Analysis of power distribution in fuel pins using neutron diffusion equation

Abstract

This thesis applies neutron diffusion theory to analyze power distribution in nuclear fuel pins, comparing one-group and two-group approaches. Using cylindrical geometry and analytical solutions of the diffusion equation, both methods are evaluated for fuel pins with varying enrichment levels (3%, 5%, and 10%). The one-group model predicts center-peaked power distributions that follow Bessel function behavior, while the two-group analysis reveals edge-peaked distributions. Results demonstrate that higher enrichments significantly increase edge-to-center power ratios, with the two-group model showing ratios up to 1.85 for 10% enriched fuel. The two-group approach showcases important effects at the fuel cladding interface that the one-group model fails to predict, highlighting important implications for thermal safety margins. While diffusion theory provides valuable insights into fuel pin behavior, its limitations near material interfaces are discussed. This work contributes to understanding the fundamental neutronics of nuclear fuel and provides a foundation for more advanced analysis methods in reactor physics.