The gray body approximation for radiative heat transfer in evacuated tube solar collectors: Effects of envelope infrared transparency

A theoretical and experimental analysis is carried out of radiative heat transfer in the coaxial geometry of evacuated tube solar collectors. The gray body approximation implicit in the use of an effective emissivity does not strictly apply to evacuated tube solar collectors due to selective absorber coating and partially transmitting outer glass in the thermal infrared, especially when constructed from borosilicate. We develop analytic expressions for the heat transfer through the outer envelope and show the equations no longer follow a simple form where an effective emissivity for the system can be defined. To test all approximations in practice, an experiment is performed using an evacuated solar collector manufactured in the 1980s by the Nitto Kohki company in Japan using the effective emissivity approximation to determine the typical heat transfer characteristics using net radiative heat flows in both directions. This method enabled a good fit to temperature-time data for cooling and heating of the inner tube for temperatures between 10 and 85{\deg}C. The results confirm that the effective emittance method can be used in situations with typical glass wall thickness and temperatures. At temperatures greater 100{\deg}C, the spectral distribution of the emitted radiation falls significantly within the transmitting region of the outer glass and can no longer be neglected. The work has verified the stability of the vacuum in this type of collector as the tube still functions well, maintaining a low emissivity and good vacuum after approximately 40 years in storage conditions.