A probabilistic study of the influence of parameter uncertainty on thermal radiation heat transfer

The influence of uncertainty in the boundary conditions on the solution of the radiative transfer equation is studied using probabilistic methods. We consider the problem of a heated slab, the surfaces and volume of which are at fixed temperatures. The basic problem stemmed from the need to study a hypothetical accident scenario in a fast breeder nuclear reactor in the cover gas region which may contain a sodium aerosol. The emissivities of the surface of such a region will be uncertain and estimates must be made. We demonstrate how the uncertainties in these data parameters are transmitted to the solution of the associated transfer equation and define sensitivity coefficients for the configuration factors. We also consider a number of different material surfaces, the emissivities of which are only known within certain limits, and obtain sensitivity coefficients for them as well as mean values, variances and, in some cases, the probability distribution of the configuration factors. A variational method is used to solve the basic equation, but for more general problems where such methods are inapplicable we describe a technique based on polynomial chaos theory.