The methodology of theoretical studies of heat exchange processes in boiler units based on the mathematical model of burning coal dust has been developed. For the first time, the continuous curve of the fractional composition of an ensemble of coal particles is presented. The mathematical model is consistent with the aeromechanical and thermal characteristics of the torch, obtained on the basis of calculated and experimental data. The concept of a torch continuum is introduced as a continuous medium in which the processes of combustion and heat exchange are investigated. The methods of dividing the combustion chamber into zones, the equations of stationary and non-stationary heat conduction, radiation and convective heat exchange are used. These methods have been tested on a number of high-temperature installations, including boilers with natural circulation, for example, E-220 at the CHP plant in Bishkek, Kyrgyz Republic in the Central Asian region. In the course of the experiments, coals with different thermal characteristics were burned. In a special computer program obtained a 3D image of burning coal dust. Analysis of the calculated and experimental data showed a discrepancy between them of 4-5%. Analysis of computer simulation data showed a discrepancy with the calculated data of 3-4%, and with experimental 5-6%. Thus, the dependence of the parameters of the heterogeneous flame on the mathematical description of the fractional composition of coal dust is substantiated and the characteristics of the combustion process, previously not taken into account in the theory of heat transfer, are revealed. The task was solved-theoretically confirmed new methodological approaches to the theory of heat transfer in the furnace of the boiler unit.

The existing theories of heat transfer in combustion chambers of boiler units fail to take into account a number of important factors that affect the reliability of results, and the methodological approaches to optimizing combustion processes can be revised in view of the spatial and temporal parameters of flame. Hence, the research aimed to improve the fundamental theoretical and methodological principles of studying heat transfer in coal dust combustion in the combustion chambers of industrial steam generators. The authors proposed to extend the theory of heat transfer with the mathematical description of particle size distribution of coal dust. In addition, the authors used the developed mathematical model of coal dust combustion based on a continuous curve of the particle size distribution in the ensemble. The mathematical model is consistent with the aeromechanical and thermal characteristics of flame. This work introduced a concept of flame continuum as a continuous medium, where the processes of combustion and heat transfer are studied. To achieve the research aim, in this paper, the methods of combustion chamber zoning, the equations of stationary and non-stationary heat conduction, radiation, and convective heat transfer, were used. These methods were tested on a number of high-temperature units.

The authors of the paper emphasize that when the Nyquist-Shannon sampling theorem is used in practice, there arise several problems, which can be explained only through the use of new methodologies and mathematical models. The review of the researchers' works, as well as the authors' own practical research in the course of processing the statistical sample, which is described by a wave-like sine-cosine function, leads to the conclusion that it is necessary to take into account optimization criteria for high-tech processes and innovative indicators of building functions for the statistical sample, for example, when signals are transmitted and sampled using neural networks at production facilities. In the practice of economic calculations, for example, when making a graphic presentation of trend lines based on the functions built subject to the sampling conditions by the Nyquist theorem, the authors propose to use new methods for approximating piece linear functions, which allow for achieving a smaller error as compared to standard calculation methods. The work resulted in the creation of a neural network regulation algorithm, which will be trained based on the collected data and adapted to a specific type of a boiler unit. Besides, it was established that the task of neural network algorithms in the program is to find the optimal value of the weight coefficient for each argument of the resulting function to obtain the maximum number of predictions of the flare level and the particle burn-up time, which are consistent with reality. The use of these methods for the first time made it possible to significantly reduce the error, which is confirmed not only by calculations, but also by experimental data.

439 1 Coal-water slurry (CWS) is a mixture of pulverized coal and water with or without additions of surfac tants. CWS is fluid and can be moved via pipelines by pumps; in can be atomized in boiler furnaces and fired to form a flame, which makes it similar to fuel oil, die sel fuel, and other kinds of liquid fuels [1][2][3][4][5]. Power engineering applications of CWS include its use at thermal power stations (TPSs) and boiler houses placed in regions where it is not possible to construct railways, make systems for delivering dry coal on a conveyor belt, and where areas for receiving and stor ing dry fuel are not available. In addition, these may be TPSs receiving lump coal via a pipeline in water flow; large fractions of coal delivered in such a way are sup plied to a traditional coal pulverization system, and settled sludge residue (a kind of CWS) is supplied to boiler atomizers for being utilized in flames. CWSs containing solid coal particles from wastes of petro leum oil products can also be used.Foreign specialists dealing with commercial use of CWSs are oriented at suspensions obtained from high quality low ash (in particular, bituminous) coals with 1 In Russia, the question about advantages and drawbacks of using watered solid fuel in power engineering has been discussed with variable success for more than 50 years. At the same time, the majority of programs that were adopted abroad Russia for devel opment of technologies for preparing and using coal water fuel (CWF) had been implemented by the early 21st century. It has been shown in numerous publications that almost all technical problems connected with CWF have already been solved, but the use of this technology for power engineering applications is in the majority of cases economically unprofitable. Positive experience connected with the use of CWF has been demon strated only for transportation of coal from the places of its pro duction to locations at which it is consumed. In Russia, studies in this field are being continued. The two arti cles written by K.V. Osintsev "Studying Flame Combustion of Coal-Water Slurries in the Furnaces of Power Generating Boil ers" and by G.R. Mingaleeva et al. "An Experimental Study of the Viscosity of Coal-Water Slurry with a Bifractional Compo sition of Its Dispersed Phase" that are published below serve as a confirmation to this statement-Eds.a heating value ≥ 35000 kJ/kg, content of mineral inclusions per dry mass A d ≤ 2%, and yield of volatiles per combustible mass V c ≥ 40% (Fig. 1). CWS pre pared from these coals has a high heating value (more than 24 000 kJ/kg) with the working content of mois ture W r ≤ 30% and maximal size of solid particles R max ≈ 200 µm. This slurry can be delivered to users from locations at which coal is produced and CWS is prepared (at moderate transportation costs) and stored for a long period of time without becoming stratified [1][2][3][4][5]. Developers of such projects point to advantages of using CWSs at coal fired TPSs, which are stemming from simplified technology of receiving ...

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