Transient heat conduction problem with radiation boundary condition of statistically inhomogeneous materials by second-order two-scale method

• A statistical second-order two-scale analysis method is proposed.
• Heat conduction problem with radiation boundary condition is investigated.
• Porous materials with statistically inhomogeneous microstructure are considered.
• Numerical results are given to validate the statistical two-scale method.

This paper develops a statistical second-order two-scale (SSOTS) method for predicting transient heat transfer performance of statistically inhomogeneous porous materials. In these materials, the complicated microscopic information of inclusions, including their shape, size, orientation, spatial distribution, volume fraction and so on, leads to changes of the macroscopic thermal properties. Also, heat radiation effect at microscale has an important impact on the macroscopic temperature field. A novel unified homogenization procedure, based on two-scale asymptotic expressions depending on the position variables, has been established. The second-order two-scale formulations for computing the transient heat transfer problem are given successively. Then, the statistical prediction algorithm based on the proposed two-scale model is described in details. Finally, numerical examples for porous materials with varying probability distribution models are calculated by the algorithm given, and compared with the data by the theoretical results. The comparison shows that the statistical two-scale computational method developed is useful for determination of the heat transfer properties of porous materials and demonstrates its potential applications in actual engineering computation.