Arbitrary-Order Spherical Harmonics Method for Radiative Heat Transfer in Semitransparent Medium

A radiative transfer model for a linearly or nonlinearly anisotropic scattering medium is developed. An arbitrary-order spherical harmonics method (PN-approximation) was presented to decompose the radiative transfer equation into a set of coupled partial differential equations which solved by the tridiagonal matrix method. By using PN-approximation formulation, the greenhouse effect from carbon dioxide on atmosphere temperature profile was simulated. The results show that the spherical harmonics method is an effective method which has any desired high-order of accuracy. The increase of carbon dioxide concentration causes the enhancement of air temperature.