Interaction of Radiation and Conduction in Glass

Abstract

The interaction of radiation and conduction was rigorously treated for one-dimensional heat transfer, both transient and steady-state. In this paper only some steady-state results are discussed. They show that the interaction of radiation and conduction affects temperature distributions and heat fluxes in a variety of ways, depending on physical properties and boundary conditions. The illustrations include a computer simulation of experiments to measure the thermal conductivity of glass and an attempt to predict the vertical temperature profile in a glassmelting tank.

Heat Transfer During Glass Forming

“…Discarding the earlier concept of apparent radiative conduction, which was dependent upon the glass thickness, and which did not take into consideration the effects of the glass surface or multiple reflections, Gardon (1956Gardon ( , 1958Gardon ( and 1961 was the first to develop a model incorporating radiation in a comprehensive manner [also Chui and Gardon (1969)l. McGraw (1961) used the Gardon-type model to interpret his experimental data for thin glass sections and found that radiation played an unimportant role in the heat transfer during normal pressing operations.…”

Spectral and boundary effects on coupled conduction-radiation heat transfer through semitransparent solids

“…factor of 5. Chui and Gardon [3] have made a similar comparison under the more favorable condition of a smaller temperature gradient and found the total energy transfer to be in error by a factor of 2. The radiative conductivity as computed by Rosseland's approximation is hence inadequate even for estimation purposes.…”

“…With the exception of gases, little is known about simultaneous energy transfer m realistic nongray materials and the influence of the emission-reflection characteristics of the bounding surfaces. Notable exceptions are the works of Gardon, et al [2,3] which employed a band model for the absorption spectrum of glass, Crosbie and Viskanta [4] in which two rectangular spectral absorption coefficient models were studied, and Timmons and Mingle [5,6] who investigated the effect of specular and directional emission-reflection by the bounding surfaces on the energy transfer through gray materials. Men and Sergeev [7] have also studied simultaneous heat transfer through fused quartz, selenium-arsenic glass and cadmium sulfide for conditions modeling a melting tank.…”

Thermal analysis for transient radiative cooling of a conducting semitransparent layer of ceramic in high-temperature applications

“…The values of temperature at the Gaussian abscissas are obtained using cubic spline interpolation [20], with temperature specified, the values of R and dR/dt are obtained from the solution of Eqs. (2), (3), (11) and (12). The exponential integral functions E 3 and values of R and dR/dt are then calculated using the Nystrom interpolation [20].…”

“…Much research has been directed toward the combined effects of conduction and radiation in glass. Chu and Gardon [12] under took the study of combined transfer in gray glasses. Su and Sutton [13] predicted temperatures and heat fluxes with 16 spectral bands in the silicate glass plate Nomenclature D thickness of the medium, m E 1 , E 2 , E 3 the exponential integral functions, E n ðxÞ ¼ R 1 0 l nÀ2 À expðÀx=lÞ dl k thermal conductivity of the medium, W/m K N conduction-radiation parameter, k=4rT 4 i D n refractive index of the medium Q incidence radiation, W/m 2 q 1 , q 2 radiosity from the interior of the two boundaries, W/m 2 q 1 ; q 2 dimensionless radiosities, [14], and more recently, I and my colleague, [15], used finite difference procedure to predict transient temperature distribution in a semitransparent material with a refractive index of one.…”