## 1 Introduction
[10] proposed an algorithm to reduce the modelling order for multi-circuit FTHXs with multiple identical circuit types. Using this method, for 5 out of 23 identical circuits in an air-to-water FTHX, the simulation time was reduced to less than 1% and the difference in capacity to 3% relative to the segment-by-segment method. [PERSON] et al. [11] focused on exergy and energy analysis to optimize the heat transfer of FTHXs through new pin types. A multi-objective model was defined to obtain the optimal and critical values of operational and geometric parameters, and several correlations were fitted to estimate three objective parameters, i.e., thermal effectiveness, dimensionless exergy loss and dimensionless work. [PERSON] et al. [12] optimized the design of multi-stream plate-fin heat exchangers using multiple fin types. A new design model was proposed for mix-and-match fin types, and the mixed integer nonlinear programming model was converted to a linear programming model. Case studies were also carried out to validate the effectiveness of the new methodology. [PERSON] et al. [13] simulated the airflow through FTHXs with rectangular winglet pairs as vortex generators. The performance parameters evaluated were the Nusselt number, the vorticity and the quality factor. The results showed that the heat transfer performance improved significantly due to nozzle-like flow passages created by the winglet pair. These above studies showed the effectiveness of enhancing the heat transfer performance of FTHXs from the air side, providing guidelines to obtain this improvement. In addition to studies focused on each side of the FTHX separately, research on a circuitry design that could couple the heat transfer characteristics of both refrigerant and air is also important. [PERSON] et al. [14] used a disturbed model to study the evaporator performance with a complex circuitry and found that a 5% reduction in heat transfer area could be obtained by properly branching or joining the refrigerant circuits of the FTHX. [PERSON] et al. [15] studied the effect of the circuit number on an FTHX performance in both evaporator and condenser modes. The results showed that the evaporator generally performed better with more circuits, while the condenser worked preferably with fewer circuits. [PERSON] and [PERSON] [16] proposed the interleaved circuitry for FTHXs to improve the performance of a packaged air conditioner. The interleaved circuitry was suitable to route the refrigerant from the circuit with high airflow to that with low airflow, and vice versa. The results showed that the superheating rates in different circuits were uniformized, and the cooling capacity of the air conditioner was increased by 16.6%. [PERSON] et al. [17] studied the cross-fin conduction in a multi-circuit FTHX with three different circuitries, i.e., interleaved, vertical and block circuitries. The results showed that the coil capacity deterioration due to the cross-fin conduction increased with the number of inactive circuits, which was more pronounced in the interleaved circuity than in the blocked one. [PERSON] et al. [18] optimized the circuitry of a rooftop air conditioner using evolutionary algorithms and improved its capacity by 2.2% and its COP by 2.9%. [PERSON] and [PERSON] [19] used a dual-mode intelligent search algorithm to optimize the refrigerant circuitry of FTHXs. The knowledge-based computational module determined the tube number for each FTHX under non-uniform air velocity distribution, and the permutation-based one established the optimal sequence in which the tubes were linked. The results showed a 6\(\sim\)10% higher capacity of the FTHX in the part-load cooling conditions under European Standard EN14825. [PERSON] et al. [20] proposed a scheme of variable-path circuitry for the FTHXs, which was divided into two regions with a single-way valve in the vapor header, and each region was equipped with an electronic expansion valve (EEV) and a distributor. In addition, an ON/OFF valve was added upstream of the bottom region.