Arbitrary-Order Spherical Harmonics Method for Coupled Heat Transfer in Semitransparent Materials

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. 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. Keywords: semitransparent material, coupled heat transfer, numerical simulation, spherical harmonics method