Question 19.2: Suppose you are asked to homogenize a reactor fuel assembly ......
Suppose you are asked to homogenize a reactor fuel assembly where the moderator-to-fuel ratio is 2 to 1. If the thermal flux in the moderator is twice the thermal flux in the fuel, what is the average macroscopic absorption cross section for the fuel assembly if the average macroscopic absorption cross section for the fuel is 0.17 cm^{−1}, and the average macroscopic absorption cross section for the moderator is 0.02 cm^{−1}?
The average macroscopic absorption cross section for the fuel assembly must conserve the overall absorption rate in the fuel assembly. Hence we must find the value of <Σ_a> from the expression <Σ_a> = (ϕ_{fuel}Σ_{fuel a}V_{fuel} + ϕ_{mod}Σ_{mod a}V_{mod})/(ϕ_{fuel}V_{fuel} + ϕ_{mod}V_{mod}). Plugging in the appropriate values for each of these quantities, we find that <Σ_a> = (1 × 0.17 × 1 + 2 × 0.02 × 2)/(1 × 1 + 2 × 2) = (0.25)/5 = 0.05 cm^{−1}.