Article: On the analytical solution of the neutron SN equation in a rectangle assuming an exponential exiting angular flux at boundary Journal: International Journal of Nuclear Energy Science and Technology (IJNEST) 2012 Vol.7 No.1 pp.45 - 56 Abstract: In this work, we report an analytical solution for the set of SN equations for the angular flux, in a rectangle, using the double Laplace transform technique. The main steps are: application of the Laplace transform in one space variable, solution of the resulting equation by the LTSN method and reconstruction of the double Laplace transformed angular flux using the inversion theorem of the Laplace transform. We perform the Laplace inversion of the transformed angular flux in the x-direction by the LTSN method; meanwhile we evaluate the inversion in the y-direction performing the calculation of the corresponding line integral solution by the Stefest method. Based on the good results attained by the nodal LTSN method, we assume that the angular flux at boundary is approximated by an exponential function. We also report numerical comparisons of the obtained results against the ones of the literature. Finally, we need to mention that this sort of solution for the angular flux is not found in the literature. Inderscience Publishers - linking academia, business and industry through research

Title: On the analytical solution of the neutron S_N equation in a rectangle assuming an exponential exiting angular flux at boundary

Authors: Cynthia Feijó Segatto; Marco Tùllio Vilhena; Tìfani Teixeira Gonçalez

Addresses: Mechanical Engineering Post-Graduation Program, Universidade Federal Rio Grande do Sul – UFRGS, Rua Sarmento Leite, 425 – sala 314 Porto Alegre, Rio Grande do Sul, Brazil. ' Mechanical Engineering Post-Graduation Program, Universidade Federal Rio Grande do Sul – UFRGS, Rua Sarmento Leite, 425 – sala 314 Porto Alegre, Rio Grande do Sul, Brazil. ' Mechanical Engineering Post-Graduation Program, Universidade Federal Rio Grande do Sul – UFRGS, Rua Sarmento Leite, 425 – sala 314 Porto Alegre, Rio Grande do Sul, Brazil

Abstract: In this work, we report an analytical solution for the set of S_N equations for the angular flux, in a rectangle, using the double Laplace transform technique. The main steps are: application of the Laplace transform in one space variable, solution of the resulting equation by the LTS_N method and reconstruction of the double Laplace transformed angular flux using the inversion theorem of the Laplace transform. We perform the Laplace inversion of the transformed angular flux in the x-direction by the LTS_N method; meanwhile we evaluate the inversion in the y-direction performing the calculation of the corresponding line integral solution by the Stefest method. Based on the good results attained by the nodal LTS_N method, we assume that the angular flux at boundary is approximated by an exponential function. We also report numerical comparisons of the obtained results against the ones of the literature. Finally, we need to mention that this sort of solution for the angular flux is not found in the literature.

Keywords: DLTS_N method; discrete ordinates; rectangular domain; Laplace transform; angular flux.

DOI: 10.1504/IJNEST.2012.046984

International Journal of Nuclear Energy Science and Technology, 2012 Vol.7 No.1, pp.45 - 56

Received: 01 Sep 2011
Accepted: 10 Feb 2012
Published online: 05 Dec 2014 *

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Title: On the analytical solution of the neutron SN equation in a rectangle assuming an exponential exiting angular flux at boundary

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Title: On the analytical solution of the neutron S_N equation in a rectangle assuming an exponential exiting angular flux at boundary