## 3 Results and Discussion
### The Heat Exchange Performance between the Tube Bundle and the Cold Fluid
#### 3.4.3 Influence of Relative Humidity of the Ambient Air on the Tube Pressure Drop  
In order to reasonably match the power of the IDF, the variations in the \(\Delta p_{t}\) with different \(RH_{0}\) values were investigated, and the results are shown in Figure 11. Similar to the variation trends in \(h_{s}\), \(\Delta p_{t}\) also increases with the increase in \(RH_{0}\), which might be caused by the fact that the dynamic viscosity of the ambient air (\(\mu\)) increases with the increase in the \(RH_{0}\) and leads to the decrease in the Re, further leading to the increase in \(\Delta p_{t}\), which can be summarized from Equations (11) and (16). A similar finding was reported by [PERSON], [PERSON] et al. for the heat and pressure drop variation characteristics in a low GWP refrigerant in a brazed plate heat exchanger [44]. The average \(\Delta p_{t}\) under different \(RH_{0}\) values of 80%, 85% and 90% was ascertained to be 12.854, 14.623 and 16.138 Pa, respectively. A quadratic model describing the relationship between \(\Delta p_{t}\) and \(RH_{0}\) was established where the \(R^{2}\) is equal to 1, indicating that the model has a good fitting performance and can be used as the reference for designing the distribution of the tube bundles. 4.4 Influence of Relative Humidity of the Ambient Air on the Exergy Performance of the Heat Exchanger  
Exergy analysis and its related concepts such as the sustainable index and improvement potential are widely used to evaluate the exergetic performance of an energy-intensive operation unit [45]. In the present work, the evaluation indexes including \(\eta_{HE}\), \(SI\) and \(\overset{\bullet}{IP}\) were used to investigate the exergetic performance of the HE. The variations in the \(\eta_{HE}\), \(\overset{\bullet}{IP}\) and \(SI\) with different \(RH_{0}\) values are depicted in Figure 12a-c, respectively. Interestingly, it was found that the \(\eta_{HE}\) decreases with the increase in the \(RH_{0}\), which is contrary to the trend in \(h_{s}\) shown in Section 3.4.2. The phenomenon might be caused by the fact that the humidity ratio of the air is proportionate to the relative humidity of the air, and the exergy of the air increases with the increase in the humidity ratio of the air, as is shown in Equations (18) and (23). Similar results were reported by [PERSON] et al. for the hot air drying process of grains [46]. Moreover, it can be seen from Figure 12a that the average \(\eta_{HE}\) for the different \(RH_{0}\) values of 80%, 85% and 90% is 12.57%, 12.16% and 11.46%, respectively. Though the \(\eta_{HE}\) is slightly higher than that in some other industrial heat exchangers, such as the exergy efficiency (\(\eta_{HE}=4.1\%\)) of an air heat exchanger for the cooling of residential buildings [47], it should be further improved. Figure 11: The variations in \(\Delta p_{t}\) with different \(RH_{0}\) values. Improvement potential (\(IP\)) is an effective index for evaluating the improvement in the exergy efficiency for a process or a system. The variations in the \(IP\) with different \(RH_{0}\) values are depicted in Figure 12b. As can be seen from the figure, the \(IP\) increases with the \(RH_{0}\), and the average values for the \(RH_{0}\) of 80%, 85% and 90% are found to be 208.27, 235.609 and 272.887 kW, respectively, indicating that they reach the goal of the maximum improvement in the exergy efficiency or minimized exergy loss (irreversibility). In 2001, [PERSON] and [PERSON] [48] proposed an interdisciplinary triangle covered by the exergy analysis. They proposed that the exergy is the confluence of energy, environment and sustainable development, and the exergy efficiency is directly proportionate to the sustainability. In this study, to investigate the sustainability of the HE under different ambient conditions, the variations in \(SI\) with different \(RH_{0}\) values were investigated, and the results are shown in Figure 12c.