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

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 an...

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Main Authors:	Mohammed Shqair, Ahmad El-Ajou, Mazen Nairat
Format:	Article
Language:	English
Published:	MDPI AG 2019-07-01
Series:	Mathematics
Subjects:	multi-group diffusion equation residual power series radial flux
Online Access:	https://www.mdpi.com/2227-7390/7/7/633

id	doaj-5e849f30fa0e4ed7ae167df38e90466e
record_format	Article
spelling	doaj-5e849f30fa0e4ed7ae167df38e90466e2020-11-25T01:07:49ZengMDPI AGMathematics2227-73902019-07-017763310.3390/math7070633math7070633Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series MethodMohammed Shqair0Ahmad El-Ajou1Mazen Nairat2Physics Department, Faculty of Science and Humanities, Prince Sattam bin Abdulaziz University, 11942 Al-kharj, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanDepartment of Physics, Faculty of Science, Al Balqa Applied University, Salt 19117, JordanIn 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.https://www.mdpi.com/2227-7390/7/7/633multi-groupdiffusion equationresidual power seriesradial flux
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mohammed Shqair Ahmad El-Ajou Mazen Nairat
spellingShingle	Mohammed Shqair Ahmad El-Ajou Mazen Nairat Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method Mathematics multi-group diffusion equation residual power series radial flux
author_facet	Mohammed Shqair Ahmad El-Ajou Mazen Nairat
author_sort	Mohammed Shqair
title	Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method
title_short	Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method
title_full	Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method
title_fullStr	Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method
title_full_unstemmed	Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method
title_sort	analytical solution for multi-energy groups of neutron diffusion equations by a residual power series method
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-07-01
description	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.
topic	multi-group diffusion equation residual power series radial flux
url	https://www.mdpi.com/2227-7390/7/7/633
work_keys_str_mv	AT mohammedshqair analyticalsolutionformultienergygroupsofneutrondiffusionequationsbyaresidualpowerseriesmethod AT ahmadelajou analyticalsolutionformultienergygroupsofneutrondiffusionequationsbyaresidualpowerseriesmethod AT mazennairat analyticalsolutionformultienergygroupsofneutrondiffusionequationsbyaresidualpowerseriesmethod
_version_	1725185143264509952

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

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