DEVELOPMENT OF A GENERALIZED ZONAL METHOD FOR ANALYSIS OF RADIATIVE TRANSFER IN ABSORBING AND ANISOTROPICALLY SCATTERING MEDIA

Abstract

The generalized zonal method ( GZM) for the analysis of radiative heat transfer in absorbing, emitting, and anisutropically scattering media is developed and implemented. It is shown to be applicable both for media with arbitrary scattering phase function and general nondiffuse reflecting surfaces. Mathematically, the GZM is a generalization of the conventional zonal method ( CZM). In addition to the exchange factors utilized by the CZM, the GZM introduces scattering and reflecting exchange factors. These factors characterize the scattering properties of the medium and the reflectivities of the bounding surfaces. Expressions for the scattering and reflecting exchange factors are shown; their numerical and analytical properties are identified. To illustrate the implementation of the GZM, cubic enclosures in radiative equilibrium are analyzed. Based on numerical data, the effect of anisotropic scattering on three-dimensional radiative heat transfer is assessed.