# Heat and Flow Study of the Internally Finned Tubes with Different Fin Geometries
## 1 Introduction  
The improvement of the energy systems is a critical pillar for achieving the Sustainable Development Goals [1]. The enhancement of the energy systems or devices can be based on the development of more efficient subsystems or by the introduction of new materials. In thermal engineering, the flow and heat enhancement methods have gained a lot of interest and numerous methods have been tested [2]. The utilization of nanofluids [3] and the use of turbulators [4] are the most usual choices for enhancing the flow in order to increase the heat transfer rate. Moreover, there is also research about the combination of the aforementioned techniques [5] as a proper choice for thermal enhancement with high performance. Between the use of turbulators and nanofluids, the turbulators seem to be a more efficient choice [5], while nanofluids are associated also with stability and other issues [6]. Therefore, the use of turbulators can be an effective choice for the direct application of energy devices, while the use of nanofluids in commercial systems needs some extra steps before being a mature and reliable choice. In the literature, there is a plethora of examined ideas about the use of turbulators in engineering applications. Usually, the turbulators are applied in devices like solar thermal collectors, refrigerators, heat exchangers, radiators, and solar stills, but they can be applied in other applications when there is a performance enhancement margin. Different kinds of turbulators can be used, and generally, they can be separated into the inserts and the internal fins, while there are also turbulators with modified tube geometry. In the studies with turbulators, the emphasis is given to the enhancement of the heat transfer, while thepressure drop increase is also taken into consideration [7]. Usually, the proper criteria are applied for examining the overall flow enhancement by considering both the increase of the heat transfer rate and the higher pumping work demand. The most usual criterion for flow enhancement is the Performance Evaluation Criterion (PEC), as it is defined below [7]:  
\[\text{PEC}=\frac{\left(\frac{\text{Nu}}{\text{Nu}_{0}}\right)}{\left(\frac{ \text{f}}{\text{f}_{0}}\right)^{\frac{1}{3}}} \tag{1}\]  
where the Nusselt number (Nu) is used for the heat transfer enhancement, and the friction factor (f) is used for evaluating the penalty on the pressure drop increase. The subscript \"0\" regards the reference case (e.g., empty tube). If PEC > 1, then it is assumed that there is flow enhancement. [PERSON] et al. [8] examined the idea of using circular disk inserts with hollows in a heat exchanger. They conducted an experimental work, and they found the ratio of the Nusselt number (Nu/Nu\({}_{0}\)) to be up to 4.5, while they found the PEC to be up to 1.42, which is a promising value for effective flow improvement. [PERSON] and [PERSON] [9] studied experimentally the enhancement of the airflow by the use of V-nozzle turbulators. They found the Nusselt number ratio up to 3.7, while the PEC up to 1.19. In some designs, the PEC received values lower than 1. In another work, [PERSON] [10] studied the use of coiled square wires experimentally with air. It was found that the Nusselt number ratio reaches up to 2.6, and the PEC up to 1.3. [PERSON] et al. [11] studied the use of delta-winglet twisted tape inserts with water as the working fluid experimentally. They found the PEC to be up to 1.24, but in some cases, they found it to be lower than 1. In another investigation, [PERSON] et al. [12] examined with a numerical model the use of louvered strip inserts in airflow and they found the PEC to be in the range of 1.60 to 2.05. [PERSON] et al. [13] investigated the use of double-helical tape inserts for enhancing the airflow. According to their calculations, the Nusselt number ratio was found to be up to 4.05, while the PEC was found to be up to 3.15. [PERSON] et al.