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The burning of organic fuel is one of the main factors influencing the greenhouse effect on the climate of the planet. The article examines the influence of the properties of lignite and coal–water slurries on the amount of carbon dioxide molecules formed as a result of chemical reactions. The authors give an overview of the results of other researchers in recent years and give the results of their research and development in the field of burning lignite and coal–water slurries in industrial recycling plants. The authors present the results of experimental studies of the thermophysical properties of coal and a coal–water mixture. The results obtained were compared with the results of calculations using a mathematical model and the results of numerical modeling in Ansys. New methods of approximation of step functions were used for the mathematical model. These methods make it possible to reduce errors in the approximation of the functions of the thermal properties of coal. The proposed methods do not have the disadvantages of traditional decompositions of step functions into Fourier series and can be used in problems of mathematical modeling of a wide class of processes and systems. In particular, when determining the coefficient of kinematic viscosity, ash content, and humidity by the method of approximation of the obtained data, the use of new mathematical methods makes it possible to reduce the error in calculations. In addition, data on numerical modeling of hydraulic transport and combustion processes are provided, and a data validation procedure is carried out. The data convergence shown and their location in the selected band of uncertainties satisfy the requirements for verification of experimental data adopted in the European Union and in the Eurasian Union. [ABSTRACT FROM AUTHOR]