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.
Highlights
In two previous reports by the same authors, a single-short-pulse thermal flow sensor on a chip has been introduced [1, 2]
The objective of the present experimental, numerical, and theoretical study is to create an analytical model of the transient temperature behavior of the sensor to replace the existing two mode-specific empirical data reduction equations
The second method, the numerical one, deals with five differentordered datasets, n-tuples, each of n = 501 members, comprising the experimental and the related theoretical data. These are (1) the sequence of the observation time points themselves, ⟨t⟩ ; (2) the sequence of experimental voltage points, ⟨U⟩ ; (3) the sequence of fitted voltage data according to the regression model, Eq 6, ⟨R⟩ ; (4) the sequence of calculated voltage data according to the ideal model, Eq 1; ⟨I⟩ ; and the fifth set presents the solution data, ⟨SI⟩, the sequence of voltages calculated from the novel semi-ideal model of the pulsed thermal flow (PTF) sensor
Summary
In two previous reports by the same authors, a single-short-pulse thermal flow sensor on a chip has been introduced [1, 2]. The objective of the present experimental, numerical, and theoretical study is to create an analytical model of the transient temperature behavior of the sensor to replace the existing two mode-specific empirical data reduction equations. In addition to the existing mode-specific empirical working equations, a fit function for the transient output signal of the device is available. It reliably predicts both measurands, ΔTmax and tmax. Attempts to generate relationships between the purely numerical fit-parameter set and the actual measurands revealed that the transient temperature response of the PTF sensor is too complex to be modeled within the idealized scenario of the selected heat equation solution. It has to be decided whether the restriction(s) that has/have to be obeyed are soft or hard with respect to the above-mentioned basic discrepancies
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