A Generalized Boundary Integral Equation For Isotropic Heat Conduction With Spatially Varying Thermal Conductivity

    Authors

    A. J. Kassab;E. Divo

    Comments

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    Abbreviated Journal Title

    Eng. Anal. Bound. Elem.

    Keywords

    Boundary Element Methods; Heat Conduction; Space Dependent Properties; Generalized Fundamental Solution; Generalized Boundary Integral Equation; Inhomogeneous-Media; Element Method; Engineering, Multidisciplinary; Mathematics, Interdisciplinary; Applications

    Abstract

    In this paper we derive a generalized fundamental solution for the BEM solution of problems of steady state heat conduction with arbitrarily spatially varying thermal conductivity. This is accomplished with the aid of a singular nonsymmetric generalized forcing function, D, with special sampling properties. Generalized fundamental solutions, E, are derived as locally radially symmetric responses to this nonsymmetric singular forcing function, D, at a source point xi. Both E and D are defined in terms of the thermal conductivity of the medium. Although locally radially symmetric, E varies within the domain as the source point, xi changes position. A boundary integral equation is formulated. Examples of generalized fundamental solutions are provided for various thermal conductivities along with the corresponding forcing function, D. Here, four numerical examples are provided. Excellent results are obtained with our formulation for variations of thermal conductivity ranging from quadratic and cubic in one dimension to exponential in two dimensions. Problems are solved in regular and irregular regions. Current work is under way investigating extensions of this general approach to further applications where nonhomogeneous property variations are an important consideration. (C) 1997 Elsevier Science Ltd.

    Journal Title

    Engineering Analysis with Boundary Elements

    Volume

    18

    Issue/Number

    4

    Publication Date

    1-1-1996

    Document Type

    Article

    Language

    English

    First Page

    273

    Last Page

    286

    WOS Identifier

    WOS:A1996XH58700003

    ISSN

    0955-7997

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