Direct solar absorption and storage in a molten glass thermocline

At high temperature, the effective thermal conductivity of molten glass becomes dominated by its transparency in the UV-to-2-micron passband. In the previous post it was calculated that molten glass at 2000 degrees K, with a 1/e (i.e., -4.3 dB) absorption length of 1 meter in the UV-to-2-micron passband (a loss rate of 4300 dB/km) would have an effective thermal conductivity of about 456 W/m-°K. The correlations for molten glass reported by Laurent Pilon et al., summarized in this chart, indicate an effective thermal conductivity of molten soda-lime glass at 2000 °K of 137 W/m-°K. From that value it can be estimated that the 1/e absorption length of soda-lime glass of commercial purity is about 137/456 m = 0.3 m. That is a figure that comports with everyday experience (e.g., looking through a glass panel edgewise.)

Thermophysical properties of molten glass at high temperature, including effective thermal conductivity, calculated from correlations in Laurent Pilon et al.

Absorption in the UV-to-2-micron passband of glass is almost entirely due to metal ion impurities, mainly iron. Thus improving the purity of ordinary glass by a factor of ten would extend the absorption length to 3 meters and increase effective thermal conductivity to about 1400 W/m-°K—about three times the room-temperature thermal conductivity of silver.

High effective conductivity also suppresses natural convection since natural convection starts out as a wiggle in an isotherm that enlarges by gravitational instability—despite viscosity slowing it down—faster than it can be damped out by thermal diffusion.

Solar radiation is 90% within the UV-to-2-micron passband of glass, so it plays by the same rules as the conductivity-dominating thermal radiation. A net flux of say, 0.4 MW/m2, onto the top of the glass melt will not penetrate any more deeply if it is the result of solar radiation or thermal radiation (aka, effective conduction.) Sunlight has relatively more short wavelength energy, of course, but under the assumption of spectrally uniform absorption in the UV-to-2-micron band, this makes no difference.

Flux is flux. That greatly simplifies modeling.

Solar heating of a glass melt from above stores heat in a stable thermocline. Later radiant cooling of the melt from above "excavates" the stable thermocline removing heat by natural convection from successively deeper and deeper levels until the whole melt is at the "empty" temperature. Temperatures in the diagram are measured relative to empty. Modeled in Energy2D.  Depth 10 m, absorption length 10 m, shown after 6 hours of solar heating.