Development of a mathematical model of a thermal fire detector from a thermocouple

Durieiev Viacheslav

National University of Civil Protection of Ukraine

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

Oliinyk Volodymyr

National University of Civil Protection of Ukraine

https://orcid.org/0000-0002-5193-1775

Bondarenko Serhiy

National University of Civil Protection of Ukraine

http://orcid.org/0000-0002-4687-1763

Antoshkin Oleksiy

National University of Civil Protection of Ukraine

http://orcid.org/0000-0003-2481-2030

Maliarov Murat

National University of Civil Protection of Ukraine

http://orcid.org/0000-0002-4052-7128

Murin Mikhail

National University of Civil Protection of Ukraine

https://orcid.org/0000-0002-9898-0128

DOI: https://doi.org/10.52363/2524-0226-2025-42-6

Keywords: detector, sensitive element, mathematical model, thermocouple, time constant, operation parameters, inertia

Аnnotation

A mathematical model of a thermal fire detector with a thermocouple as a sensitive element has been developed, which takes into account the dependence of the electromotive force on temperature. The obtained dynamic equations take into account the parameters of convection heat transfer, thermoelectric characteristics of the junctions, the dependence of the electrical conductivity and electromotive force of the thermocouple on temperature, the composition, shape, and structure of the material of the sensitive element on its operating parameters. The mathematical model is a system of heat balance equations and equations of the dependence of the electromotive force on temperature. A characteristic feature of the model is the consideration of the influence of the composition, shape, and structure of the material of the detector's sensitive element on its operating parameters. The equations are identified as real proportional links. The electromotive force and ambient temperature are presented in terms of relative variables, and the detector inertia and its gain parameter are constant coefficients. Dynamic equations are convenient when conducting studies of the operation and parametric calculations of the char-acteristics of the operation of thermal fire detectors with a thermocouple, taking into account the dependence of the electromotive force of the thermocouple junction on temperature. The results obtained from the presented model of the detector operation confirm the validity of the accepted hypothesis, and the calculated parameters of the detector operation have a qualitative coincidence with the experimental data. The limitation of the model is the use of known data of the temperature dependences of the electrical conductivity of the thermocouple junction, parameters and conditions of temperature influence and certain characteristics of the composition, shape and structure of the sensitive element. The recommendation for improving the operation characteristics is to increase the area and reduce the mass of the thermocouple junction to improve the conditions of convection heat transfer, to improve the inertia, time and temperature of operation.

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