Radiative entropy production

Abstract

THE radiative tensor obtained from the specular moments of the transfer equation is considered. The radiative entropy production is expressed in terms of this tensor. Contents The theory of gas radiation dates back to studies Rayleigh made over a century ago on the illumination and polarization of the sunlit sky. Since then, the theory has rapidly grown because of the efforts of astrophysicis ts and later of applied scientists and engineers. However, the entropy production associated with radiation apparently remains untreated and is the motivation of this study. As is well known, the entropy production results from dissipative processes (involving mass, species, momentum, and/or heat transfer and electromagnetic or nuclear transport). Less known is the fact that the dissipation may have a diffusive or hysteretic origin, the diffusion being directional and the hysteresis being cyclic. However, except for a few cases (such as strain hardening and the magnetic saturation), the majority of dissipative processes (including the dissipation of radiation) are of diffusive nature. A recent study by Arpaci 1 shows, in terms of the radiative stress obtained from the specular (kinetic) moments of the transfer equation, the diffusive nature of radiation for any optical thickness. Accordingly, the expression to be developed for entropy production is in terms of this stress and includes also the dissipation resulting from the conduction of heat and viscous friction. First, some remarks on the radiative stress are needed. These will be made in terms of spectrally averaged radiation because of its simplicity. A monochromatic approach, which may be needed for a quantitative study, is not essential here because of the conceptual nature of the intended study. As pointed out by Felske and Tien,2 there are a variety of practical situations in which scattering is not important. For these situations, consider the spectrally averaged transfer equation,