Abstract
This chapter aims to obtain analytical solutions for the neutron diffusion equation in three-dimensional Cartesian geometry by the separation of variables method, in homogeneous and heterogeneous domains, considering mono-energetic and two-energy groups, and a group of delayed neutron precursors. The present work is a continuation of the study of Oliveira et al. (Ann Nucl Energy 99: 253–257, 2017; Ann Nucl Energy 133:216–220, 2019) that uses the same methodology in the models but considering cylindrical geometry. Considering mono-energetic neutrons, we present simulations of the insertion of control rods at different values for the z variable. Considering two-energy groups, we assume the spatial functions of the fluxes and precursor concentration differ by a non-zero scale factor. The computational implementation of the algorithm associated with the obtained solution will be validated with the results of the literature.
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Tumelero, F., Vilhena, M.T., Bodmann, B.E.J. (2022). On the Mono-Energetic Neutron Space Kinetics Equation in Cartesian Geometry: An Analytic Solution by a Spectral Method. In: Constanda, C., Bodmann, B.E., Harris, P.J. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-07171-3_23
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