Radiative transfer in a semitransparent glass foam blanket

In this paper a theoretical model is developed to analyse radiative heat transfer through a semitransparent (absorbing and scattering) foam blanket with application to glass melting. First, an approach for calculating the effective extinction (absorption and scattering) coefficients and scattering phase function for composite materials, such as glass foams in particular, is formulated based on the bubble size distribution function and the complex indices of refraction of the material components. Then a Schuster-Schwartzchild two-flux approximation is employed to solve a radiative transfer equation (RTE) which results in the analytical expressions for internal reflectance, transmittance and absorbance of the plane parallel foam layer. Both cases of collimated and diffuse radiation incidence are considered. Finally, the analytical expressions for total apparent reflectance, transmittance and absorbance of the foam layer are derived by accounting for external and internal reflecting boundaries of the layer. The results of sample calculations obtained using the theoretical methodology developed are reported and discussed in detail.