Combined Radiation and Conduction in Glass Foams

Abstract

Understanding of heat transfer in glass foams and the development of theoretical tools for predicting heat transfer properties of glass foams is critical to improving the efficiency of glass manufacturing. In this paper, combined radiation and conduction heat transfer in a semitransparent glass foam layer is analyzed. The foam layer is thin and of the uniform thickness, bounded by hot combustion gases on top and glass melt on bottom, and exposed to isotropic radiation originating from hot refractories. Heat transfer is assumed to be one-dimensional perpendicular to the plane-parallel foam layer. A previously developed model is used to calculate effective extinction coefficients and scattering phase function of the foam layer using a void size distribution and assuming all voids to be spherical. These radiation properties are then used along with a Schuster-Schwarzchild two-flux approximation to solve the radiative transfer equation (RTE). A method for obtaining the effective thermal conductivity of the foam layer is also presented. The RTE and the energy conservation equations are simultaneously solved using a numerical iteration procedure. The effect of foam thickness and bubble size on the temperature distribution in the foam layer is studied.