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

• Published in: Progress in nuclear energy (New series) Vol. 50; no. 7; pp. 747 - 756
• Main Authors: Lemos, R.S.M., Vilhena, M.T., Silva, F.C., Wortmann, S.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Tarrytown, NY Elsevier Ltd 01.09.2008; Oxford Elsevier
• Subjects: Auxiliary function; Diffusion equation; Exact sciences and technology; Laplace Transform; Neutron physics; Nuclear engineering and nuclear power studies; Nuclear physics; Physics; Laplace Transform; Diffusion equation; Auxiliary function; Neutron flux; Multiplication; Digital simulation; Boundary conditions; Equation system; Adjoint flux; Multilayers; Laplace transformation; Analytical solution; Comparative study; Nuclear physics
• ISSN: 0149-1970
• DOI: 10.1016/j.pnucene.2008.01.006

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.