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

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    Type
    Article
    Authors
    Salama, Amgad cc
    Sun, Shuyu cc
    El-Amin, M. F.
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computational 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
    2013-03-20
    Online Publication Date
    2013-03-20
    Print Publication Date
    2013-04-01
    Permanent link to this record
    http://hdl.handle.net/10754/562686
    
    Metadata
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    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.
    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:10.1115/1.4023228
    Publisher
    ASME International
    Journal
    Journal of Heat Transfer
    DOI
    10.1115/1.4023228
    ae974a485f413a2113503eed53cd6c53
    10.1115/1.4023228
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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