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Received: 9 October 2019 Accepted: 22 January 2020 The need to increase the accuracy of decisions and the depth of analysis of complex heat power systems determines the relevance of modeling and regulation of heat and mass transfer processes with the development of theoretical models and the development of a new methodology. Uncertainty of the environment increases the significance of the problems of insufficient efficiency of the available numerical approaches to the modeling of dynamic processes and the regulation of heating elements. Therefore, the aim of the article was to develop the applied aspects of the theory of solving nonlinear problems, provisions of the analytical methodology and the methods for regulating stepwise thermodynamic processes based on adapted tools for approximating generalized and step functions. The following tasks were solved: the structure of mechanisms was determined, including regulators of the energy efficiency of the flare device of the boiler unit with an expanded combustion zone; a model of integration-balancing regulation of heat transfer with four types of unsteady processes determined by indicators of changes in the direction and sign of the entropy of the effects of the regulators is proposed. Quantitative meters of energy efficiency of combustion and heat transfer processes in boiler units have been developed. Mathematical adapted and developed technical and organizational methods for solving problems: approximation of the original functions (generalized Dirac and stepwise) by a sequence of recursive periodic functions; simulation of spasmodic heat transfer processes based on step functions; structuring the mechanism for regulating heat transfer, including four types of regulators; empirical modeling of the assessment and regulation of energy efficiency, taking into account the directivity and severity of the effects of regulators displayed by derivatives of higher orders of approximation of energy efficiency functions. The results were obtained: mathematical ones were adapted and new approximation models for generalized functions were built; quantitative measuring instruments of process dynamics for regulating the technical and organizational mechanisms of heat transfer were obtained.

Approximation Methods for Analysis and Formation of Mechanisms for Regulating Heat and Mass Transfer Processes in Heat Equipment Systems