Statistical Second-order Two-scale Method for Nonstationary Coupled Conduction-Radiation Heat Transfer Problem of Random Porous Materials

Abstract

This paper develops a novel statistical second-order two-scale (SSOTS) method to predict the heat transfer performances of three-dimensional (3D) porous materials with random distribution. Firstly, the mesoscopic configuration for the structure with random distribution is briefly characterized Secondly, the SSOTS formulas for calculating effective thermal conductivity parameters, temperature field and heat flux densities are derived by means of construction way. Then, the algorithm procedure based on the SSOTS method is described in details. Finally, numerical results for porous materials with varying probability distribution models are calculated by SSOTS algorithm, and compared with the data by finite element method (FEM) in a very fine mesh and theoretical methods. They show that the SSOTS method is not only valid, but also accurate to predict the coupled heat transfer performances of random porous materials and demonstrate its potential applications in thermal engineering.