Steady-state heat transfer analysis in a spherical domain revisited

The paper discusses the numerical solution of the one-dimensional radially axi-symmetric non-linear second-order differential equation to model the conduction and radiation transfer through a spherical domain as a result of an exothermic heat source. The equation is transformed to a non-dimensional...

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Autores principales:	du Toit Jat, Pretorius Christiaan
Formato:	article
Lenguaje:	EN FR
Publicado:	EDP Sciences 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/377ec0dc14ba4053bf8487443c06929c
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id	oai:doaj.org-article:377ec0dc14ba4053bf8487443c06929c
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spelling	oai:doaj.org-article:377ec0dc14ba4053bf8487443c06929c2021-12-02T17:13:35ZSteady-state heat transfer analysis in a spherical domain revisited2261-236X10.1051/matecconf/202134700006https://doaj.org/article/377ec0dc14ba4053bf8487443c06929c2021-01-01T00:00:00Zhttps://www.matec-conferences.org/articles/matecconf/pdf/2021/16/matecconf_sacam21_00006.pdfhttps://doaj.org/toc/2261-236XThe paper discusses the numerical solution of the one-dimensional radially axi-symmetric non-linear second-order differential equation to model the conduction and radiation transfer through a spherical domain as a result of an exothermic heat source. The equation is transformed to a non-dimensional form. The dimensionless numbers emanating from the transformation represent the effect of the reaction rate, reaction type, activation energy, radiation and the convection on the temperature. The non-dimensional differential equation for the temperature distribution was previously solved using the Runge-Kutta-Fehlberg method coupled with a Shooting technique. In this paper the solution of the non-dimensional differential equation using an iterative Galerkin finite element method approach employing the Picard method is described. The commercial finite element code Comsol is also employed to solve the non-dimensional differential equation. The current study was motivated by inconsistencies that were observed in the previous results that were presented. Although the assumed underlying physics is used to evaluate the results, the study focuses purely on the numerical solution of the non-dimensional differential equation. The results obtained by the Galerkin finite element code and Comsol were found to be in exact agreement and also exhibit no inconsistencies.du Toit JatPretorius ChristiaanEDP SciencesarticleEngineering (General). Civil engineering (General)TA1-2040ENFRMATEC Web of Conferences, Vol 347, p 00006 (2021)
institution	DOAJ
collection	DOAJ
language	EN FR
topic	Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 du Toit Jat Pretorius Christiaan Steady-state heat transfer analysis in a spherical domain revisited
description	The paper discusses the numerical solution of the one-dimensional radially axi-symmetric non-linear second-order differential equation to model the conduction and radiation transfer through a spherical domain as a result of an exothermic heat source. The equation is transformed to a non-dimensional form. The dimensionless numbers emanating from the transformation represent the effect of the reaction rate, reaction type, activation energy, radiation and the convection on the temperature. The non-dimensional differential equation for the temperature distribution was previously solved using the Runge-Kutta-Fehlberg method coupled with a Shooting technique. In this paper the solution of the non-dimensional differential equation using an iterative Galerkin finite element method approach employing the Picard method is described. The commercial finite element code Comsol is also employed to solve the non-dimensional differential equation. The current study was motivated by inconsistencies that were observed in the previous results that were presented. Although the assumed underlying physics is used to evaluate the results, the study focuses purely on the numerical solution of the non-dimensional differential equation. The results obtained by the Galerkin finite element code and Comsol were found to be in exact agreement and also exhibit no inconsistencies.
format	article
author	du Toit Jat Pretorius Christiaan
author_facet	du Toit Jat Pretorius Christiaan
author_sort	du Toit Jat
title	Steady-state heat transfer analysis in a spherical domain revisited
title_short	Steady-state heat transfer analysis in a spherical domain revisited
title_full	Steady-state heat transfer analysis in a spherical domain revisited
title_fullStr	Steady-state heat transfer analysis in a spherical domain revisited
title_full_unstemmed	Steady-state heat transfer analysis in a spherical domain revisited
title_sort	steady-state heat transfer analysis in a spherical domain revisited
publisher	EDP Sciences
publishDate	2021
url	https://doaj.org/article/377ec0dc14ba4053bf8487443c06929c
work_keys_str_mv	AT dutoitjat steadystateheattransferanalysisinasphericaldomainrevisited AT pretoriuschristiaan steadystateheattransferanalysisinasphericaldomainrevisited
_version_	1718381313552023552

Steady-state heat transfer analysis in a spherical domain revisited

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