## 1 Introduction  
The finned-tube heat exchanger (FTHX) is widely used in air conditioning and refrigeration areas, due to its properties of high efficiency, wide adaptability, good reliability and easy manufacturing [1, 2]. It fundamentally consists of heat transfer tubes, connecting bends and fins. In practical applications, heat transfer tubes are usually U-shaped with all elbows arrayed on one side. The bends then connect the tubes on the other side to form different flowpaths for the refrigerant. Moreover, the fins are attached onto the outer surface of the FTHX to increase the heat transfer area. Since FTHX directly exchange heat between the refrigerant and the air, the performance enhancement of FTHXs has long been studied. Accordingly, efforts have been focused onto the tubes, the circuitry arrangement and the fins. Many researchers have investigated the internal treatment of the tubes to enhance the refrigerant's heat transfer performance. [PERSON] et al. [3] reported an experimental study of the effect of geometry on heat transfer using internally grooved tubes. The heat transfer enhancement obtained reached 63% with a circular groove, 58% with a trapezoidal groove and 47% with a rectangular groove compared with those of smooth tubes at 38,000 Reynolds number. [PERSON] et al. [4] experimentally investigated the heat transfer and pressure drop of internal flow in corrugated tubes, conducting the experiments in laminar, transitional and turbulent regimes at a Reynolds number of 429-6212. The results showed that the friction factor of the corrugated tubes changed more smoothly in the transition from laminar to turbulent regime. In addition, the Nusselt number for the corrugated tube increased up to 4.7 times compared to that for a smooth tube with a 6 mm helical pitch and 3.8 times when using a 12 mm helical pitch. [PERSON] et al. [5] studied the single-phase pressure drop and heat transfer in an internally helical-finned tube and found that the conventional criterion Re > 10,000 was hardly suitable for identifying a turbulent flow in this kind of tubes. Therefore, they developed a new correlation that predicted the heat transfer coefficient within a 5% relative error. [PERSON] and [PERSON] [6] examined the turbulent single-phase flow and heat transfer inside a micro-finned tube with a Reynolds number of 3300-22,500 and a Prandtl number of 2.9-4.7. The heat transfer data were correlated using the Dittus-Boelter correlation, and the pressure drop data using the Blasius correlation. It was found that the rough-tube Gnielinski and Haaland correlations could predict the finned-tube Nusselt number and friction factor, respectively, in the tested Reynolds number range. [PERSON] et al. [7] studied the heat transfer characteristics of refrigerant condensation in horizontal microfin tubes experimentally and found that a 5 mm tube produced both higher heat transfer coefficient and higher pressure drop than a 9.52 mm tube. The increased surface tension and sheer stress at the gas-liquid interface were the reason of these differences. In general, the internal treatment of the tube effectively improved the overall performance of the FTHX, though it also caused an additional pressure drop. Therefore, a rifled inner surface is widely adopted in the heat transfer tubes of FTHXs. Investigators have also explored the effect of fin geometry on the air-side heat transfer performance of FTHXs. [PERSON] et al. [8] comparatively studied three fin types for outdoor FTHXs and found that the flat fin exhibited the best overall performance in frosting/defrosting conditions, followed by the wavy and flat fins, sequentially. The stall zone of the axial fan caused by frost blockage of the FTHX should be taken into consideration in designing an FTHX. [PERSON] et al. [9] introduced perforations to the wavy fins and enhanced the air-side heat transfer of a herringbone FTHX. Meanwhile, they found that a constant power was the optimal criterion to evaluate the performance of the new FTHX. [PERSON] et al.