Radiative heat transfer in processing of glass‐forming melts

Abstract

The paper summarizes the findings of a study on mathematical modeling of heat transfer in glass melts using the commonly employed diffusion or Rosseland approximation (R) for optically thick media and the more general, spectral discrete ordinates (DO) approach. The systems considered were the melting of an ultra‐clear glass in a furnace (optical thickness ~ 10) and heat transfer in 2 glass melts with different levels of iron oxide flowing through a delivery channel (optical thicknesses of ~17 and ~80). The results showed that the use of the R approach for modeling heat transfer in the ultra‐clear glass will lead to serious errors in the prediction of important practical parameters such as the refractory temperature, energy efficiency, and the quality of glass melt. The results for the channels showed that differences between the 2 thermal radiation models began to narrow as the optical thickness value approached 17. The paper also presents brief reviews of high‐temperature absorption spectra of commercial glass melts and the theoretical background on thermal radiation in participating media. In addition, a relatively simple system involving 1‐dimensional radiation heat transfer in a participating medium is used to illustrate the implications of using the diffusion approximation.

Characterization of high temperature optical spectra of glass melts and modeling of thermal radiation conductivity

“…In several studies, see for example Ref. [1,2] the determination of the so-called Rosseland, thermal radiation or photon conductivity from high temperature optical spectra of glass melts has been described.…”

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

“…Silicate glass melts are semitransparent to radiation below the wavelength of about 4 μm and opaque at wavelengths greater than this value. Figure 2 shows the absorption spectrum of a fiberglass melt at 1473 K. 10 When viewing absorption spectrum such as that shown in Figure 2, it should be remembered that for any given composition, there can be considerable variation in the spectra depending upon the amounts and nature of the transition metal ions present and on the oxidation state of the glass. As seen in Figure 2, the glass melt is weakly absorbing in the 0.7 < λ < 2.5 μm wavelength range.…”

Modeling batch melting: Roles of heat transfer and reaction kinetics

“…Nevertheless, estimating the melting rate based on the heat‐transfer properties of the batch blanket still dominates the commercial CFD market of glass melter models, being used by many companies worldwide . This is because implementing the heat transfer model is relatively simple, and because when such a model is validated by operational data from a particular plant, it provides acceptable boundary conditions for the CFD model of the molten glass below to resolve the molten glass flow and temperature in the furnace.…”

“…Numerical simulations of large‐scale industrial melting processes that involve heat and mass transfer, electrical and combustion heating, chemical reactions, and multiphase flow are exceedingly computationally intensive . Despite continuous advances in high‐performance computing, CFD models still have to resort to various simplification techniques, such as grids that are too coarse to resolve bubbles in molten glass (this also includes cases with forced bubbling, where only the force that bubbles exert on the glass is simulated, not individual bubbles), or employing simplified approaches to radiative heat transfer modeling (eg, the Rosseland approximation instead of the ray tracing methods).…”