Open AccessExact solution of the one-dimensional neutron diffusion kinetic equation with one delayed precursor concentration in Cartesian geometry
Author(s) -
S. M. Khaled
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022686
Subject(s) - laplace transform , cartesian coordinate system , mathematical analysis , neutron flux , analytic geometry , boundary value problem , neutron transport , diffusion equation , mathematics , flux (metallurgy) , work (physics) , space (punctuation) , diffusion , physics , differential equation , laplace's equation , neutron , kinetic energy , geometry , classical mechanics , thermodynamics , chemistry , nuclear physics , computer science , economy , organic chemistry , operating system , economics , service (business)
In this article we use one-dimensional, monoenergetic diffusion kinetic equation with one delayed neutron precursor concentration in Cartesian geometry to reconstruct the neutron flux of a reactor from the nuclear parameters, boundary, and initial conditions. The mathematical model is governed by a system of linear partial differential equations with prescribed boundary and initial conditions. As a matter of fact, the exact solution for any physical problem, if available, is of great importance which inevitably leads to a better understanding of the behavior of the involved physical phenomena. The present work represents an attempt for doing so, where the flux and precursor equations are solved by the help of Laplace transform in both spatial and time variables and consequently the exact expressions for the flux and concentration in space and time are established. We report numerical simulations as well study of numerical convergence of the obtained results.