Mathematical modelling of industrial thermometers

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Abstract
The dynamic response of temperature sensors is of importance to both the designer and user of sensors. Understanding the factors affecting the dynamic response of such sensors would be beneficial. The present paper reports on research conducted in the development and application of mathematical models to predict the dynamic behaviour of a complex thermometer assembly. It is shown that such models can be used to predict step fluid temperature responses and deliberate self-heating responses both to within a few per cent. Distributed-parameter and lumped-parameter models were developed and validated for a platinum resistance thermometer with and without a well. These relate thermometer performance to material properties and detailed geometry and hence to constructional features. Such models can be used for (a) thermometer design studies including sensitivity analysis to find the significant contributions to the thermometer dynamics and (b) in situ response testing from the electrical port using the deliberate self-heating response. These application areas are briefly discussed.

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