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

作者：Yang, Zhiqiang^*; Sun, Yi; Cui, Junzhi; Yang, Zihao; Guan, Tianyu

来源：International Journal of Heat and Mass Transfer, 2018, 125: 1196-1211.

DOI：10.1016/j.ijheatmasstransfer.2018.05.024

• Three-scale homogenization algorithms
• Conduction-radiation problems
• Micro-meso-macro formulations
• Porous materials

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 multi scale 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.

• 出版日期2018-10
• 单位中国科学院数学与系统科学研究院; 哈尔滨工业大学; 西北工业大学