Second-order two-scale computations for conductive–radiative heat transfer problem in periodic porous materials

In this paper, a kind of second-order two-scale (SOTS) computation is developed for conductive–radiative heat transfer problem in periodic porous materials. First of all, by the asymptotic expansion of the temperature field, the cell problem, homogenization problem, and second-order correctors are obtained successively. Then, the corresponding finite element algorithms are proposed. Finally, some numerical results are presented and compared with theoretical results. The numerical results of the proposed algorithm conform with those of the FE algorithm well, demonstrating the accuracy of the present method and its potential applications in thermal engineering of porous materials.