Effects of radiation on the effective thermal conductivity in packed beds

Abstract

A multiple-layer model for packed beds is presented and discussed in this contribution aiming at dealing with the radiation and conduction phenomena and their mutual interaction. According to the multiple-layer model, the bed is geometrically represented as a succession of identical layers of mono-sized spheres in the direction of the temperature gradient. Grey and opaque particles with sizes much larger than the thermal radiation wavelength and diffuse emission and reflection in a non-participating fluid are assumed. Under these hypotheses and some other proper simplifications, close and relatively simple expressions for the radiative and for the conductive contributions to the effective thermal conductivity can be derived, in which the coupling of conductive and radiative parameters clearly arises. This approach has been termed “half layer approximation” (HLA) and the associated expressions can be easily implemented in any basic computing platform. The HLA features and estimations are compared with the well-known expressions of unit-cell models and other multiple-layer approaches. In addition, results from the HLA are successfully validated against numerical simulations using the Monte Carlo method and a large set of experimental data from several sources, covering a wide range of temperatures in beds of a variety of particle materials and sizes.