Integral transform solution of natural convection in a square cavity with volumetric heat generation
Autor(a) principal: | |
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Data de Publicação: | 2013 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Brazilian Journal of Chemical Engineering |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322013000400020 |
Resumo: | The generalized integral transform technique (GITT) is employed to obtain a hybrid numerical-analytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers. |
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Brazilian Journal of Chemical Engineering |
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Integral transform solution of natural convection in a square cavity with volumetric heat generationNatural convectionSquare cavityVolumetric heat generationIntegral transformHybrid solutionThe generalized integral transform technique (GITT) is employed to obtain a hybrid numerical-analytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers.Brazilian Society of Chemical Engineering2013-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322013000400020Brazilian Journal of Chemical Engineering v.30 n.4 2013reponame:Brazilian Journal of Chemical Engineeringinstname:Associação Brasileira de Engenharia Química (ABEQ)instacron:ABEQ10.1590/S0104-66322013000400020info:eu-repo/semantics/openAccessAn,C.Vieira,C. B.Su,J.eng2014-01-10T00:00:00Zoai:scielo:S0104-66322013000400020Revistahttps://www.scielo.br/j/bjce/https://old.scielo.br/oai/scielo-oai.phprgiudici@usp.br||rgiudici@usp.br1678-43830104-6632opendoar:2014-01-10T00:00Brazilian Journal of Chemical Engineering - Associação Brasileira de Engenharia Química (ABEQ)false |
dc.title.none.fl_str_mv |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
title |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
spellingShingle |
Integral transform solution of natural convection in a square cavity with volumetric heat generation An,C. Natural convection Square cavity Volumetric heat generation Integral transform Hybrid solution |
title_short |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
title_full |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
title_fullStr |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
title_full_unstemmed |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
title_sort |
Integral transform solution of natural convection in a square cavity with volumetric heat generation |
author |
An,C. |
author_facet |
An,C. Vieira,C. B. Su,J. |
author_role |
author |
author2 |
Vieira,C. B. Su,J. |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
An,C. Vieira,C. B. Su,J. |
dc.subject.por.fl_str_mv |
Natural convection Square cavity Volumetric heat generation Integral transform Hybrid solution |
topic |
Natural convection Square cavity Volumetric heat generation Integral transform Hybrid solution |
description |
The generalized integral transform technique (GITT) is employed to obtain a hybrid numerical-analytical solution of natural convection in a cavity with volumetric heat generation. The hybrid nature of this approach allows for the establishment of benchmark results in the solution of non-linear partial differential equation systems, including the coupled set of heat and fluid flow equations that govern the steady natural convection problem under consideration. Through performing the GITT, the resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from the IMSL Library. Therefore, numerical results under user prescribed accuracy are obtained for different values of Rayleigh numbers, and the convergence behavior of the proposed eigenfunction expansions is illustrated. Critical comparisons against solutions produced by ANSYS CFX 12.0 are then conducted, which demonstrate excellent agreement. Several sets of reference results for natural convection with volumetric heat generation in a bi-dimensional square cavity are also provided for future verification of numerical results obtained by other researchers. |
publishDate |
2013 |
dc.date.none.fl_str_mv |
2013-12-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322013000400020 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322013000400020 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0104-66322013000400020 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Brazilian Society of Chemical Engineering |
publisher.none.fl_str_mv |
Brazilian Society of Chemical Engineering |
dc.source.none.fl_str_mv |
Brazilian Journal of Chemical Engineering v.30 n.4 2013 reponame:Brazilian Journal of Chemical Engineering instname:Associação Brasileira de Engenharia Química (ABEQ) instacron:ABEQ |
instname_str |
Associação Brasileira de Engenharia Química (ABEQ) |
instacron_str |
ABEQ |
institution |
ABEQ |
reponame_str |
Brazilian Journal of Chemical Engineering |
collection |
Brazilian Journal of Chemical Engineering |
repository.name.fl_str_mv |
Brazilian Journal of Chemical Engineering - Associação Brasileira de Engenharia Química (ABEQ) |
repository.mail.fl_str_mv |
rgiudici@usp.br||rgiudici@usp.br |
_version_ |
1754213174237724672 |