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This paper seeks to review the literature on methods for solving the radiative transfer equation (RTE) and integrating the radiant energy quantities over the spectrum required to predict the flow, the flame and the thermal structures in chemically reacting and radiating combustion systems.

The focus is on methods that are fast and compatible with the numerical algorithms for solving the transport equations using the computational fluid dynamics techniques. In the methods discussed, the interaction of turbulence and radiation is ignored.

The overview is limited to four methods (differential approximation, discrete ordinates, discrete transfer, and finite volume) for predicting radiative transfer in multidimensional geometries that meet the desired requirements. Greater detail in the radiative transfer model is required to predict the local flame structure and transport quantities than the global (total) radiation heat transfer rate at the walls of the combustion chamber.

The RTE solution methods and integration of radiant energy quantities over the spectrum are assessed for combustion systems containing only the infra‐red radiating gases and gas particle mixtures. For strongly radiating (i.e. highly sooting) and turbulent flows the neglect of turbulence/radiation interaction may not be justified.

Methods of choice for solving the RTE and obtaining total radiant energy quantities for practical combustion devices are discussed.

The paper has identified relevant references that describe methods capable of accounting for radiative transfer to simulate processes arising in combustion systems.