Determination of the effective temperature of a flat layer of nontransparent medium with emitting and reflecting walls

By means of exact solution of the radiation transfer equation in nontransparent nonscattering media bounded by surfaces with different radiation properties, an expression is obtained for the intensity of radiation emitted from a layer. For an axisymmetric temperature distribution, the hemispherical effective blackness degree of the layer is found. An expression is derived for determining the effective temperature of a nonisothermal layer, which depends on the form of the temperature profile and the optical thickness of the medium. Eight types of temperature distribution of practical importance along the layer are considered, for which the limits of applicability of the mean-arithmetic and mean-geometric methods of determining the temperature are found.