## 3 Results and Discussion
### The Heat Exchange Performance between the Tube Bundle and the Cold Fluid  
#### 3.4.1 Influence of Relative Humidity of the Ambient Air on the Heat  
Exchange Performance  
The physical meaning of the Nusselt number (\(Nu\)) is that it is not only a standard number to express the intensity of convective heat transfer, but also the ratio of heat conduction resistance and convective heat transfer resistance at the bottom layer of a fluid laminar flow [19]. Figure 9 depicts the relationship between the \(Nu\) and Re for the different \(RH_{0}\) values. As can be seen from the figure, the \(Nu\) increases with the increase in the Re for all the \(RH_{0}\) values; a similar finding was reported by [PERSON] et al. in regard to the heat transfer characteristic of a H-type finned elliptical tube [42]. Moreover, it can be found that the Re for the \(RH_{0}\) of 80%, 85% and 90% is in the range of 1256.275-1923.969, 1414.882-1857.943 and 1484.459-2210.554, respectively, while the \(Nu\) is in the range of 21.337-27.548, 23.759-28.001 and 25.156-32.415, respectively, which can be regarded as the reference parameters for designing and optimizing the HE. In order to quantitatively describe the relationship between the \(Nu\) and Re, three exponential models were established, and the corresponding equations are as follows:  
\[N\text{u}_{\text{80\%}}=0.2946\text{Re}^{0.59996},\ R^{2}=0.9946 \tag{28}\]  
\[N\text{u}_{\text{85\%}}=0.2660\text{Re}^{0.61886},\ R^{2}=0.9611 \tag{29}\]  
\[N\text{u}_{\text{90\%}}=0.2900\text{Re}^{0.61176} \tag{30}\]3.4.2. Influence of Relative Humidity of the Ambient Air on the Heat Transfer Coefficient  
The \(h_{s}\) is one of the most important parameters for the thermodynamic characteristics of heat exchangers, and is also the key index for studying the ventilation cooling mechanism, drying behavior and drying efficiency of agricultural product drying [42]. In the present work, the average \(h_{s}\) under different \(RH_{0}\) values (80%, 85% and 90%) were investigated, and the results are depicted in Figure 10. It can be concluded from Figure 10 that the h\({}_{s}\) increases with the increase in \(RH_{0}\), indicating that a high \(RH_{0}\) can enhance the heat exchange performance between the HE and the inlet ambient air, which might be caused by the fact that the effective heat exchange surface of the HE tube bundle increases with the increase in \(RH_{0}\). This finding was also reported by [PERSON] et al. for the heat exchange performance in an air-source heat pump heater [43]. Moreover, the average \(h_{s}\) under different \(RH_{0}\) values of 80%, 85% and 90% was ascertained to be 8.247, 9.450 and 10.515 kW\(\cdot\)m\({}^{-2}\).K\({}^{-1}\); in other words, 8.247, 9.450 and 10.515 kJ of thermal energy are transferred when the ambient air temperature in a unit area increases by 1 K. In order to simplify the relationship between the \(h_{s}\) and \(RH_{0}\), a quadratic model was established where the R\({}^{2}\) is equal to 1, indicating that the model has a good fitting performance and can be used for monitoring the heat exchange performance of the HE.  
Figure 10. The variations in average \(h_{s}\) with different \(RH_{0}\) values.  
Figure 9. The relationship between the \(Nu\) and Re for different \(RH_{0}\) values.