Upgrading the dynamic mathematical model of temperature sensors in gaseous media for low Biot number (Bi < 0.1)

Abstract

A mathematical model incorporating the transient response of NTC thermistors is presented. The internal thermal conduction resistance of the sensor relative to the thermal convection resistance of the medium results in a low Biot number , yielding a fast dynamic response in gaseous media. This is advantageous in applications requiring minimal fluid interaction. However, negligible energy exchanges occur, introducing measurement uncertainty and ignoring the behavior of the measuring instrument. Therefore, this work proposes an improvement strategy for the mathematical model of these sensors, complementing the conventional model based on the concept of time constant. The strategy considers the heat flow through the thermistor wires in the energy balance, assuming they are semi-infinite solids and applying an approximation to the heat flow formula. Satisfactory improvement results were obtained compared to the conventional model, based on controlled laboratory tests with various gases.