A Multiscale Method for Coupled Steady-State Heat Conduction and Radiative Transfer Equations in Composite Materials

The prediction of coupled conduction-radiation heat transfer in periodic composite materials is important for the application of the materials in high-temperature environment. Homogenization method is widely used for the heat conduction problem, but the coupled radiative transfer equation is seldom studied. In this work, the homogenization method is extended to the coupled conduction-radiation heat transfer in composite materials with periodic microscopic structures, in which both the heat conduction and radiative transfer equations are analyzed. The homogenized equations are obtained for the macroscopic heat transfer. The unit cell problems are also derived, which provide the effective coefficients for the homogenized equations and the local temperature and radiation corrections. The second-order asymptotic expansion of the temperature field and first-order asymptotic expansion of the radiative intensity field are established. A multiscale numerical algorithm is proposed to simulate the coupled conduction-radiation heat transfer in materials doped with isotropic or anisotropic particles. According to the numerical examples in this work, comparing with the fully-resolved simulations, the errors of the multiscale model are less than 13% for the temperature and less than 8% for the radiation. The computational time can be reduced from more than 300 hours to less than 30 minutes. Therefore, the proposed multiscale method can maintain the accuracy of the calculation and significantly improve the computational efficiency. It can provide both the average temperature and radiation for engineering utilizations and the local information corresponding to the microstructure of the composite materials.