# 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
#### 4.2.2 Flat-Tube Finned Heat Exchanger  
As previously stated, another tube shape, namely the flat tube, is also analyzed in this work in order to determine the ideal tube configuration that delivers the highest thermal-flow performance. Aiming to inspect the effect of tube flatness, four geometries of flat tubes have been examined numerically in this study, as shown in Table 1. For all the flat-tube shapes, Figure 10a illustrates the thermal exchange rate vs. the Re. As highlighted, the thermal exchange rate \(\varphi\) increase with the tube flatness and the Reynolds number due to the reduction in the dead region and the increase of the heat transfer area of annular fins with the flatness of tubes. We can also observe that F1-shaped tubes outperform the other flat-tube geometries for the whole range of Reynolds numbers. The F1-shaped tube shows the increased heat transfer rate of 5.2% at Re = 2600 and 3.8% at Re = 10,200, compared to the O5 shaped tube.  
Figure 10b shows the variation of the convective coefficient (\(l\)) for all of the inspected flat tube shapes at various Reynolds numbers. Of the flat tubes, the F1-shaped tube with annular fins provides 13-16% and 25-33% higher heat transfer coefficient compared to the F3 and O5 shaped tubes, respectively; the reason is the same as for the case of oval tubes in Figure 8b.  
The variation of the non-dimensional Colburn factor J with the tube flatness for the range of 2600 \(\leq\) Re \(\leq\) 10,200 is depicted in Figure 10c. The simulations show that the decrease in flatness decreases for all the values of Re. All flat tubes reveal higher Colburn factor values than the circular tubes (O5), and the factors of all the flat tube geometries also decrease with Re.  
Figure 9: Comparison of oval tube shapes at varying Reynolds number: (**a**) Pressure drop; (**b**) friction factor.  
The predicted pressure drop (\(\Delta\)P) and friction factor \(f\) are plotted in Figure 11a,b, respectively. For the whole range of Re, the value of \(\Delta\)P decreases with the increase of tube flatness (Figure 11a). We can observe that O5 and F3 tube shapes provide, respectively, 40-42% and 16-18% higher pressure losses compared with the F1 tube design; the cause is the same as that for oval tubes in Figure 9a. Moreover, the difference in the values of \(\Delta\)P between the five patterns of flat tubes becomes considerable when the Reynolds number increases.  
Figure 11: Comparison of flat tube shapes at varying Reynolds numbers: (**a**) Pressure drop and (**b**) friction factor.  
Figure 10: Comparison of flat tube shapes at varying Reynolds number: (**a**) heat transfer rate, (**b**) convective heat transfer coefficient, and (**c**) Colburn factor.  
In Figure 11b, the values of \(f\) are illustrated for various flat tube geometries and Reynolds numbers. In contrary to the oval tube shape, F4 provides a lower \(f\) in comparison to the other tube geometries. The O4 tube shape provides a 13.2-18.5% lower friction factor than those of the other tube shapes when the Reynolds number increases from 2600 to 10,200. Furthermore, the circular tube has the highest \(f\) values of all examined flat-shaped tubes due to an increased blockage in air flow.