# 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  
Finding the tube geometry that reduces the inactive heat transfer region (recirculation zone) and improves the heat transfer intensity is very important [7]. The velocity vectors near the fins and behind the tubes of the second rows for both oval and flat tube configurations are illustrated, respectively, in Figure 5a,b, at the maximum inlet velocity. For all tube designs, the recirculating vortices may be seen starting from the flow separation point, moving alongside the mean flow, and then returning to touch the rear wall of the tube (dotted circles). However, the size of this recirculation clearly decreases with the increase of ellipticity and flatness of tubes where the size of the wake region shrinks for O1 and F1 tube shapes. For all cases, the maximum fluid velocity is always found at the narrowest cross-section flow passage between two adjacent tubes; because of this, the right and left sides of the fin surface are characterized by higher heat transfer than the other regions. Figures 6 and 7 show the local temperature distribution around the oval and flat tubes finned heat exchangers, respectively. The temperature distribution is presented in the middle of the fin thickness at a higher inlet velocity of air flow. Bigger temperature gradients along with the longitudinal flow direction of oval-shaped tubes (O1, O2, O3, and O4) and flat-shaped tubes (F1, F2, F3 and F4) comparatively with the conventional circular tube (O5), indicate a larger global thermal exchange rate between the annular finned-tube and air flow, as the axis ratio of oval tubes and flatness of flat tubes increases air-side heat transfer increases. This might be due to the fact that the ellipticity and flatness of tubes reduce the area of the inactive zone of annular fins; moreover, the right and left sides of the fin surface, which are characterized by higher convective heat transfer, become more spacious. Furthermore, increasing ellipticity and flatness of tubes raise the thermal exchange area of annular fins; for example, the circular finned-tube O5 can have up to 2.44% less surface area compared with the oval tube O1 and flat tube F1. For both oval and flat-shaped tubes, the temperature gradient at the downstream part of the fin surface is lower than the upstream due to the wake flowing behind the tubes. Figure 6: Temperature contours in the middle of the fin thickness for all the geometries of the oval tube. Figure 7: Temperature contours in the middle of the fin thickness for all the geometries of the flat tube. Figure 8b shows the convective heat transfer coefficient (\(h\)) versus Reynolds number for each oval tube design. Similar to the heat transfer rate, we can see that \(h\) increases with the increase of both axis ratio and Reynolds number (O1 tube shape provides 13-18% and 36-39% higher \(h\) values as compared to the O3 and O5 tube shape, respectively). This is due to the fact that the increase in the axis ratio reduces the area of the dead region (recirculation zone) behind each tube and enlarged the right and left sides of the fin surface, which are characterized by higher values of \(h\). On the other hand, it is crucial to explore the thermal exchange and flow behavior in terms of dimensionless numbers. Thus, the variation of the Colburn factor J with the air-side Reynolds number is depicted in Figure 8c. Similar to the overall heat transfer rate, J is the greatest for the O1 tube shape and the lowest for the circular tube (O5). Whatever the shape of the oval tube, the Colburn factor decreases with the rise of Re. In the construction of heat exchangers, the permissible pressure drop (\(\Delta\)P) is limited. As a result, examinations of the pressure losses are frequently conducted after assessments of heat transfer characteristics in these devices. As illustrated in Figure 9a, the ellipticity of tubes and Reynolds number has a strong impact on pressure drop through the annular FTHEs.