Mathematical modeling of mass transfer of dust-air mixture to increase the solid fuel combustion efficiency

Introduction. The relevance of the study is due to the prevalence and importance of dusty gas flows in mining, energy, and transport, which dictates the need to study the patterns of interaction of particles with surfaces and the development of models of two-phase flows. The purpose of this study is to develop a direct analytical solution to an n–dimensional sequence of recurrent relations of first-order differential equations with a linear dependence describing the process of ignition of coal fuel. Materials and methods. The general form of the solution is obtained in the form of the sum of products of exponential multipliers with constant coefficients determined by the weights of a tree graph characterizing sequential integration. Results and discussion. The results of a numerical study of mass transfer during coal ignition are presented, which made it possible to theoretically substantiate the key physical models of the behavior of a pulverized coal stream. Conclusion. For the first time, a direct analytical solution to the mathematical modeling problem for a plasma system for thermochemical treatment of solid fuels has been obtained. Resume. Using the example of the ignition process of a pulverized coal mixture, the ignition of which is carried out using a plasma torch, the application of the developed model is shown. The proposed solution is integrated and can be used in other mathematical models. Suggestions for practical applications and future research directions. The creation of a mathematical model in the future will allow an experimental study of the physical model of the aerodynamic drag of the plasmatron – fuel system complex and evaluate the accuracy of measurements.