Numerical analysis of effective thermal conductivity with thermal conduction and radiation in packed beds

Thermal radiation in a packed bed is controlled by temperature, emissivity, particle size, and bed structure, including void fraction, particle configuration, and the number of contact points. Thus, thermal radiation plays an important role in higher temperature operation of bed reactors. In this study, effect of the radiation/conduction ratio, namely, the Biot number with a thermal radiation coefficient, on effective thermal conductivity was investigated to clarify heat transfer in a packed bed. The Biot number for thermal radiation was defined as a function of temperature, particle size, emissivity, and configuration factor. The results obtained by the homogenization method showed that effective thermal conductivity with thermal radiation is simplified by the Biot number. Finally, the behavior of thermal radiation in the packed bed can be expressed by a sigmoidal function with the Biot number, even though the bed structure is complex.