A multipoint flux approximation of the steady-state heat conduction equation in anisotropic media
Type
ArticleAuthors
Salama, Amgad
Sun, Shuyu

El-Amin, M. F.
KAUST Department
Applied Mathematics and Computational Science ProgramComputational Transport Phenomena Lab
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Environmental Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2013-03-20Online Publication Date
2013-03-20Print Publication Date
2013-04-01Permanent link to this record
http://hdl.handle.net/10754/562686
Metadata
Show full item recordAbstract
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.Citation
Salama, A., Sun, S., & El Amin, M. F. (2013). A Multipoint Flux Approximation of the Steady-State Heat Conduction Equation in Anisotropic Media. Journal of Heat Transfer, 135(4). doi:10.1115/1.4023228Publisher
ASME InternationalJournal
Journal of Heat Transferae974a485f413a2113503eed53cd6c53
10.1115/1.4023228