\left(-\frac{\tilde{a}}{2}\right)=\phi\left(\frac{\tilde{a}}{2}\right)=0 Use the eigen function expansion approach to compute the multiplication factor k for this problem, and the flux in the reactor assuming that the fission rate in the system is normalized to 1.0 × 10º fissions per second. 2. Write a code to implement the finite volume diffusion solution approach described in class and solve this problem with a spatial mesh of 100cells of length 0.5 cm. 3. Compare both the multiplication factor and the flux computed by your code with the analytic solution you obtained. [Compute the maximum relative error in the numerical solution compared to the analytic solution.] 1. What would you expect your code to calculate for the multiplicationfactor if the boundary conditions were changed to -D \frac{\partial \phi}{\partial x}\left(-\frac{\tilde{a}}{2}\right)=-D \frac{\partial \phi}{\partial x}\left(\frac{\tilde{a}}{2}\right)=0 5. Suppose this material was used in a homogeneous cylindrical reactor,also with extrapolated endpoint boundary conditions, of radius R= 20cm and height H = 28 cm. What is the multiplication factor and flux shape? [Don't worry about the magnitude..]

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