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A Novel Solution of the Multi-Group Neutron Diffusion Equation by the Hankel Transform Formalism

In: Integral Methods in Science and Engineering

Author

Listed:
  • R. A. S. Klein

    (Federal University of Rio Grande do Sul)

  • J. C. L. Fernandes

    (Federal University of Rio Grande do Sul)

Abstract

In the present work, we discuss the multi-group neutron diffusion equation solution in a homogeneous cylinder geometry case. We construct two kinds of solutions for the related problem considering two energy groups and a steady-state case. Upon applying the finite Hankel transform to the diffusion equation, one obtains a generalized system for the both neutron fluxes (fast and thermal), which may be solved in a closed form solution and depends on the specific source terms. As an equivalent approach we solve the problem by the infinite Hankel transform. Comparison of the two results shows that both methods provide acceptable solutions which are comparable to the ones in the literature. Applications for four parameter sets allow to conject that the infinite Hankel transform is the simpler approach although approximate, but providing solutions comparable to the exact solution by the finite Hankel transform.

Suggested Citation

  • R. A. S. Klein & J. C. L. Fernandes, 2022. "A Novel Solution of the Multi-Group Neutron Diffusion Equation by the Hankel Transform Formalism," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Paul J. Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 157-168, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-07171-3_11
    DOI: 10.1007/978-3-031-07171-3_11
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