Two-Mesh Method for Coupled Conduction-Radiation Computations in Multi-layer Systems

The study aimed to develop a new method for coupled conductive-radiative heat transfer computations in multi-layer systems, potentially reducing the computational cost with as little as possible loss of accuracy. The analysis focused on the accuracy of obtained predictions without aiming at simulation time. The general concept of the proposed two-mesh method is to use separate grids of different densities (number of elements) to solve the radiative transfer equation (coarser mesh) and other equations, e.g., energy equation (finer mesh). Due to the coupling of equations, the appropriate data transfer methods were proposed. The temperature field from the energy equation solution needed as input for the thermal radiation model was provided using volume averaging. A much more sophisticated approach was developed to provide information on radiation incident intensity, which is the output from the radiation model. An approximation using radial basis functions was used with an appropriate normalization to ensure the conservativeness of the approach. The finite volume method was applied to solve the energy and radiation transfer equations for a non-gray, multi-layer medium, accounting for the optical phenomena on interfaces. An extended analysis of the implemented method was conducted considering the effects of the share of thermal radiation in the total heat transfer, the optical thickness of the medium, the occurrence of optical phenomena at boundaries, the type of boundary conditions, and the wavelength dependence of thermal radiation. The improvement of solution accuracy using the proposed approach over coarse mesh computations was most pronounced close to the cold wall.