The characteristics of this process can be controlled within the framework of transient models, but this approach requires a large number of calculations at a small time step, which leads to large computational resources. The authors of [25; 26] present a complex approach to the development of a mathematical model for the formation of slag deposits on the heat exchange surface during the combustion of solid fossil fuel. As a condition for ash particles' build-up, critical values of viscosity were used, which, in turn, were obtained from the results of experimental studies. The developed model [25] is represented by several sub-models for calculating the characteristics of the various following stages of slagging: the formation and transport of fly ash particles, particle build-up to the surface and growth of the sediment layer and particle collision. [PERSON] and [PERSON] [25] obtained a good qualitative agreement between the theoretical and experimental results, but due to the multifactorial nature of the process (the formation of ash primary layer, the variability of the slag particles properties, the spontaneous deposits destruction, etc. ), the quantitative results differ. The review [27] presents general recommendations for improving mathematical models of heat exchange surfaces slagging. The following areas for improvement have been highlighted [27]: to increase the reliability, it is necessary to complicate the models, including by refining the spatial grid and the integration step; for an adequate description of real physical processes, it is necessary to carefully choose the criteria of build-up particles, to consider the non-uniformity and variability of their viscosity; it is necessary to consider the formed deposits' structure, the processes of erosion and spontaneous shedding [27]. Given the wide variety of processes occurring during boiler slagging, as well as the recommendations formulated above, it can be concluded that there is a need for complex mathematical models of slagging. They should describe the processes occurring during the combustion of fuel in the boiler at the macro level (on the scale of the entire furnace) and on the micro level (on the scale of one particle or one element of the heat exchanger). It should be noted that recently, an urgent task in practice is the transfer of coal-fired steam boilers to fuel mixtures, including in the form of slurries. Therefore, the mechanisms for a reliable assessment of the dynamics of heating surfaces' slagging are the basis for the development of scientifically based practical measures aimed at changing the thermal regime of the boiler. When boilers are transferred to non-design composite fuels containing low-grade combustible components and water, the flame temperature, as a rule, decreases. At the same time, the problem of slagging remains relevant, as many components of multicomponent fuels (for example, some industrial waste and biomass) are characterized by a relatively high content of alkali and alkaline earth metals [28; 29]. The structure of ash and slag deposits forming during combustion of CWS and CWSP can be multi-layered and heterogeneous in chemical composition, which complicates the fight against this negative phenomenon by standard means. The objectives of this work are as follows: (1) the development of two interrelated mathematical models of slagging in the furnace of a steam boiler with flame combustion of a fuel; (2) study of the effect of combustion parameters for three fuels (coal dust, droplets of CWS and CWSP) on the slagging characteristics of heating surfaces. The developed predictive complex is one of the components of a comprehensive algorithm for assessing the prospects of the practical use of composite fuels instead of solid fossil fuels.