Effective thermal conductivity of high-purity glass melts

The effective conductivity of high-purity glass melts increases rapidly with temperature because the melt is semi-transparent to its own thermal radiation. At wavelengths shorter than 2 microns a high purity glass melt may permit its own thermal photons to travel some meters, in some cases even tens of meters, before being re-absorbed. At temperatures used for solar thermal storage, 1840 °K to 2070 °K, about a quarter to a third of blackbody radiation is in the below-2-micron passband of glass. Since effective thermal conductivity is proportional to the average distance a blackbody photon travels before it is reabsorbed, the effective conductivity of a glass melt is a function of its level of purity.



At absolute temperature T, blackbody radiation is

σT⁴,

where σ is the Stefan-Boltzmann constant,

σ = 5.7 E−8 W m−2 K−4 .

The derivative of blackbody flux with respect to T is:

 4σT³ W/m2-°K,

 which is the transfer between two blackbody surfaces differing slightly in temperature. At glass-melt storage temperatures only about a quarter of the blackbody radiation is in the below-2-micron passband of the melt, so we are only concerned with a differential flux of about

σT³ W/m2-°K.

If the average temperature is 2000 °K and photons in the passband travel a distance of one meter, the effective thermal conductivity (ignoring actual phonic conduction which will be relatively small) is

(5.7 E−8 W m−2 K−4)(2000 °K)³(1 m) = 456 W/m-°K

Compare the thermal conductivity of silver at room temperature is 429 W/m-°K.