Radiative heat transfer in an absorbing-emitting semi-transparent medium enclosed in a two-dimensional parallelogram cavity with diffuse reflecting boundaries

An exact analytical description of the internal radiative field inside an emitting-absorbing gray semi-transparent medium at radiative equilibrium, enclosed in a two-dimensional parallelogram cavity bounded by diffuse reflecting surfaces is proposed. The exact expressions of the incident radiation and the radiative flux field are angularly and spatially discretized with a double Gauss quadrature, and the temperature field is obtained in an iterative way. Some examples show that the proposed method gives perfectly smooth results of good accuracy for both the temperature and flux fields inside the medium.