Analytical solution for two-group diffusion equations in a multilayered slab using Laplace Transform Technique

In this work, we report an analytical solution for the neutron and adjoint neutron fluxes by solving, respectively, the real and adjoint diffusion equations in a two-layered slab by the Laplace Transform Technique. We also present a solution for the effective multiplication factor by solving the algebraic system equation resulting from boundary condition and interface continuity for the flux and current by the bisection method. We also report analytical solutions for a properly said fixed source problem and for the auxiliary function using the same method developed for the previous problems. We report numerical simulations and comparisons with results in the literature.