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

摘要

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 percent to 50 percent. Quantitative results obtained for pore contents up to 20 percent 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.