# Numerical Investigation of Thermal-Flow Characteristics in Heat Exchanger with Various Tube Shapes
## 1 Introduction  
Independent finned-tube heat exchangers (FTHEs) are widely utilized in heat generation systems, such as cryogenics [1], air conditioning [2], radiators of automobiles [3], aerospace [4], and nuclear power stations [5]. The intent of FTHEs is to dissipate the heat generated to the external environment to improve the efficiency of the engineering systems. Generally, the large thermal resistance of FTHEs is yielded by the air-side due to the thermo-physical property of air [6, 7]. The energy efficiency on the gas side of theindependent FTHEs may be increased by changing the tube and fin shapes [8; 9; 10; 11; 12]. Furthermore, the fluid recirculation in the thermally dead zones and the pressure drop due to the drag force are widely affected by the tube shape [13; 14; 15; 16]. For that, numerous studies have been performed to enhance the thermohydraulic characteristics on the air-side of thermal devices by designing and comparing the performance of different tube geometry [17; 18; 19]. For flat tubes, several researchers analyzed the effect of flat tube dimensions and compared their thermal flow characteristics with the conventional circular tubes. [PERSON] et al. [20] compared the hydrothermal details for a staggered three-row bundle with circular and flat tubes using the liquid crystal thermography method. For a Re range of (600-3000), they reported that the longitudinal vortices yield a significant thermal enhancement for flat tubes (100%), but only a marginal increase in the thermal exchange (10%) for circular tubes. However, the pressure drop of the conventional circular tubes is twice that in flat tubes. The naphthalene sublimation technique was employed by [PERSON] et al. [21] to calculate the local thermal exchange coefficients of plain FTHEs with and without vortex generators and for circular and flat tubes. For the case of thermal devices with VGs, the flat tubes provide significant thermal exchange compared to the conventional circular-shaped tubes. Moreover, in the case of thermal devices without VGs, the convective thermal exchange coefficient of fin flat-tubes is lower than those of FTHEs with circular tubes. Both experiment and numerical simulations were conducted by [PERSON] et al. [22] to study the thermohydraulic details of wavy fin-and-flat tube thermal exchangers with longitudinal delta winglet vortex generators. Compared with the traditional smooth wavy fin-and-flat-tube, the Nusselt number increased by 21% to 60% for a Re range of (1500-4500). However, for a range of Re of (500-4500), the friction factor increased by 13% to 83%. For a one-row annular fin-and flat-tube, [PERSON] et al. [23] compared the turbulent hydrothermal characteristics of non-perforated annular fins and various perforation shapes of annular fins (circular, square, and triangular perforation shapes). Recently, [PERSON] et al. [24] numerically investigated the impact of tube bundle arrangement, flat-tube dimensions, transverse, and longitudinal tube pitches on natural convection thermal exchange. They observed that the circular tube and flat-shaped tube with an axis ratio of 1:2.1 were the most efficient configurations. [PERSON] and [PERSON] [25] applied the Taguchi method to explore the impact of flat tube configurations (without fins). [PERSON] et al. [26] conducted numerical simulations to investigate the thermal and hydraulic details of a plain plate-fin with varying inlet air velocity \(0.5\leq V_{in}\leq 3.5\;m/s\) and flat-tube aspect ratio \(0.33-1\). The simulation results indicate that reducing the aspect ratio of the flat tube from 1 to 0.33 lowered the pressure loss by 33.7% (at \(V_{in}=0.5\;m/s\)) and 57.3% (at \(V_{in}=3.5\;m/s\)). On the other hand, the thermal exchange increased by 52.9% (at \(V_{in}=0.5\;m/s\)) and 111.5% (at \(V_{in}=3.5\;m/s\)). Next to the flat-shaped tubes, the oval or elliptic tube configuration has a major role in the thermal exchange performance of a FTHE. [PERSON] and [PERSON] [27] achieved experiments and simulations on annular-finned tubes under wet and dry conditions.