Comonotonic global spectral models of gas radiation in non-uniform media based on arbitrary probability measures

Abstract

• A universal theoretical formulation of global methods for gas radiation is proposed. • Detailed mathematical treatments of non-uniform paths are described. • Relationship with copula theory is emphasized. • It provides a theoretical justification of the newly proposed Rank Correlated SLW model. The aim of the present work is to provide a universal theoretical formulation of global methods for radiative heat transfer in non-uniform gaseous media. Starting from the definition of an arbitrary probability measure on the wavenumber axis, it is shown that no gas reference state is required to develop rigorously a full spectrum model, both in uniform and non-uniform media. This general formulation, which constitutes a novel mathematical modeling of gas radiation, is then applied for: (1) the theoretical justification of new developments introduced recently in the so-called Rank Correlated SLW method in non-uniform media, (2) emphasizing the differences and similarities between the SLW and FSK methods, from the point of view of the way these two techniques treat path non-uniformities. The theoretical results provided in the present work can also be used to enlighten the concept of “spectral correlation”, widely encountered in gas radiation modeling.