Multiscale analysis and computation for coupled conduction, convection and radiation heat transfer problem in porous materials

This paper discusses the multiscale analysis and numerical algorithms for coupled conduction, convection and radiation heat transfer problem in periodic porous materials. First, the multiscale asymptotic expansion of the solution for the coupled problem is presented, and high-order correctors are constructed. Then, error estimates and their proofs will be given on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale method are introduced and some numerical results are given in detail. The numerical tests demonstrate that the developed method is feasible and valid for predicting the heat transfer performance of periodic porous materials, and support the approximate convergence results proposed in this paper.