Improvement of the design method of thermal networks: serial connection of heat exchangers

Abstract

The mathematical model of the system is considered consisting of a series connection of three heating devices. A system of
equations based on the energy conservation law is constructed, which turns out to be incomplete. It is shown that, given the known
requirements for the system, expressed only in the efficiency of the system, the formalization of design often becomes insoluble. The
system of equations is supplemented with expressions in accordance with the hypothesis of the proportionality of the amount of
energy in an element and is presented in matrix form. The design task is reduced to determining the elements of the matrix by the
value of the determinants. Analysis of the mathematical model made it possible to obtain an expression for the efficiency of the
system as a function of energy exchange in its elements. This made it possible to obtain solutions for flows and their relationships in
the elements of the system. In addition, the efficiency of inter-network and intra-network energy exchange has been determined,
which satisfy the principles of equilibrium and minimum uncertainty in the values of the average parameters of the system. As an
application, one of the main parameters, NTU, is considered, which determines the area of heat exchange with the external
environment and the mass and dimensional characteristics of the heat exchange system. Models of direct and opposite switching on
of flows with variations of flows and the value of the surface of devices when meeting the requirements for the efficiency of the
system are considered. The results of comparing the design process with the iterative calculation method are presented and the
advantages of the proposed approach are shown