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

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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
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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
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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
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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

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method, discrete ordinates, rectangular domain, Laplace transform, angular flux

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