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

An exact analytical description of the internal radiative field inside an emitting-absorbing grey semi-transparent medium at radiative equilibrium, enclosed in a cylindrical annular cavity bounded by hot and diffusely reflecting surfaces is proposed. It is shown that the radiative field can be completely described by purely geometrical weighting coefficients which allow determining the temperature field for any combined heat transfer with radiation, so as the two-dimensional vectorial radiative flux field. It is worth noting that no ray effect occurs since the only numerical discretization is purely spatial. Some examples show that the proposed method gives perfectly smooth results of good accuracy for both the temperature and flux fields inside the medium.

► A semi-analytical analysis to the radiative transfer in cylindrical annuli is presented. ► Diffuse reflection at the boundary surfaces has been investigated. ► Weight coefficients which describe completely the problem have been defined and calculated. ► Numerical situations are presented and compared with available results showing excellent agreement.