For the heat transfer enhancement, internally micro-fin tubes are widely used in commercial HVAC applications. It is commonly understood that the micro-fin enhances heat transfer but at the same time increases the pressure drop as well. In the open literature, majority of the works were focused on the development of correlations in a particular flow regime, especially in the turbulent region. Those correlations were developed based on different micro-fin geometries (fin spiral angle, fin height, and number of fins per cross-sectional area). However, the previous studies lacked information about the optimal fin geometry. It is of interest to know the optimal fin geometry because it can provide the best performance, i.e., the higher heat transfer and the lower friction loss.

A new and original optimization method, Algorithms of Changes (AOC), was successfully developed in the authors’ previous publications for solving the heat exchanger design problem (1), bin packing problem (2), and the traveling salesman problem (3). It is based on the transformation operators of hexagrams in I Ching, one of the Chinese classic texts. In this study, we extended the capability of the AOC method to find out the optimal fin geometric variables (The fin spiral angle, fin height-to-diameter, and number of fins per cross-sectional area) of the micro-fin tube based on the objective function, the efficiency index. The empirical heat transfer and friction factor correlations were adopted to find out the efficiency index. For comparison purposes, the Genetic Algorithms (GA) was also used to seek out the optimal fin geometry. From the results, both numerical methods can find out the optimal solution in a short iterative process. Furthermore, the AOC and GA results outperform the efficiency index computed by the fin geometries used in the past studies. Therefore, it was proved that the AOC can be applied not only to the heat exchanger design (1) but also to the optimization of thermal systems. [Keywords: turbulent region; internally microfin tubes; fin geometries; optimization; Algorithms of Changes (AOC); Genetic Algorithms (GA).]