# Numerical Investigation of Thermal-Flow Characteristics in Heat Exchanger with Various Tube Shapes
## 4 Findings and Analysis
### Impact of Tube Shape on Flow Pattern and Local Temperature Distribution
#### 4.2.3 Impact of Tube Shape  
The global performance criterion \(G_{pc}\) is employed to obtain the optimum configuration of tubes. For the five geometries of oval tubes, Figure 12a depicts the variation of \(P_{cc}\) for the range of 2800 \(\leq\) Re \(\leq\) 10,200. O1 is clearly superior, not only to the conventional circular tube (O5), but also to all other tube designs for any value of Re. As expected, the performance evaluation criterion of O1 is higher by around 61.6-64.2% than that of O4, depending on Re. Generally, the performance \(P_{cc}\) of the oval tube fin heat exchanger decreases as the ellipticity of tubes decreases, which is due to the higher heat transfer enhancement and lower pressure losses at a higher axis ratio. Furthermore, the difference of \(P_{cc}\) between O4 and O5 is very small, where it does not exceed 1.8% for the whole range of Re. These results agree well with the numerical results of [PERSON] et al. (2018) for the case of plate fins.  
Figure 12b shows the variation of the global performance criterion \(G_{pc}\) versus the Reynolds number for all of the oval tube geometries. It is a proven fact that when the axis ratio (RMX/RMN) grows, the heat transfer rate increases, but the power required by the fan \(\Delta PV\) lowers, resulting in a greater thermal-hydraulic performance. Therefore, the O1 tube shape outdoes all the other tube designs in terms of \(G_{pc}\), which is estimated to be 21.2%, 35.2%, and 45.9% higher than that for O3, O4, and O5, respectively, at lower values of Re. For the higher Reynolds number values, the difference in \(G_{pc}\) between all of the oval-shaped tubes becomes negligible. Finally, when the overall heat transfer and power consumption are taken into account, the O1 tube geometry provides the best thermal-hydraulic performance.  
Similarly, the impact of the flatness tube on the performance evaluation criterion \(P_{cc}\) and the global performance criterion \(G_{pc}\) is plotted in Figure 13a,b, respectively, for the range of Re of (2600 \(\leq\) Re \(\leq\) 10,200). As shown in Figure 13a, the pressure drop lowers as the flatness grows, implying that increasing the tube flatness would result in greater performance. For all the flat tube shapes, F1 shows the highest values of \(P_{cc}\). In addition, F1 provides 28.9-32.6% and 54-58.6% higher \(P_{cc}\) than those for the F4 and O5, respectively.  
Figure 12: Influence of oval tube shapes and Reynolds number: (a) performance evaluation criterion and (b) global performance criterion.  
Figure 13b illustrates the variation of the \(G_{pc}\) versus the Reynolds number for all of the flat-shaped tubes. As observed, \(G_{pc}\) decreases rapidly with an increasing Reynolds number for the entire flat tube shapes because the fan power consumption grows rapidly in tandem with the sluggish increase in the heat transfer rate. For the whole range of Re, the \(G_{pc}\) offered by F1 tube geometry is the most substantial of all the other flat tubes, being 27.34-36% and 48.9-52.2% higher than the F4 and O5, respectively. This can be explained by the increase of heat exchange area and the decease of dead region when the flatness increases. However, the circular tube (O5) provides the lowest \(G_{pc}\) values at all Re because O5 requires more power consumption, hence shows worst thermal-flow performance.  
It is also observed from the numerical results envisioned in Figures 12 and 13 that the best oval tube shape (O1) gave the highest values other than the flat tube F1. On the contrary, F1 has the highest \(P_{cc}\) values of all the tube designs and over all values of Re.