Natural element method for NON-GRAY radiation heat transfer problems

Abstract

A radiation code based on the meshless Natural Element Method (NEM) for spatial discretization and on the Discrete Ordinates Method (DOM) for angular discretization of radiative transfer equation was developed for realistic calculation of the radiative heat transfer in two-dimensional complex geometries containing real gases with non-gray behavior (namely mixtures of H2O, CO2 and N2). The spectral line-based weighted-sum-of-gray-gases (SLW) model was used to calculate the radiative properties of the medium. The boundaries are assumed to be opaque, diffuse and gray. The shape functions in the NEM are constructed by interpolations from the natural neighbors, and the essential boundary conditions can be imposed directly. The predictive accuracy of the proposed method is assessed by applying it to five test problems and comparing its predictions with other numerical solutions reported in the literature. The predictions are also compared with those of the gray gas model. A good agreement was observed between the results of the NEM/DOM/SLW method and other numerical methods, and it is shown that the natural element method has good accuracy, and can be used for the solution of radiative heat transfer problems in irregular enclosures containing non-gray media.