Independent theory versus direct simulation of radiation heat transfer in packed beds

Abstract

Radiation heat transfer in packed beds of relatively large spherical particles is considered. The common practice is to follow the theory of independent scattering as long as C/[lambda]/s > 0.5, where C is the average interparticle clearance and[lambda] the wavelength. The single particle properties are related to the radiative properties of the bed by volume averaging. The equation of transfer is then solved by an approximate method such as the method of discrete ordinales or the two-flux method. In this study, the Monte Carlo method is used to examine the thermal radiative transfer through packed beds of large (geometric range) particles. Opaque, semi-transparent and emitting particles are considered. The results are compared to the independent theory and to the available experimental results, and they indicate that the independent theory fails even when this C/[lambda] criterion is satisfied. The success of independent theory in systems with low porosities, noted by previous researchers, is shown to be either a special ease existing only for a small range of the optical properties or arising due to some unjustifiable assumptions. For the same radiative particle properties, the deviation from the independent theory is shown to increase with decrease in the porosity. This deviation can be significant even for porosities as high as 0.935.