Geometric optics based analysis of radiation heat transfer in glass melting furnace foams

Abstract

AbstractThe paper describes a simple, geometric optics‐based model to analyze thermal radiation through glass foam layers that form on the surface of the glass melt in many industrial glass melting operations. The large value of radiation size parameters (>1000) characteristic of glass foams combined with an idealized foam morphology is used to derive recursive algebraic relations relating the effective reflectivity, transmissivity, and absorptivity of the foam to key parameters of gas bubble size, porosity, thickness, and glass melt absorption spectra. A sample of calculated results are presented to illustrate the application of the model. The findings are in qualitative agreement with what is known from practice and more elaborate analyses involving Mie scattering and solution of radiation transport equations. The analysis of extinction coefficient for the foam reinforces the physical intuition that, for the large size parameter characteristic of glass furnace foams, the scattering from the bubble is equivalent to reflection from a planar surface. The combination of simplicity and essential physics of radiation through glass foams makes the model developed here ideally suited for both glass manufacturing engineers and the glass furnace modeling community.