An approximation function model for solving effective radiative heat transfer in packed bed

Radiative heat transfer is significant but rather complicated in the bed packed with lots of high temperature particles. Unfortunately, it cannot use traditional radiative transfer equation (RTE) to efficiently predict thermal radiation between particles in packed beds. With continuum assumption, an approximation function model (AFM) is proposed here. A generic physical equation of radiation exchange factor of packed bed is given, which is determined by surface emissivity and particle-scale packing structure. Compared with discrete element method (DEM) simulation, current radiation interaction function (RIF) gives a good estimation of the obstructed view factor of packed bed. The radiation in AFM is equivalent to that of heat conduction at size parameter ξ ≪ 1, and effective thermal conductivity (ETC) in central region of packed bed is higher than that of the whole bed. The AFM is also applicable for pebble bed with both radiative and conductive heat transfer, and it can predict consistent radial temperature distributions with that in experiments. The AFM works as a good replacement of traditional radiative transfer equation (RTE), and is also feasible to apply current equation to analyze other radiation models.