Purpose. Solving analysis problems and improvement of modern physically inhomogeneous heat supply and heating systems. Developing the mathematical models that are suitable for applying all the features of the theory of energy circuits. Methodology. The study was conducted through applying fundamental laws of physics, fundamental principles of the theory of energy circuits and sectoral theories of hydraulic and electrical circuits, formalized methods for analysis of utility networks, methods of mathematical modeling. Findings. Contour and nodal mathematical models were improved as an instrument of a generalized ap- proach to the modes analysis of heat supply and heating systems. It has been shown that the mathematical models can adequately reproduce modes of studied systems. The models take into account the nature of the power and features of the two forms of mechanical energy - kinetic and potential. It is important for the analysis of mine heating modes, as there are considerable differences in height and emergency modes, due to leakages of heat-transfer agent to the environment. Originality. The generalized approach complies with all the requirements by principles of the metrical and energy analogies. It allows applying previously unavailable tools for the modes analysis of heating systems, in particular, power balance. The important advantage of this approach is the observance of unified system variables, which allows describing the phenomenon in circuits of different physical nature. Practical value. The developed mathematical models provide an effective tool for analysis of the planned and existing modern heat supply systems and their optimization in terms of minimizing energy costs.

 Наукова періодика України 

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