Definition and Evaluation of Mean Beam Lengths for Applications in Multidimensional Radiative Heat Transfer: A Mathematically Self-Consistent Approach

A set of mathematically self-consistent definitions of mean beam length is introduced to account for surface-surface, surface-volume, and volume-volume radiative exchanges in general three-dimensional inhomogeneous medium. Based on these definitions, the generic exchange factor (GEF) formulated by the recently introduced multiple-absorption-coefficient-zonal-method (MACZM) can be written in an equivalent one-dimensional form. The functional behavior of the proposed mean beam lengths is shown to be readily correlated by either simple algebraic relations or neural network based correlations. They can be implemented directly with MACZM in general computational code to account for the radiation effect in complex three-dimensional systems. In addition, these definitions of mean beam length can also be used to assess the accuracy of the conventional mean beam length concept currently used by the practicing engineering community.