A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media

Handle URI:
http://hdl.handle.net/10754/562686
Title:
A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media
Authors:
Salama, Amgad ( 0000-0002-4463-1010 ) ; Sun, Shuyu ( 0000-0002-3078-864X ) ; El-Amin, M. F.
Abstract:
In this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described. Copyright © 2013 by ASME.
KAUST Department:
Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computational Transport Phenomena Lab; Earth Science and Engineering Program
Publisher:
American Society of Mechanical Engineers
Journal:
Journal of Heat Transfer
Issue Date:
20-Mar-2013
DOI:
10.1115/1.4023228
Type:
Article
ISSN:
00221481
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

Full metadata record

DC FieldValue Language
dc.contributor.authorSalama, Amgaden
dc.contributor.authorSun, Shuyuen
dc.contributor.authorEl-Amin, M. F.en
dc.date.accessioned2015-08-03T11:01:27Zen
dc.date.available2015-08-03T11:01:27Zen
dc.date.issued2013-03-20en
dc.identifier.issn00221481en
dc.identifier.doi10.1115/1.4023228en
dc.identifier.urihttp://hdl.handle.net/10754/562686en
dc.description.abstractIn this work, we introduce multipoint flux (MF) approximation method to the problem of conduction heat transfer in anisotropic media. In such media, the heat flux vector is no longer coincident with the temperature gradient vector. In this case, thermal conductivity is described as a second order tensor that usually requires, at least, six quantities to be fully defined in general three-dimensional problems. The two-point flux finite differences approximation may not handle such anisotropy and essentially more points need to be involved to describe the heat flux vector. In the framework of mixed finite element method (MFE), the MFMFE methods are locally conservative with continuous normal fluxes. We consider the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element method with a special quadrature rule that allows for nodal velocity elimination resulting in a cell-centered system for the temperature. We show comparisons with some analytical solution of the problem of conduction heat transfer in anisotropic long strip. We also consider the problem of heat conduction in a bounded, rectangular domain with different anisotropy scenarios. It is noticed that the temperature field is significantly affected by such anisotropy scenarios. Also, the technique used in this work has shown that it is possible to use the finite difference settings to handle heat transfer in anisotropic media. In this case, heat flux vectors, for the case of rectangular mesh, generally require six points to be described. Copyright © 2013 by ASME.en
dc.publisherAmerican Society of Mechanical Engineersen
dc.subjectAnisotropic mediaen
dc.subjectCell-centered finite differenceen
dc.subjectConduction heat transferen
dc.subjectMixed finite elementen
dc.subjectMultipoint flux approximationen
dc.titleA multipoint flux approximation of the steady-state heat conduction equation in anisotropic mediaen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalJournal of Heat Transferen
dc.contributor.institutionNuclear Research Center, Atomic Energy Authority, 13759 Cairo, Egypten
dc.contributor.institutionMathematics Department, Faculty of Science, Aswan University, 81718 Aswan, Egypten
kaust.authorSalama, Amgaden
kaust.authorSun, Shuyuen
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