Use of eigenfunctions for solving radiation transfer in anisotropically scattering, plane-parallel media

Radiation transfer in an absorbing, emitting, gray, anisotropically scattering, plane-parallel medium is solved by using the naturally occurring eigenfunctions, and expressions for the forward and backward radiation intensities, the incident radiation, and forward and backward radiation heat fluxes are presented. To illustrate the method of solution, the situation involving an externally incident isotropic radiation at the boundary surface x=0 and no energy sources in the medium is considered for the cases of four different scattering phase functions. It is shown that the convergence to the exact results is fast, and that lower order approximations are accurate. In addition, the present method of solution has an excellent potential for generalization to problems of plane-parallel media without azimuthal symmetry and to problems in cylindrical and spherical geometries.