A Generalized Boundary-Element Method For Steady-State Heat Conduction In Heterogeneous Anisotropic Media
Abbreviated Journal Title
Numer Heat Tranf. B-Fundam.
INHOMOGENEOUS-MEDIA; POTENTIAL PROBLEMS; Thermodynamics; Mechanics
A generalized boundary integral equation (BIE) is formulated for heat conduction problems in anisotropic media with spatially varying thermal conductivities arising from material heterogeneity. The generalized integral equation is expressed in terms of contour integrals only. This is accomplished with the aid of a generalized fundamental solution E and with the definition of a singular nonsymmetric generalized forcing function, D. Generalized fundamental solutions, E, are derived as locally radially symmetric responses to this nonsymmetric singular forcing function, D. Both E and D are defined in terms of the thermal conductivity of the medium. Although it is locally radially symmetric about the source point, E varies within the domain as the source point changes position. Examples of generalized fundamental solutions are provided for various thermal conductivities along with the corresponding forcing function, D. Numerical implementation is discussed. Numerical results are provided for several examples with spatially variable thermal conductivity in isotropic, orthotropic, and fully anisotropic heterogeneous media. Problems are solved in 2-D and 3-D regular and irregular regions with single- and multiply-connected domains. Close agreement found between the generalized BIE solution and exact solutions validates the formulation developed in this article.
Numerical Heat Transfer Part B-Fundamentals
"A Generalized Boundary-Element Method For Steady-State Heat Conduction In Heterogeneous Anisotropic Media" (1997). Faculty Bibliography 1990s. 1884.