# Numerical Analysis of Tube Heat Exchanger with Trimmed Star-Shaped Fins
## 3 Results and Discussion
### Flow Characteristics  
Flow characteristics were analyzed for a tube bundle with five staggered rows of tubes. The material of the tubes and fins is stainless steel with a thermal conductivity of 16 W (m\({}^{2}\)K). All figures below show the flow characteristics for the star-shaped fins and the trimmed star-shaped fins at a diameter of 28 mm. Cases for other trimming diameters are not shown because they were similar to the case shown. The global temperature, velocity, kinetic turbulence energy and pressure distribution in the heat exchanger bundle are important for the comprehension of the local flow and heat transfer processes. The thermal conductivity of the fin material strongly affects the temperature distribution along the fin. In our case, the fin is thin and the temperature differences in the transverse direction within the fin are small compared to the temperature differences between the fin and the environment. Figure 6 presents the local feature of the temperature fields for analyzed fins. The temperature field over the fin area is not uniform and the temperature of the fin tip is different for each needle. The temperature profile for both variants is almost the same. The average temperature of the trimmed fins is lower by less than 1 K.  
The velocity fields, turbulence kinetic energy fields, pressure-drop fields, and y+ fields for star-shaped fins and trimmed fins are almost identical (Figures 7-10). Figure 6: Temperature fields (**a**) for star-shaped fins and trimmed fins; (**b**) fin temperatures in the third row (middle section). The fluid particles on the middle plane hit the tube at the stagnation point, bringing the fluid to a standstill and thus increasing the pressure at that point. The pressure decreases in the direction of flow while the velocity of the liquid increases. A wake region is formed behind the tubes, and vortex formation is particularly evident after the fifth row of the tube. In this region, the pressure is much lower than the pressure at the stagnation point. Owing to the lower air velocity in the wake regions, heat exchange is lower and temperatures are higher. Figure 8: Turbulent kinetic energy fields for star-shaped fins and trimmed fins. Figure 10: The \(y^{+}\) fields for star-shaped fins and trimmed fins. Figure 7: Velocity fields for star-shaped fins and trimmed fins. Figure 9: Pressure-drop fields for star-shaped fins and trimmed fins. The degree of turbulence and thus the difference in heat transfer coefficient increases with the number of rows due to the combined effects of the upstream rows. Figure 11 shows the dependence of the \(Nu\) number on the \(Re\) number for the star-shaped fins, the perforated star-shaped fins (see [12]) and for the fins cut to diameters of 28, 31 and 34 mm. From the figure, it can be seen that the worst results are obtained with the ordinary star-shaped fins, while the best results are obtained with the perforated fins and the fins with a cut diameter of 28 mm. Figure 12 shows the efficiency of the fins. From the figure, it can be seen that in the range of small \(Re\) numbers there is a small difference in efficiency between the studied fins. At higher \(Re\) numbers, the perforated fins are the least efficient, and the ordinary star-shaped fins have the highest efficiency. The efficiency of the trimmed fins is very similar to the efficiency of the ordinary star-shaped fins. Figure 11: \(Nu\) number versus \(Re\). Figure 12: Fin efficiency. Figure 13 shows the dependence of the heat transfer coefficient on the \(Re\) number. The results are similar to those in Figure 11. It can be seen from Figure 13 that the worst results are obtained by the ordinary star-shaped fins, while the best results come from the perforated fins and the fins with a trim diameter of 28 mm. Figure 14 shows the dependence of the heat transfer coefficient on the \(Re\) number. From this figure, the fins. From this figure, it can be seen that the best heat transfer results are obtained with trimmed fins.