Effect of void shape and highly conducting boundary on 2D conductivity of porous materials

In this paper, the heat conductivity of two-dimensional (2D) media made of an arbitrarily thermal anisotropic material and containing pores with arbitrary shape and superconductive boundary is considered. In addition to the bulk behavior, the line conduction model is used for the boundary behavior. Such idealized mathematical model can be seen as the limit case of very thin material layer with very high conductivity. The fundamental heterogeneity problem in the micromechanics of a single void embedded in an infinite matrix with both boundary and bulk behavior is then investigated and solved with the complex variable and the Conformal Mapping (CM) techniques. The heterogeneity problem results are then used to obtain the effective heat conductivity of the porous material with different homogenization schemes.