Modelling radiative heat transfer in packed beds

Abstract

A comprehensive approach for modelling dependent radiative heat transfer in beds of large (geometric range) spherical particles is presented. Such a system of large spheres lies in the dependent range even for large porosities. We show that the dependent properties for a bed of opaque spheres can be obtained from their independent properties by scaling the optical thickness while leaving the albedo and the phase function unchanged. The scaling factor is found to depend mainly on the porosity and is almost independent of the emissivity. We show that such a simple scaling for non-opaque particles is not feasible. The transparent and semi-transparent particles are treated by allowing for the displacement across an optical thickness (because of transmission through a particle) while solving the equation of radiative transfer. When combined with the scaling approach, this results in a powerful method of solution called the dependence included discrete ordinates method (DIDOM). The results obtained from the DIDOM give good agreement with the results obtained from the Monte Carlo method.

Optimization Method for Developing Spectral Controlling Cosmetics: Application for Thermal Barrier Cosmetic

“…A considerable difference arises in the dense cosmetic layer on account of dependent scattering, which is actually a mutual influence of scattering particles. Dependent scattering has no effect on the phase function [16]. Dependent scattering is assumed in our calculations.…”

Radiative heat transfer in enhanced hydrogen outgassing of glass

“…The difference lies in the fact that effective thermal conductivity of the bed must be used and scattering by the hollow microspheres must be accounted for. Heat transfer analysis in packed beds [48][49][50][51] can be adapted to predict the temperature inside a bed of hollow glass microspheres heated by a resistive 20 heater or an incandescent lamp.…”

Modeling of thermal radiation of polymer coating containing hollow microspheres

“…As a result of obvious substitutions, we derive . (19) Therefore, the problem is closed: at the first step of solution in calculating the radiation transfer we assume ∆T = 0; after that, we use formula (19) and repeat the calculations.…”

“…Modern methods of calculation of interaction between an electromagnetic wave and clusters containing spherical and nonspherical particles are described in reviews [10,11] and in the monograph [12]; important particular cases are treated in [13][14][15][16][17]. The monograph [18] is devoted to the study of radiation characteristics of close-packed disperse systems; solutions for particular cases are given in [19][20][21][22]. Nevertheless, no general computational model exists at present that would be suitable for describing the radiation field in an arbitrary semitransparent coating with disperse phase.…”