Heat Conduction in Multiply Adjoined Anisotropic Media with Embedded Point Heat Sources

Abstract

In this article the direct domain-mapping technique is applied in the boundary element method (BEM) to investigate the heat conduction in composites consisting of multiple anisotropic media with embedded point heat sources. By use of a linear coordinate transformation, the physical domain is mapped to an auxiliary plane for 2D or space for 3D, where the heat conduction is considered isotropic. However, the interfaces of adjoined materials with dissimilar properties will overlap or separate in the mapped plane or space. For the use of the subregioning technique in BEM to solve such problems, the thermal equilibrium condition for interfaces is developed to account for boundary distortions. In the mapped plane or space, not only the locations but also the strength of heat sources are transformed accordingly. After the problem is solved in the mapped plane or space, the obtained numerical solution is thereafter interpolated and transformed back to the one in the physical domain.