Radiative heat transfer in a semi-transparent medium enclosed in a two-dimensional square cavity

An exact analytical description of the internal radiative field inside an emitting-absorbing gray semi-transparent medium at radiative equilibrium, enclosed in a square cavity bounded by hot and black surfaces is proposed. It is shown that purely geometrical coefficients (in the case of optical constants non-depending on the temperature) completely describe the radiative field inside the cavity. The temperature field and two-dimensional vectorial radiative flux field are then easily deduced. It is worth noting that no angular discretization has to be done (no ray effect), the only numerical discretization being 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.

Research Highlights► A new semi-analytical solution to the radiative transfer equation is presented. ► A two-dimensional square cavity with three different temperature boundary conditions has been investigated. ► Weight coefficients which describe the problem completely have been defined