High-order Spherical Harmonics Method for Transient Coupled Heat Transfer in Non-linear Anisotropic Scattering Semitransparent Materials

摘要

An advanced numerical model and its application in thermal processing of nonlinearly anisotropic scattering semitransparent materials are presented in this paper. The decomposition of the radiative transfer equation is deduced using spherical harmonics (PN-approximation) method. Considering the transient problem, coupled radiative and conductive heat transfer model based on arbitrary-order PN-approximation method is established. With the coupled model, the calculation accuracy of high-order PN-approximation method is verified through comparison with theoretical solution and by the simulation results of other methods. The influences of material optical thickness, surface emissivity, and albedo on the transient temperature distribution are analyzed. Comparison shows that the arbitrary-order PN-approximation method reproduces results with a high accuracy for linear and non-linear anisotropic scattering, while it can easily treat the nonlinear anisotropic scattering phase functions with desired order. According to analyzing results of linear scattering and nonlinear scattering, it is found that the temperature differences of forward and backward scattering are about 20K comparing with the results of isotropic scattering.