THERMAL PROCESSES OF FIRE DETECTORS’ HEAT-RESISTANT SENSITIVE ELEMENTS

Abstract

The purpose of the article. The article deals with thermal processes in the heat-resistant sensitive element of fire detectors when an electric current flows through it. Such processes are described by an inhomogeneous equation of mathematical physics with boundary conditions of the third kind. Methodology. The Hankel integral transformation is used to solve the differential equation that describes the thermal processes in the heat-resistant sensitive element of fire detectors. As a result of the transformations, a general expression was obtained for the temperature of the heat-resistant sensitive element of fire detectors under the condition that an electric current flows through it without restrictions on its parameters. This expression is represented as a series of Bessel functions. Results. The results of scientific research confirmed that due to the small size of the fire detectors’ sensitive element, the expression for its temperature is presented in the form of an average value over the sensitive element volume. Scientific novelty. For the first time, a general expression for the temperature of the heat-resistant sensitive element of fire detectors is obtained, which allows obtaining its main technical characteristics, and also serves as a basis for moving to other mathematical descriptions. Practical value. Also, using the integral Laplace transformation, an expression for the transfer function of the fire detectors’ heat-resistant sensitive element was obtained and it was confirmed that with an error of no more than 4,6 %, it is described by the transfer function of the inertial link.