A new efficient method of solution to radiation transfer in absorbing, emitting, isotropically scattering, homogeneous, finite or semi-infinite, plane-parallel media

Abstract

A new efficient method of analysis, which utilizes the natural eigenfunctions of the problem, is developed for solving radiation transfer in an absorbing, emitting, gray, isotropically scattering, homogeneous, finite or semi-infinite, plane-parallel medium. Expressions for the forward and backward radiation intensities, the incident radiation and forward and backward radiation heat fluxes are included. Since the physical aspects of the problem are well documented, attention is focused on the presentation of the method of analysis and discussion of its convergence and accuracy. For the test case involving uniform incident radiation on the boundary surface at x = 0, it is shown that the solution converges extremely rapidly to the exact results, and that lower-order approximations are highly accurate. For example, the first-order solution predicts values of the incident radiation, reflectivity and transmissivity that are less than 1% in error in almost all cases, for optical thicknesses in the range 0.1 ⩽ L ⩽ 10 and single-scattering albedos in the range 0.1 ⩽ ω ⩽ 0.99. The present method of solution has an excellent potential for generalization to anisotropic scattering and to radiation transfer in spherical and cylindrical geometries.