Radiation transfer in absorbing, emitting, isotropically scattering, homogeneous cylindrical media

One-dimensional radiative transfer in an absorbing, emitting, gray, isotropically scattering, homogeneous, solid cylinder having a diffusely reflecting boundary surface and externally incident radiation is solved by using the appropriate expansion functions. Expressions for the radiation intensity, incident radiation and net radiative heat flux are presented. To illustrate the computational aspects of the method, the following two situations are considered: (1) a uniform externally incident radiation and (2) a source within the medium of the form Q(r) = (1-ω) [1-(r/R)²]. For the first case, it is shown that the convergence of the numerical results is fast and that first-order approximations are accurate; for the second case, results accurate to five significant digits are shown. Since the solution method does not require the knowledge of a particular solution, it is a viable approach for solving the radiation part in problems in which the radiation interacts with either conduction or convection. Furthermore, the method also has the potential for generalization to problems involving anisotropic scattering.