A numerical and experimental investigation of the heat losses in thermometric fixed-point cells

Heat loss is one of the key parameters that cause temperature errors during the calibration of thermometers in metal-freezing-point cells and thus increases the measurement uncertainty. At temperatures above the freezing point of tin, thermal radiation becomes the dominant mode of heat transfer. In addition, radiative heat transfer is especially important in the cells' glass structures, where total internal reflection (known as “light piping”) can occur. A quantitative measure of the radiative heat loss is difficult to determine with measurements, but a qualitative check can be performed by measuring the vertical temperature profile in a cell during a freezing-point realization. These measurements can be interpreted with numerical modeling, but most commercial tools do not provide sufficient rigor for this particular task. Our custom-built model is capable of modeling both the radiative and conductive heat transfers and can deal with complex radiation phenomena specific to the particular case study. The model is based on established finite-difference and discrete-ordinates methods, but the major novelty is a comprehensive treatment of radiation intensity on the glass-air boundary, with special emphasis on radiation scattering. Through the introduction of a scattering factor, the influence of the level of sandblasting of the glass parts on the light piping can be modeled although currently this factor cannot be experimentally determined for specific glass geometries at higher temperatures. The modeling and experimental work should be used together in an iterative process, where experiments confirm the validity of the model and the model is used to interpret the results of the experiments. The modeling and experimental results are used to give an estimation of the error due to heat losses.