Radiative transfer of energy in a cylindrical enclosure with heat generation

Radiative transfer in cylindrical symmetry systems is studied using the higher order differential approximations, that is, the P1, P3, and P5 approximations of the spherical harmonics method. Attention is given to the heat transfer between concentric cylinders for the case of a medium in radiative equilibrium, where the heat transfer decreases with increasing optical thickness. In the limiting case of zero optical thickness, the respective percentage overestimates of heat flux as found from the P5, P3, P1 and diffusion approximations are 2%, 5%, 33%, and 100% for a radius ratio of 0.5; for a radius ratio of 0.1 the overestimates are about 35%, 55%, 81%, and 100%. The maximum percentage errors of P3, P1 and layer approximations relative to the Monte Carlo are observed to be about 4%, 8% and 5%, respectively.