Numerical Modeling of Heat Flux in Fixed-Point Cells Due to the Hydrostatic-Head Effect

Abstract

The article presents the numerical analysis of a particular thermal effect, which occurs during the calibration of standard platinum resistance thermometers in fixed-point cells. The temperature within the fixed-point cell varies linearly with the immersion depth due to the hydrostatic-head effect, so a quasi-linear temperature gradient in the vertical direction is inherently present. If there is a temperature gradient, a resulting heat flux will appear. This heat flux flows across the thermal conductivities, which change with depth, so the resulting temperature field is distorted. The key issue that is tackled in this article is the magnitude of these temperature deviations and their influence on the measurement accuracy. This effect should not be confused with the perturbing heat exchange toward the thermal enclosure and ambient. These are independent effects that are in real systems superimposed on each other. To get a better insight into this phenomenon, a numerical model based on a finite-difference method was developed. The model allows the simulation of the measurement of the thermometer immersion profile and of the use of different bushings, as two of the methods for assessing the thermal effects. The results of the modeling showed that there is an inherent difference between the temperature measured by the thermometer sensor and the temperature at the point of the phase transition, even if the immersion depth was infinite and there was no perturbing heat exchange toward the thermal enclosure and ambient. Nevertheless, in several cases the thermometer would still almost perfectly follow the immersion-profile curve. The only exception is near the bottom of the cell, where a small deviation from the immersion profile was observed. This is in agreement with previously presented experimental results, where this behavior was noticed, but never satisfactorily explained.