Alternative Approach to Solving the Radiative Transfer Equation

When polymeric, metal, or ceramic cellular materials are subjected to high-temperature conditions, heat transfer rates are mainly governed by radiation, and the analysis of this volumetric heat transfer phenomenon is complex because of the directional and spectral nature of the radiation propagation. Thus, this work presents an alternative approach for solving the radiative transfer equation in rectangular and cylindrical coordinate systems for gray and nongray media. The solution method is based on a combination of the fundamental principles of the physical phenomenon (balance law for the variation of the radiation intensities), the formal solution of the radiative transfer equation (RTE), and the use of the discrete ordinate method (DOM, to handle the directional dependence of the radiation). The performance of the proposed method was evaluated for classical 2D and 1D cylindrical and planar problems. The results obtained using the proposed approach agreed with those published in the literature for radiation-only or coupled conduction–radiation problems. Therefore, the proposed method can be an alternative tool for solving the integral–differential radiative transfer equation for participant (semitransparent) media.