The steady energy transfer equation for simultaneous conduction and radiation in an absorbing, emitting, and nonscattering gray planar medium is studied theoretically. For extremely high-temperature applications, where radiative transfer plays an important role, ceramic-matrix composites, considered as semitransparent materials, are being explored for potential use in turbine and compressor components, spacecraft structures, engine control systems, and nuclear reactors. Exact solution of the above-mentioned radiative problems is seldom possible and time-consuming numerical approximations are then used. A technique combining an accurate physical formulation, the two-flux model, coupled to a fast numerical procedure for the calculation of the temperature and heat fluxes is described.

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