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Title: Thermal Mass Flow Sensor Similarity Theory - Comparison With Experiments
Author: Chiun Wang
Source: 2008 Measurement Science Conference
Year Published: 2008
Abstract: A similarity theory was previously proposed for the thermal mass flow sensor to describe the nonlinear relationship among the sensor output, the gas flow rate, and the gas thermal-physical properties. In a compact form, the theory expresses the ratio of the sensor output to the gas thermal conductivity, S/k, as a function of the Peclet number of the flow in the sensor tube in a compact form. In the present paper, the similarity theory is further compared against experimental data collected from various semi-conductor process gases using mass flow controllers equipped with constant-temperature capillary thermal mass flow sensors. The similarity theory was primarily confirmed by scaling the live-gas data using gas thermal-physical property constants listed in common physics and chemistry handbooks. Minor discrepancies between the experimental data and the theory are associated with: (1) the simplifying approximations made in deriving the heat transfer mathematical theory leading to the similarity model and (2) uncertainties in the gas thermal-physical property constants used for the data analysis. For practical applications these discrepancies were compensated by adjusting the gas specific-heat and thermal-conductivity coefficients by using two multiplying constants, ec and ek respectively, until the theory and the data match to within tight tolerances. Among the 20 or so semi-conductor process gases tested, the established multiplying constants are all fairly close to 1, suggesting that the current thermal-mass flow sensor theory is sound. Although the original similarity theory was developed for the constant-temperature thermal mass flow sensors, an argument is provided to show that the theory might also be used to explain the operation of a constant-current thermal mass flow sensor and its gas conversion factors.

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