# Numerical Analysis of Tube Heat Exchanger with Trimmed Star-Shaped Fins
## 1 Introduction  
Finned surfaces are often used for efficient heat exchange between liquids and gases. They are placed on the gas-side to increase the heat exchange area. In heat exchanger design, a common requirement is to have as little weight as possible, i.e., as little heat transfer area as possible. To meet this requirement, various geometric shapes of fins have been studied, based on analytical models of heat transfer on the extended surfaces and on numerical analysis and experimental studies. [PERSON] and [PERSON] [1] presented a method for calculating the efficiency of fins of arbitrary shape mounted on tubes of arbitrary shape using the finite element method. The paper also analyses the accuracy of calculating the efficiency of fins with complex shape using analytical and approximated methods: equivalent circular fin methods and sector methods. [PERSON] et al. [2] examined eight configurations of finned oval and flat tubes and compared them with conventional circular tubes. The configuration was tested in the interval \(2600<Re<10\),200. The analysis of the effects of the flatness of the tubes and the axial ratio of the oval tubes on the heat flow properties showed that tubes with higher flatness gave a better result. [PERSON] et al. [3] attempted to optimize the shape of the ring fins in a heat exchanger with multiple rows to improve thermal performance. They performed a numerical analysis and concluded that a local approach to optimize the fin shape is a good technique to further improve the performance of finned tube heat exchangers while reducing their cost. [PERSON] et al. [4] numerically and experimentally tested serrated fins of \(1\) mm thickness with circular perforations under natural convection and radiation. They varied the fin width (4 to 7 mm), the number of perforations (0 to 3), and the size of the perforation (\(\mathcal{O}\)2 to \(\mathcal{O}\)4 mm). The results showed that the variant with perforated surfaces had about 7% to 12% lower thermal resistance than the nonperforated surfaces. [PERSON] et al. [5] analyzed the position of the tube in an annular fin that maximizes heat transfer and minimizes pressure drop. They used computational fluid dynamics (CFD) and the analysis was performed for the range \(4500\leq Re\leq 22\),500. For small fin spacing, an eccentrically placed tube in the fin is more efficient than a concentric one. [PERSON] et al. [6] analyzed the cooling efficiency of a heat exchanger for cars using numerical analysis. The aim was to find the optimal shape of the heat exchanger that would reduce the coolant temperature to the required value and have the lowest weight. [PERSON] and [PERSON] [7] studied the characteristics of five fin designs in tubular heat exchangers: a concentric annular fin, an eccentric annular fin, a perforated annular fin, a serrated fin and a star-shaped fin. The Reynolds number ranged from 4300 to 15,000, and the conventional concentric circular fins gave the lowest performance criterion, while the serrated fins gave the highest performance evaluation criterion. According to the criterion of weight performance, star-shaped fins achieved the best result. Numerous researchers [8; 9; 10; 11; 12; 13; 14; 15; 16] have published papers in which they studied the effect of fin perforation on the flow characteristics in a heat exchanger. In general, all researchers concluded that perforation increases the degree of turbulence and thus improves heat transfer. One of the proposals to reduce the weight of heat exchangers while improving heat transfer is to use star-shaped fins [17; 18; 19; 20]. The authors designed a tubular heat exchanger with star-shaped fins and analyzed it using CFD simulation. The results were compared with the equivalent case of solid annular fins. With a 43.4% lower weight of the star-shaped fins compared to standard annular fins, the heat transfer coefficient of the star-shaped fins was 10% to 15% higher in the range \(2300<Re<11\),500. Recently, many other researchers have used CFD to study heat transfer properties [21; 22; 23; 24].