Mathematics (Jul 2019)

Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

  • Mohammed Shqair,
  • Ahmad El-Ajou,
  • Mazen Nairat

DOI
https://doi.org/10.3390/math7070633
Journal volume & issue
Vol. 7, no. 7
p. 633

Abstract

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In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension.

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