Numerical calculations of the thermal conductivity of porous ceramics based on micrographs

The overall thermal conductivity of a porous material is strongly sensitive to the volume fraction and spatial distribution of the pores. For this second aspect analytical models predicting thermal conductivity as a function of pore volume fraction are obliged to make a simplifying assumption concerning the pore shape. In order to describe the effects of the microstructure on heat transfer in greater detail, we have developed a method involving 2D finite element calculations based on real micrographs of the porous solid. The approach was tested on micrographs of tin oxide samples with pore contents from 10% to 50%. Quantitative results obtained for pore contents up to 20% give very good agreement to Rayleigh's model. Higher pore contents lead to a number of difficulties but the qualitative results are used to support the choice of Landauer's effective medium expression as an appropriate general analytical model for the thermal conductivity of a porous ceramic material.