Combined effects of pores and cracks on the effective thermal conductivity of materials: a numerical study

Porous solids are commonplace in engineering structures and in nature. Material properties are inevitably affected by the internal inhomogeneity. The effective thermal conductivity of porous materials has been and remains to be a subject of extensive research. Less attention has been devoted to thermal conductivity impacted by internal cracks. This study is devoted to theoretical analyses of the combined effects of pores and cracks on the effective thermal conductivity. Systematic numerical simulations using the finite element method are performed based on two-dimensional models, with periodic distributions of internal pores and cracks. The parametric investigations seek to address how individual geometric layout can influence the overall thermal conduction behavior. In addition to circular pores and isolated cracks, angular pores with cracks extending from their sharp corners are also considered. It is found that both isolated cracks and cracks connected to existing pores can significantly reduce the effective thermal conductivity in porous materials. Since it is much easier to microscopically detect internal pores than thin cracks, care should be taken in using the apparent porosity from microscopic images and density measurements to estimate the overall thermal conductivity. Quantitative analyses of the detailed geometric effects are reported in this paper.