A general steady state mathematical model for fin-and-tube heat exchanger based on graph theory

Fin-and-tube heat exchangers are widely used in air conditioners, chillers, etc. A lot of factors, including arrangement of refrigerant circuits, configure specification of fins and tubes, and operating conditions, have significant influence on the performance of fin-and-tube heat exchangers. For the purpose of fast design of high performance heat exchangers, a simulator reflecting the influence of these factors is necessary. In this paper, a general steady state mathematic model based on the graph theory is presented. With the help of the directed graph and graph-based traversal methods (Breadth-first search and Depth-first search), this model is capable to describe any flexible refrigerant circuit arrangement, and quantify the refrigerant distribution in the refrigerant circuit and heat conduction through fins. An alternative iteration method is also developed to solve the conservation equations, which can shorten the simulating time effectively. The model is verified with the experimental results, and the maximum error is within ±10.0%. A simulator based on this model has been used for designing practical fin-and-tube heat exchangers.