Question

# In this problem, consider a homogeneous slab of length a = 10 cm with nuclear data given by: E, = 1.5 cm-1, E, = 2.2 cm-1, īo = 0. A constant source of strength Q = 1.0 × 10° neutrons per cc per second exists inside the slab. The boundary condition at x = 0 is reflecting: J(0)=-D \frac{\partial \phi}{\partial x}(0)=0 and the boundary condition at x = a is an extrapolated endpoint boundary condition: o(ã) = 0. 1. Solve this diffusion equation using the variation of constants approach to find ø(x). 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 0.1 cm. 3. Plot the two solutions on the same graph and comment on the agreement between the two plots. [Compute the maximum relative error in the numerical solution compared to the analytic solution. 4. Could the boundary condition employed in your code on the right side of the slab be contributing to any differences you observe? Could you use an alternate boundary condition? 5. The magnitude of the flux at x = 0 will approach what value as a ncreases toward infinity?  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7  Fig: 8  Fig: 9