Abstract
Transfer functions of typical heat exchangers, resulting from their partial differential equations, usually contain irrational functions which quite accurately describe the spatio-temporal nature of the processes occurring therein. However, such an accurate but complex mathematical representation is often not convenient from the practical point of view, and some approximation of the original model would be more useful. This paper discusses approximate rational transfer functions for a typical thick-walled double-pipe heat exchanger working in the parallel-flow configuration. Using the method of lines with the backward difference scheme, the original symmetric hyperbolic partial differential equations describing the heat transfer phenomena are transformed into a set of ordinary differential equations and expressed in the form of N subsystems representing spatial sections of the exchanger. Each section is described by a rational transfer function matrix and their cascade interconnection results in the overall approximation model expressed by a matrix of rational transfer functions of high order. Based on the rational transfer function representation, the frequency and steady-state responses of the approximate model are evaluated and compared with those resulting from its original irrational transfer function model. The presented results show better approximation quality for the “crossover” input–output channels where the in-domain heat conduction effects prevail as compared to the “straightforward” channels, where the transport delay associated with the heat convection dominates.
Highlights
Contemporary mathematical models of heat exchange processes describe their steady-state behavior and their dynamic properties, which are relevant, e.g., to design effective control algorithms
Visual comparison of the frequency responses and the steady-state temperature distribution obtained from the original, irrational transfer functions of the heat exchanger with the responses resulting from the rational approximation models of different orders
We presented some results concerning the approximate rational transfer function model for the double-pipe heat exchanger working in the parallel-flow mode
Summary
Contemporary mathematical models of heat exchange processes describe their steady-state behavior and their dynamic properties, which are relevant, e.g., to design effective control algorithms. The main advantage of this method is that the knowledge of the transfer function of the system allows determining its steady-state, as well as frequency- and time-domain responses, focusing on the relationship between its input and output signals It constitutes a convenient starting point for computer-based implementation of different control algorithms. Many works in the literature have been devoted so far to the transfer function-oriented modeling of heat exchange phenomena These models are often expressed by the extremely simplified transfer functions, such as first or second order with time delay, which may, be useful for some applications such as control design [25,26,27].
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