Modeling of the heat loss in a thermal sensor for water made of NTC thick film segmented thermistors

Abstract

NTC thick film segmented thermistors were realized by screen printing of a low resistivity paste and conductive PdAg paste printed for electrodes. Two thick film thermistors as thermal sensors were placed in plastic tube housing connected to the water mains to form a calorimetric type of flow-meter, e.g. to measure the input water temperature and the thermistor self-heating temperature. Range constant voltage (RCV) was applied for self-heating thermistor power supply in different ranges of input water temperature. Modeling of the heat loss in the flow-meter for water was derived from heat balance equations for a self-heated thermistor in static water and in water flow conditions (static and dynamic thermistor temperature). Both temperatures (static and dynamic) were related to self-heating currents. The input water temperature was measured independently by a cold thermistor. Other parameters such as water thermal conductivity, thermistor exponential factor B and nominal thermistor resistance at room temperature were included in the thermistor heat balance equations. The logarithmic behavior of self-heating thermistors in the water flow enable modeling of heat loss as a function of static and dynamic currents related to static and dynamic thermistor temperatures. The model achieved was used in the fitting procedure of measured data of the flow-meter response.