Application of the parameter concentration method to modeling non-stationary processes in low-temperature heat exchangers

BACKGROUND: Currently, programmed controllers are used as means of regulating low-temperature installations. Controllers have limited operational memory and require simple mathematical models for their application. The use of an approximate solution to complex systems of equations describing non-stationary operating modes of heat exchangers allows for a significant reduction in the requirements for the operational memory of controllers. AIMS: Obtaining an approximate solution to systems of equations describing non-stationary operating modes of heat exchangers. METHODS: Using the coordinate-based parameter concentration method, a system of partial differential equations with respect to coordinate and time is reduced to a system of total differential equations with respect to time. This system of equations has an analytical solution by averaging the thermophysical properties of the flows and the heat-transfer wall over the temperature range under consideration, or a solution using the Runge-Kutta method by taking into account the dependence of changes in thermophysical properties on temperature. RESULTS: Systems of equations have been obtained that describe non-stationary operating modes of heat exchangers, making it possible to simulate the operation of a low-temperature installation and program the controllers used in this installation. CONCLUSIONS: A new method for obtaining approximate solutions to equations systems describing the transient operating conditions of heat exchangers is proposed. Using these solutions, one can easily obtain an analytical or simple numerical solution for describing the transient operating conditions for a low-temperature system comprising several heat exchangers. The resulting time-dependent temperature dependences for heat exchanger flows can be used in programming controllers used for the safe and efficient operation of processes in low-temperature systems.