Radiative transfer in a semi-transparent medium enclosed in a spherical annulus with specularly reflecting surfaces

摘要

The behaviour of the radiative field inside an emitting-absorbing gray semi-transparent medium at radiative equilibrium, enclosed in a spherical annular cavity bounded by specularly reflecting hot surfaces, is described in an exact analytical way. In this approach, the incident radiation and the radiative flux are expressed as a linear combination of the internal temperatures power 4 at each point of the medium, whatever the reflection on the boundary surfaces is, the coefficients of the combination being the weighting coefficients determined from an analytical way. Some examples show that the proposed method gives perfectly smooth results of high accuracy for both the temperature and flux fields inside the medium.