Silicon Thermal Flow-Sensor Semi-ideal Model

Abstract

A so-called semi-ideal model has been derived for a pulse-operated MEMS thermal flow sensor by reciprocal numerical mapping of the ideal model of an instantaneous line heat source to the experimental data of the sensor. The novel model not only applies as a precise potential working equation for the sensor but also provides insight into the complete thermal signal transmission chain from the heater to the thermometers of the sensor. It gives answers to prominent peculiarities of the actual heat path of the sensor, prepares ways to improve its design, and offers guidance for a better control of the measuring process. The semi-ideal model was derived in order to replace the so far utilized empirical relations that require multiple calibration measurements. It was found out that the transient temperature profile of the sensor in response to an electrical pulse to the heater is substantially shaped by series thermal conduction of heat. Moreover, it is demonstrated that the impact of the thermal mass of a (practical) line heat source on its transient temperature and released enthalpy can be modeled by considering a virtual cylinder surrounding the source. The same analytical technique also applies for (practical) temperature stations. The findings of the study primarily concern the MEMS sensor. Nevertheless, the presented simple method of numerical mapping can be an effective analytical tool for mathematical modeling by means of numerical data analysis and function evaluation. The concept of a virtual cylinder can help in modeling the dynamics of practical pulsed heating.