Mathematical model of the thermistor fire detector

Viacheslav Durieiev

National University of Civil Defence of Ukraine

https://orcid.org/0000-0002-7981-6779

Alexander Litvyak

National University of Civil Defence of Ukraine

https://orcid.org/0000-0002-0242-1859

Valerii Khrystych

National University of Civil Defence of Ukraine

https://orcid.org/0000-0002-5900-7042

DOI: https://doi.org/10.52363/2524-0226-2022-35-21

Keywords: fire detector, mathematical model, sensitive element, dynamic parameter, inertia, fire

Аnnotation

The scientific task of developing mathematical models of thermistor thermal fire detectors is considered, taking into account the combined influence of the type, material, design and geometric parameters of the thermistor sensitive element on the dynamic parameters of the thermal fire detector. The analysis of literary sources proved the need for a detailed study of the existing mathematical models of thermal fire detectors in order to obtain the values of their dynamic parameters and improve their technical characteristics. The model is a system of differential equations for non-stationary heat exchange and the dependence of the resistance of the sensitive element of the detector on temperature. The solution of such a system is an inertial dynamic link that describes the operation of a thermal fire detector with a thermistor sensitive element. Mathematical models for thermistors with positive and negative coefficient of temperature resistance have been developed. The constants and values of the nominal resistances make it possible to take into account the composition of the semiconductor material, the structural design and the geometric parameters of its sensitive element in the model of the thermistor thermal detector. Dynamic links have been obtained that allow determining the dynamic parameters of thermistor thermal fire detectors, taking into account the combined influence of the type, material, design and geometric parameters of the sensitive element with a posistor and thermistor. Equations for parametric studies of the dependence of the dynamic parameters of detectors on the characteristics of sensitive elements have been determined. A comparison of the obtained results of the calculation of dynamic parameters with experimental data shows that the discrepancies do not exceed 5 %. Recommendations on the selection of geometric characteristics of thermistor sensitive elements of thermal fire detectors and ways to improve their dynamic parameters have been developed and given.

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