The statistical second-order two-scale analysis method for conduction-radiation coupled heat transfer of porous materials

A new statistical second-order two-scale (SSOTS) method was presented for predicting the performances of conduction-radiation coupled heat transfer of porous materials with random distribution of pores. The statistical second-order two-scale formulation for the Rosseland problem of porous materials was discussed, and a statistical prediction algorithm for maximum heat flux density was brought forward. Besides, the validity of the proposed method by comparison with theoretical methods with simple numerical models was verified. Finally, macroscopic thermal properties for the porous ceramic materials with varying probability distribution models including volume fraction and spatial distribution model of pores were shown. The results show that the effective thermal conductivity parameters decrease and maximum heat flux density increases with the pores volume fraction increasing. What is more, the radiation is an important factor for heat transfer at a high temperature. It is also shown that the SSOTS method is valid to predict the performances of conduction-radiation coupled heat transfer of porous materials with random distribution of pores.