Structure of thermal radiation field in an optically thick limit

The transport of radiation in the optically thick limit is investigated when the temperature profile within the medium is specified and continuous, and when the medium under consideration is not in radiative equilibrium. Results show that the equation governing the transport of incident radiation becomes mathematically singular as the optical thickness becomes large. It is shown that this singularity is an attribute of a small parameter epsilon, which is inversely proportional to the square of the optical thickness, multiplying the highest derivative of the differential equation. It is found that in the optically thick limit, away from the wall the radiation field is near equilibrium, such that up to 0(epsilon) the rates of absorption and emission of radiation are equal. In the near-wall region, however, the absorption and emission rates are different by 0(epsilon to the 1 /2). Thus, the magnitude of the divergence of radiative heat flux changes by 0(epsilon to the 1/2) as the wall is approached from the far region, and there exists a radiation boundary layer for the incident radiation in the limit of optical thickness becoming very large.