Aerodynamic Fields inside S-Shaped Baffled-Channel Air-Heat Exchangers

Unit of Research on Materials and Renewable Energies, Department of Physics, Faculty of Sciences, Abou Bekr Belkaid University, Tlemcen, Algeria Department of Engineering and Architecture, University of Parma, Parco Area delle Scienze, 181/A, Parma 43124, Italy School of Mechanical Engineering, Lovely Professional University, Phagwara 144411, Punjab, India Department of Mechanical and Ocean Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA Department of Renewable Energies and Environment, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran


Introduction
During last decades, heat exchangers (HEs) have been prevailingly utilized in different industries and domestic applications [1,2]. As a result, numerous investigations have focused on various kinds of heat exchangers (HEs) with the purpose of enhancing their performance. In this way, a numerical and experimental study on plate HEs with utilizing paraffin wax in it has been carried out by Juaifer et al. [3]. Also, thermal performance of a parallel-plate HE fractionally filled with porous media has been numerically studied by Arasteh et al. [4]. According to the results, the heat transfer coefficient of the HE is enhanced up to 19.2%. Additionally, Li et al. [5] used a numerical study to evaluate forced-convection heat transfer in a HE with inserting a twisted tape and using nanofluid. Furthermore, Aghayari et al. [6] performed an investigation focused on thermal performance of a double-pipe HE by inserting twisted tape and nanofluid. In another study, multilayer PCMs have been used in a tubular HE by Sadeghi et al. [7] for the aim of reducing the use of energy in industries. Moreover, both experimental and numerical studies have been performed by Maddah et al. [8] for the aim of enhancing the performance of heat pipe HE by using CuO/water nanofluid. As indicated in the results, the thermal performance of the HE was increased by using the nanofluid. Maddah et al. [9] examined a double-pipe HE with Al 2 O 3 -TiO 2 hybrid nanofluid with different Reynolds numbers and concentrations. Sakhri et al. [10] experimentally examined the effect of using an earth-toair HE to provide a favorable condition in winter. e influence of using Al 2 O 3 nanofluid in various kinds of HEs such as plate, double-pipe, and shell-and-tube HEs has been experimentally analyzed by Mansoury et al. [11]. According to the results, it was announced that an 11% enhancement of heat transfer coefficient was achieved in the plate HE. A study on a plate HE has been performed by Sodagar-Abardeh et al. [12] to find flow characteristics and optimum geometry of it by using the genetic algorithm. Also, a review on thermal and flow characteristics of compact fin-and-tube HEs has been performed by Adam et al. [13].
Recently, myriad engineering fields and sectors have used shell-and-tube HEs with baffles and fins. As a result of their prevailing usage, a main concern within researchers and scholars regarding these HEs can be mentioned as improving the performance. To address this issue, heat transfer and flow characteristics of shell-and-tube heat exchangers with segmental baffles and middle-overlapped helical baffles were experimentally investigated by Zhang et al. [14]. Also, by using the grid generation program Gambit and ANSYS Fluent, a model of a heat exchanger with middle-overlapped helical baffles has been simulated by Zhang et al. [15]. Miansari et al. [16] performed a numerical analysis to find the influences of circular grooves on shelland-tube HEs. Based on the results, the heat transfer rate was enhanced by 5%. Menni et al. [17] simulated turbulent forced-convection flow in a channel with V-shaped baffles. In another study, Menni et al. [18] numerically evaluated fluid flow characteristics adjacent to arc and flat-shaped baffles in shell-and-tube HEs. Based on the results, an improvement in the thermal performance could be achieved. Additionally, Hosseini et al. [19] simulated a shell-and-tube HE by utilizing CNT/water nanofluid with the purpose of evaluating heat transfer performance. Xiao et al. [20] used the CFD method to study fluid flow and thermal performance of heat exchangers equipped with various baffles tilt angles. In another study, liquid gas flow and its thermal performance in a heat exchanger at a pressure of 0.6 MPa have been numerically investigated by Afrianto et al. [21]. Furthermore, You et al. [22] with a numerical approach analyzed the permeability and porosity for the aim of obtaining the shell side thermal hydraulic performances.
Also, Du et al. [23] examined overlapped helical baffled HEs to numerically study the influence of using distinct geometric parameters on flow resistance and thermal characteristics. A 3D CFD simulation has been presented by El Maakoul et al. [24] for the objective of studying and comparing heat transfer coefficient, the shell side flow distribution, and the pressure drop at low shell side flow rates in a newly established trefoil-hole, helical baffles, and conventional segmental baffles. Furthermore, the influence of using baffle clearances on a small-scale HE developed by HTRI software has been analyzed by Leoni et al. [25]. Also, the pressure drop and heat transfer performances of a shell-and-tube HE with helical baffles on shell side have been presented by Shinde and Chavan [26]. In another study, tube and shell HEs with helical baffle have been investigated by Gustyawan et al. [27]. Also, the thermal and flow characteristics of a shell-and-tube HE have been examined by Nagre et al. [28] with the use of CFD simulation and experimental approaches. Prajapati and Makwana [29] analyzed a shell-and-tube HE with continuous helical baffles, noncontinuous helical baffles, and segmental baffles HE with the CFD method. Furthermore, an innovative shell-and-tube HE with screw cinquefoil orifice baffles has been presented by Zhang et al. [30] to obviate defects of conventional shell-and-tube HEs with these baffles. Saeedan and Bahiraei [31] presented 3D simulations of shell side of shelland-tube HE with helical baffles for various values of helix angle and overlapping. Ma et al. [32] simulated the thermal performance and fluid flow properties of HE's shell sides with trefoilhole and quadrifoil-hole baffles. Also, a CFD model was performed on a shell-and-tube HE by Ambekar et al. [33] which was equipped with different baffle structures such as A-type and B-type flowers and single, double, and triple helical baffle. In another study, one segmental baffle HE (SEG) and five trisection helical baffle HEs (10°S, 15°S, 20°S, 15°E, and 20°D) have been compared by Dong et al. [34] using numerical simulation. Additionally, a numerical investigation has been performed on a helixchanger by Shinde and Hadgekar [35] for the aim of disclosing the influences of baffle inclination angle on the pressure drop and thermal performance of the HE equipped with center tube with various baffle inclination angles. Two innovative shell-and-tube HEs with louver baffles for energy conservation have been invented and designed by Lei et al. [36]. Additionally, with the objective of achieving knowledge regarding fundamental mechanism of shell side thermal improvement, a computational fluid dynamic simulation which contained inlet and outlet nozzles has been conducted by Zhou et al. [37]. On the other hand, Rashad [38][39][40][41][42], Rashad et al. [43][44][45], Chamkha et al. [46][47][48][49], Menni et al. [50][51][52][53], Ghalambaz et al. [54,55], Mehryan et al. [56,57], Sabour et al. [58], and Tahmasebi et al. [59] have studied the fluid flow effect that could be applied in solar systems.
Different configurations and distinct thermal and hydrodynamic boundary conditions have been applied in these works. us, the most prevailing applied method in simulating HEs and flow can be mentioned as CFD. e objective of this contribution can be mentioned as an analysis of turbulent air flow by utilizing computational fluid dynamics (CFD) in shelland-tube heat exchangers fitted with bottom and top wallmounted S-shaped baffles in a staggered manner. e calculation method of finite volumes, the turbulence model of standard k-epsilon, and the discretization algorithm of semiimplicit pressure linked equation were adopted in this research by using the CFD software Fluent.

Computational Model
e aim of this research can be stated as performing a numerical analysis of dynamic behavior of an incompressible Newtonian fluid (air) under the conditions of turbulent flow and constant property within a 2D horizontal rectangular channel ( Figure 1).
is study is a complementary flow analysis in the presence of S-baffles [49]. e transverse, solid-type, and S-upstream from baffles with different stations have been embedded into the channel and fastened to the bottom as well as top walls of the channel in a staggered manner for the aim of forcing recirculation cells to augment the mixing that results in the convective heat transfer. Consequently, a critical issue which must be specified is the flow in shell-and-tube HEs. Additionally, determining turbulent viscosity, turbulent dissipation rate, turbulence kinetic energy, dynamic pressure, velocity, stream function, and turbulence-intensity distributions as well as the existence and the extension of possible recycling cells can be enumerated as a crucial step. Table 1 reports the important geometry dimensions of the computational model under study [49,60].

Numerical Model
e flow is steady, 2D, turbulent, incompressible, and Newtonian. e physical properties contributed to solid and fluid are constant. In this study, viscous dissipation, body forces, and radiation heat transfer are neglected. e computational domain and boundaries are presented as follows [49]. Inlet: Outlet: Walls: e calculation method of finite volumes [61], the turbulence model of standard k-epsilon [62], and the discretization algorithm of semi-implicit pressure linked equation with using ANSYS Fluent were considered. Various mesh node densities were realized, verified, and compared for the objective of evaluating the influence of mesh cell size on the numerical solution, and 245 × 95 nodes were regarded [49]. e detail on mathematical and numerical modeling can be found in Ref. [49]. As a validation, the obtained values for friction factor (f 0 ) and average Nusselt number (Nu 0 ) [49] are compared with the achieved values based on Dittus-Boelter [63] and Petukhov [64] correlations under equivalent flow conditions. e comparison showed that the two results related to Nu 0 and f 0 are in very good concordance.

Results and Discussion
e studied channel consists of three new transverse baffles of the shape "S." Starting with the display of air current lines (see Figure 2), regular distribution at the entrance of the channel (zone A) was detected. is distribution is disturbed in the vicinity of the first baffle located on the bottom surface of the channel (zone B). e air molecules collide with the baffle, turning towards the top of the channel (zone C). e sharp head on the front of the baffle represents the separation point of the current into three currents (zone D). e first is the main, from left to right (zone E). e second is a secondary made up of small and weakly recyclable cells in the upper front corner of the baffle (zone F). e third, also secondary, is made up of recyclable cells, large size but weak intensity, in the back of the same baffle (zone G).   is increase in velocity can be justified since a reduction in flow area and pressure augmentation (zone N). e velocity value also increases in vicinity of the lower front edge of the second baffle (zone O). Velocity amounts are paramount around the upper the channel's wall (zone P), starting from the upper left side of the third baffle (zone Q) to the exit (Figure 4). e variations of velocity across the channel are represented in Figure 5. Axial velocity can be distinguished by significant quantities in the top of the first baffle (see Figure 6), critical values below the second baffle (see Figure 7), and extremely high values near the lower surface of the channel's upper wall versus the third baffle (see Figure 8).
is increment is due to the high pressure values in these areas (see  Mathematical Problems in Engineering (zone A: see Figure 12). e second zone is adjacent to the left side in the top section (zone B: see Figure 13). e third zone is by the side of the top area (zone C: see Figure 14). e fourth region is next to the lower right corner (zone D: see Figure 15), while the fifth region is located behind the same baffle (zone E: see Figure 16), which has a large size, located in the limited area between the main stream (zone F), the upper right side (zone G), and the bottom surface of the channel (zone H), in contact with the vortex which is located next to the lower right section of this same baffle (zone D). e same behavior is observed for the two remaining baffles.

Conclusion
In this article, the air flow in a HE with three S-obstacles is studied by using CFD technique. In the addressed HE, three transverse, solid-type, S-upstream form baffles having different stations have been placed into the channel and fixed to their top and bottom walls, in a staggered manner for the aim of forcing recirculation cells to augment the mixing and hence the convective heat transfer. Also, for the objective of simulating turbulence effects, the turbulence model named k-epsilon is implemented. Furthermore, the validation and comparison with literature works are performed. e CFD analysis shows the following: below the second baffle, and extremely high values near the lower surface of the channel's upper wall versus the third baffle. is increment is due to the high pressure values in these areas as a result of significant reduction in the flow area of the fluid. (v) Five regions for recycling are due to the presence of the first baffle. e first zone is located next to the lower left side. e second zone is adjacent to the left side in the top section. e third zone is by the side of the top area. e fourth region is next to the lower right corner, while the fifth region is located behind the same baffle, which has a large size, located in the limited area between the main stream, the upper right side, and the bottom surface of the channel, in contact with the vortex which is located next to the lower right section of this same baffle. e same behavior was observed for the two remaining baffles. (vi) Finally, the simulation mentioned many physical phenomena such as the turbulence, instability, flow separation, and the appearance of reverse secondary currents. As its data are confirmed by many previous numerical and experimental results, the suggested new model of finned and baffled HE channels allows an improvement in the dynamic behavior of many thermal devices such as flat plate solar collectors. (vii) is study can be extended by the following: (1) ree-dimensional study with new boundary conditions such as the effect of solar radiation instead of temperature (2) Enhancing heat transfer using porous S-baffles (3) Improving heat transfer using perforated S-baffles (4) e effect of S-baffle dimensions on enhancing heat transfer (5) e influence of both inlet and outlet channel on S-fin heat transfer (6) Comparison of different S-baffle arrangements such as staggered, in-line, and parallel (7) e effect of thermal-physical properties of the transport fluid on S-fin heat transfer (8) e effect of S-fins with nanofluids on heat transfer and comparison of their performance with conventional fluids (9) Influence of the inclined channel with S-fins on the heat transfer for laminar and turbulent flows (10) Combination of S-fin, nanofluid, and porous media techniques to improve the performance Friction factor for the exchanger without baffles h: Height of the S-baffle, m H: Height of the exchanger, m k: Turbulent kinetic energy, m 2 s −2 k in : k at the exchanger inlet, m 2 s −2 L: Length of the exchanger, m Nu 0 : Nusselt number for the exchanger without baffles P: Pressure, Pa P atm : Atmospheric pressure, Atm s: Separation of the S-baffles, m u: Velocity in X-direction, m s −1 U in : X-velocity at the exchanger inlet, m s −1 v: Velocity in Y-direction, m s −1 w: ickness of the S-baffle, m ε: Turbulent dissipation rate, m 2 s −3 ε in : ε at the exchanger inlet, m 2 s −3 .

Data Availability
e data used to support this study are not available due to ethical/legal/commercial restrictions.

Conflicts of Interest
e authors declare that they have no conflicts of interest.