Study of unsteady thermal conductivity in a multilayer rubber-metal product during post-vulcanization cooling and after-vulcanization

The article considers analytical solutions for a non-stationary problem of heat and mass transfer in a multilayer elastomeric material. Determined are the criteria, influence the process of temperature change in the treated material. A functional relationship between the main criteria of heat transfer and the temperature of the processed material was established, which is the basic relation during the development of an engineering method for calculating an industrial installation.


Introduction
Various industries pose high demands for the anticorrosion protection of machine parts operating in strong aggressive working environments at high temperatures and pressures, with periodic changes in the composition of these media, under their effective mixing.
Rubber coating occupies a special position among the existing methods of protecting surfaces, due to the specific mechanical properties of rubber, i.e. high elasticity, shock absorption, good wear resistance, fatigue and strength characteristics, heat and frost resistance, resistance to aggressive media, heat, gas and water resistance. It is used to protect against aggressive media during the production of chemical equipment, in the automotive, aviation, and engineering industries, as well as for the production of various parts: gaskets, shock absorbers, buffers, bearings, tread rings to protect drill pipes from wear, etc.
Vulcanization of coatings is the final and most important process of the gumming cycle of any metal object, accompanied by high energy costs and it especially needs improvement.
The modes of heat treatment of rubber-metal objects are established experimentally from the laboratory tests or by measuring the product temperature and then determining the duration of vulcanization.
It is necessary to highlight not only the theoretical studies [1][2][3][4], but also the practical results of the Russian scientists [8][9], which were further used to develop the thermal regimes of heat treatment of rubber coatings for enterprises of the real sector of the economy.
A large number of works study heat transfer processes under film boiling conditions on a flat plate [3][4][5][6][7], which, in turn, influenced the mathematical model obtained in this work and became the basis for this research.
Mathematical modeling of heat and mass transfer processes in complex heat engineering systems was carried out by the authors in [10][11], as a result of which the dependences of heat transfer in non-stationary conditions were obtained.
The performed analysis of works allows us to conclude the importance and significance of the processes of heat and mass transfer during the heat treatment of gumming coatings and to state that the internal problems during heat treatment of elastomeric coatings require further studies.

Materials and methods
An internal heat release occurs at the initial moment of time during cooling of a rubber-metal product. The internal heat generation associated with the internal vulcanization reaction is proved by the fact that during vulcanization the middle part of the elastomeric coatings was heated above the temperature of the heat transfer medium. The increase in temperature is directly related to the content of bound sulfur in the elastomer. In ebonite mixtures, up to 920•103 J/kg of rubber is released during vulcanization [1,2].
The rate of vulcanization and the degree of its course (degree of vulcanization) depend on temperature, and, consequently, the amount of heat energy supplied. In turn, the heat of reaction is a function of the degree of vulcanization. During vulcanization, its speed can be  (21). Further we substitute them and expression (17) into the sought solution (8), and this completes the construction of a general solution to the problem posed. Implementation of the mathematical model Consider a rubber-to-metal plate. The initial temperature distribution over the wall thickness is constant and equal to 428 K. The heat transfer coefficients at the plate boundaries are α1=α2=200. The ambient temperature is 283 K. Figure 1 shows a graph of temperature distribution over the thickness of a rubbermetal sample (a layer of steel is covered by a layer of ebonite). The dashed lines show the interfaces between the layers. The temperature distribution was observed at different points in time. The numbers on the curves correspond to the following points in time: 1 -after 30 s, 2 -after 60 s, 3 -after 120 s, 4 -after 160 s, 5 -after 180 s, 6 -after 240 s, 7 -after 360 s, 8 -after 500 s, 9 -after 700 s, 10 -after 1530 s, 11 -after 1600 s, 12 -after 1650 s. Points correspond to the temperatures obtained experimentally. The solid line is the result of analytical solution. As one can see, the convergence of the results is quite high. With a decrease in cooling time, the discrepancy between the calculated and experimental data does not exceed 1 -2%, gradually decreasing and tending to zero.

Conclusions
The development and implementation of calculation methods for determining the thermal modes of vulcanization will intensify and optimize the process while maintaining the high quality of rubberized products.
The developed calculation methods and the presented design solutions make it possible to create new and improve the existing industrial installations, which would reduce the duration of the cooling process without compromising the quality of the rubber-metal product. The practical value of the results obtained is the development and implementation of an engineering technique for calculating the cooling of coatings of gummed objects, designed to intensify the heat treatment process, improve the quality of rubber-metal products and the performance of gumming equipment in anticorrosive shops.
The results of the study were tested at the industrial enterprises of OJSC Severstal (Cherepovets), OJSC Ammofos (Cherepovets), OJSC Agrokhim (Sokol) during production of gummed objects and became the basis of their technological process.