An ‘effective angle model’ is proposed for evaluating the radiation source term in flows of non-isothermal absorbing/emitting media confined within rectangular and cylindrical ducts. While the model possesses the simplicity of two-flux schemes, it incorporates the influence of the enclosure geometry, and is particularly suitable for parabolic flows since the source term is based on the properties of the current marching station in the solution procedure. The model is first developed for two-dimensional geometry and applied to a test case of a gray medium reproducing analytical results within a few percent. It is next applied to a two-dimensional slot burner with radiation from fuel and products of combustion accounted for, and is shown to compare favorably with a detailed calculation of the source term. With some modification, the model is extended to a cylindrical gas-fired burner. A study of various parameters and different types of boundary conditions demonstrates the promise of the model.