A three-scale homogenization algorithm for coupled conduction-radiation problems in porous materials with multiple configurations

This work establishes a novel three-scale homogenization algorithm to predict heat transfer performance of porous materials with multiple periodic configurations. The heterogeneities of porous structures are considered by periodic distributions of unit cells on the microscale and mesoscale. A new micro-meso-macro formula based on homogenization methods and multiscale asymptotic expansions is given at first. Two types of unit cell solutions in microscale and mesoscale are obtained by solving the distinct multiscale cell functions. Also, two kinds of homogenization coefficients are calculated by up-scaling procedure, and the homogenization equations are defined on global structure. Further, the temperature and heat flux fields are established as three-scale approximate solutions by assembling the various local cell solutions and homogenization solutions. Then, the associated finite element algorithm based on the three-scale homogenization methods is proposed in detail. Finally, some numerical examples are reported to validate the methods. They illustrate that the three-scale homogenization methods presented in this work are effective and accurate for calculating the heat transfer performance of the porous materials with multiple configurations.