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Background. We have earlier obtained a solution to the problem of matrix description of multistage two-flow systems of heat exchangers, in which each stage is represented as a quadrupole with two input and two output streams. However, in practice, in addition to the two main streams of cold and hot coolants, additional streams are often sent to heat exchangers, due to the drainage, purging or emergency operation of the system. The mentioned coolant flows can be supplied to different points of the  «Вестник ИГЭУ» Вып. 1 2019 г. 71 heat exchanger, which leads to different efficiency of the analyzed processes. There are currently models for calculating twoflow and multi-stage or multi-flow and single-stage systems of heat exchangers but there are none for calculating multistage multi-flow heat exchanger systems. Development of methods for calculating multi-flow multi-stage heat exchangers for analyzing their thermal efficiency is an urgent problem faced by the energy sector and related industries. Materials and methods. For the study of multi-flow heat exchanger systems and subsystems of thermal power plants, the equations of mass and energy balances are used, which are solved by the methods of higher mathematics and mathematical programming. Results. Within the framework of the matrix approach, we have developed a model of multi-flow multi-stage heat exchange systems, in which each stage can have an arbitrary number of input and output streams. The order of using and possibilities of the matrix approach are demonstrated on a four-stage three-flow system of heat exchangers as an example. Solutions to the model equations are obtained and analyzed, and the reliability and validity of the proposed approach are shown. Conclusions. The obtained results can be used to increase the validity degree of calculating systems of multi-stream heat and mass transfer devices, creating computer simulators and software tools for optimizing the modes of technological systems and subsystems of TPPs.

Matrix formalization of calculation and analysis of multi-flow multistage heat exchangers with a complex flow configuration