A Formulation of the Theory of Interreflection

As generalized equations for expressing the steady state of interreflection, a linear equation and an integral equation are formulated which are capable of representing interreflection in systems of non-diffusely reflecting surfaces having arbitrary configuration and arbitrary emission characteristics. Methods of solving these equations are considered and as for the integral equation the significance of applying the successive substitution method is pointed out. This method is successfully applied to some substantial systems, giving clear physical interpretation and useful mathematical expression of their state, namely, (1) the superposed state of emission and multiple reflections, (2) the thermodynamic equilibrium in completely closed cavities of uniform wall temprature.(3) departure from the thermodynamic equilibrium, effective emissivity, effective absorptivity and effective reflectivity of incompletely closed cavities of non-uniform wall temperature are analysed. Relation of the present work to the previous ones, especially those of Buckley, Yamauti, De Vos, Nakaji, Sparrow and Kelly is discussed