MODELLING RADIATIVE HEAT TRANSFER IN FIBROUS MATERIALS: THE USE OF PLANCK MEAN PROPERTIES COMPARED TO SPECTRAL AND FLUX-WEIGHTED PROPERTIES

Abstract

Radiative heat transport is investigated in a layer of fibrous insulation under steady-state conditions. The radiative heat transfer is modelled using the two-flux model, where the radiative properties are either Planck mean, flux-weighted or spectral properties. The purpose of the work is to investigate the accuracy of the radiative flux obtained using Planck mean properties, by comparing with spectral calculations. This is achieved by deriving and investigating a mathematical basis for applying Planck mean properties in the two-flux model and by comparing Planck mean properties to flux-weighted properties, defined in such a way that the same solution is obtained as in the spectral calculations. The mathematical assumptions justifying the application of Planck mean properties are correct within ±1% for wavelengths greater than approx. 10 μm. For wavelengths ranging from 1 to 10 μm, the deviation is up to 60%. Using Planck mean properties, the radiative heat flux in the centre of the fibrous insulation is underpredicted by about 15% for porosities lower than approx. 0.995 and less for higher porosities. The solution of radiative heat flux depends to a large extent on the asymmetry in the flux-weighted properties. For example, if the flux-weighted properties are asymmetric within 1%, the radiative heat flux increases by a factor of 5 and 14 in cases with a porosity of 0.98 and 0.9937, respectively. The asymmetry in the flux-weighted properties may explain why the small deviation from the mathematical assumption leading to the Planck mean gives large errors.