Radiative transfer in a semi-transparent medium enclosed in a spherical annulus

• Exact expressions of the incident radiation and radiative flux in a semi-transparent spherical annulus are given.
• Exact expressions of the outgoing intensities at boundaries are calculated.
• Purely geometric weighting coefficients which give the explicit descriptions are given.

The behaviour of the radiative field inside an emitting–absorbing gray and scattering semi-transparent medium at radiative equilibrium, enclosed in a spherical annular cavity bounded by hot and diffusely reflecting surfaces, is described in an exact analytical way. The field at a given point, namely the incident radiation and the radiative flux, is completely characterized by purely geometrical weighting coefficients, which allows determining the temperature field at radiative equilibrium. 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, 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.