Radiative heat transfer in a multilayer semitransparent scattering medium using the P_N-approximation method

In this paper, a numerical method is developed to be used in calculations of infrared radiative transfer in participating media with particles. The decomposition of the radiative transfer equation is made using the spherical harmonics (P_N-approximation) method, and a multilayer radiative transfer model based on the arbitrary-order P_N-approximation method is established. With the coupled radiative-conductive heat transfer model, the calculation accuracy of the high-order P_N-approximation method is established through comparison with theoretical solutions. The comparison shows that the arbitrary-order P_N-approximation method yields results for nonlinear anisotropic scattering with a high degree of accuracy. The multilayer radiative transfer model is well-suited in solving atmospheric infrared transmission problems. The influence of different scattering phase functions on the infrared transmission is analyzed within the multilayer medium. The results show that the influence of anisotropic scattering is similar to that of isotropic scattering in a steady state for optically thin media; the influence of nonlinear anisotropic scattering shows a clear linear dependence on the optical thickness in an unsteady state. With increase in the optical thickness, the apparent directional emissivity decreases.