Investigation of Overlapped Twisted Tapes Inserted in a Double-Pipe Heat Exchanger Using Two-Phase Nanofluid

This study investigated the laminar convective heat transfer and fluid flow of Al2O3 nanofluid in a counter flow double-pipe heat exchanger equipped with overlapped twisted tape inserts in both inner and outer tubes. Two models of the same (co-swirling twisted tapes) and opposite (counter-swirling twisted tapes) angular directions for the stationary twisted tapes were considered. The computational fluid dynamic simulations were conducted through varying the design parameters, including the angular direction of twisted tape inserts, nanofluid volume concentration, and Reynolds number. It was found that inserting the overlapped twisted tapes in the heat exchanger significantly increases the thermal performance as well as the friction factor compared with the plain heat exchanger. The results indicate that models of co-swirling twisted tapes and counter-swirling twisted tapes increase the average Nusselt number by almost 35.2–66.2% and 42.1–68.7% over the Reynolds number ranging 250–1000, respectively. To assess the interplay between heat transfer enhancement and pressure loss penalty, the dimensionless number of performance evaluation criterion was calculated for all the captured configurations. Ultimately, the highest value of performance evaluation criterion is equal to 1.40 and 1.26 at inner and outer tubes at the Reynolds number of 1000 and the volume fraction of 3% in the case of counter-swirling twisted tapes model.


Introduction
In thermal engineering systems, convective heat transfer involves wide applications, including fuel cells [1], refrigeration [2], electronic device cooling [3], solar air collectors [4], and aerospace engineering [5]. The rise of energy demand at the turn of the new century has provoked the attention of researchers in this field of study to promote the efficiency of thermal energy systems. To increase of 5, while it is equal to only 21% for the plain tube. Qi et al. [35] accomplished an experimental study of convective nanofluid employing rotating and static built-in twisted tapes. They showed that using rotating twisted tape along with the nanofluid results in a 101.6% enhancement in heat transfer.
Another form of twisted tape inserts technique to enhance the thermal performance over the pumping power penalty, namely overlapped twisted tapes. Hong et al. [36] conducted an empirical study of a spiral grooved tube equipped with twin overlapped twisted tapes with Reynolds numbers of 8000 to 22,000, showing an enhancement in both heat transfer and friction coefficient as the overlapped twisted ratio augments. In another study [36], they employed overlapped multiple twisted tapes in a similar experiment. They showed higher entropy generation due to friction resistance and lower entropy generation due to heat transfer for a higher number of tapes and lower overlapped twisted ratios. Eiamsa-Ard and Samravysin [37] conducted an empirical study on overlapped-quadruple twisted tape inserts comparing to typical quadruple twisted tape elements for various Reynolds number under a turbulent regime. They reported the maximum value of 1.58 for PEC number at Reynolds number of 5000. Eiamsa-Ard et al. [37] in a numerical and experimental study employed overlapped dual twisted tapes along with nanofluid using TiO 2 nanoparticles. They showed an 89% enhancement in heat transfer and 113% in thermal performance compared with the plain tube. Overlapped dual twisted tapes along with Al 2 O 3 nanofluid were studied by Rudrabhiramu et al. [38]. They reported that using 1% nanofluid volume concentration and twisted tape twist pitch ratio of 2 causes the best result compared to all other captured cases.
According to the aforementioned literature review, the simultaneous implementation of various enhancement techniques leads to hybrid effects that offer higher thermal performance relative to the corresponding values achieved from each method. Applying both nanofluid and twisted tape inserts has been introduced as a promising way. However, reviewing the preceding papers reveals that the effects of overlapped twisted tape inserts in inner and outer tubes of double-pipe heat exchangers are rarely discussed in the literature. Motivated by this research gap, the main objective of this study was to investigate the heat transfer enhancement and fluid flow characteristics of Al 2 O 3 nanofluid in a double-pipe counter flow heat exchanger equipped with overlapped twisted tape inserts in inner and outer tubes with the same and opposite angular directions. Different effective parameters, including Reynolds number and the volume fraction of nanoparticles, were also analyzed by various contour plots and diagrams. Figure 1 schematically shows the counter flow double-pipe system equipped with overlapped twisted tapes in inner and outer tubes. The inner and outer tubes diameters are 10 and 29 mm, the thickness of the twisted tape is 0.4 mm with equivalent pitches of 100 mm. Two models for embedding the overlapped twisted tapes are considered: in the first model, the inner and outer twisted tapes swirl in the same angular direction (Co-STT as an abbreviation of co-swirling twisted tapes), and, in the second model, the inner and outer twisted tapes swirl in an opposite angular direction (Counter-STT as an abbreviation of counter-swirling twisted tapes). The plain heat exchanger (PHE) is also studied compared with the twisted tape cases. Al 2 O 3 -water nanofluid enters the inner and outer tubes at a temperature of 300 K, considering four different Reynolds numbers.

Governing Equations
A steady-state laminar incompressible Al2O3-water nanofluid flow neglecting the effects of radiation and viscosity losses is studied. The two-phase mixture model is used to simulate Al2O3 nanoparticles dispersed in water as follows:  Continuity equation: Momentum equation: where the drift velocity of the secondary phase drift is computed from: Energy equation: and are the average mass velocity and mixture density, respectively, which are determined as: represents the volume fraction of the mixture k th phase. The relative velocity for the two phases and the mixture viscosity are calculated as:

Governing Equations
A steady-state laminar incompressible Al 2 O 3 -water nanofluid flow neglecting the effects of radiation and viscosity losses is studied. The two-phase mixture model is used to simulate Al 2 O 3 nanoparticles dispersed in water as follows: • Continuity equation: where the drift velocity of the secondary phase drift is computed from: V m and ρ m are the average mass velocity and mixture density, respectively, which are determined as: In Equation (5), φ k represents the volume fraction of the mixture kth phase. The relative velocity for the two phases and the mixture viscosity are calculated as: Nanomaterials 2020, 10, 1656 5 of 17 The relative velocity proposed by Manin [39] and Shiller Newman drag function [40] are used as follows: Hence, the drift velocity is given as:

Nanofluid Thermo-Physical Properties
The thermophysical properties of water-Al 2 O 3 nanofluid are presented in Equations (12)- (15). The density of water-Al 2 O 3 nanofluid is calculated using Khanafer and Vafai [41] model as follows: The specific heat capacity of water-Al 2 O 3 nanofluid is defined using Bianco et al. [42] model as Equation (13): The effective dynamic viscosity of water-Al 2 O 3 nanofluid is determined using Maiga et al. [43] model as below: The effective conductivity of water-Al 2 O 3 nanofluid is calculated using Qi et al. [35] model as the following equation: The water-Al 2 O 3 nanofluid with three values of volume fractions are listed in Table 1.

Boundary Conditions and Data Deduction
At the heat exchanger, inner and outer tubes inlet, uniform velocity and temperature profiles are applied to the boundary conditions. At the outlets, zero relative gauge pressure is considered. The outer wall of the outer tube is thermally isolated, and the coupled-wall boundary is used in the interface wall. The hydrothermal parameters employed in this study are defined as follows:

Numerical Procedure
The commercial ANSYS-FLUENT code was employed in this study using the Coupled algorithm for velocity-pressure coupling using the second-order upwind scheme. The convergence criteria for energy and Navier-Stokes equations were considered 10 −6 . Figure 2 depicts the meshing of the computational domain, which is fully structured to enhance the quality of the results along with reducing the computational time. Finer mesh near the walls due to the presence of severe velocity and temperature gradients is also considered. Nanomaterials 2020, 10, x FOR PEER REVIEW 6 of 18

Boundary Conditions and Data Deduction
At the heat exchanger, inner and outer tubes inlet, uniform velocity and temperature profiles are applied to the boundary conditions. At the outlets, zero relative gauge pressure is considered. The outer wall of the outer tube is thermally isolated, and the coupled-wall boundary is used in the interface wall.
The hydrothermal parameters employed in this study are defined as follows:

Numerical Procedure
The commercial ANSYS-FLUENT code was employed in this study using the Coupled algorithm for velocity-pressure coupling using the second-order upwind scheme. The convergence criteria for energy and Navier-Stokes equations were considered 10 −6 . Figure 2 depicts the meshing of the computational domain, which is fully structured to enhance the quality of the results along with reducing the computational time. Finer mesh near the walls due to the presence of severe velocity and temperature gradients is also considered. Grids with different numbers of mesh elements are examined considering the average Nusselt number as the criteria to examine the grid independency. Table 2 presents the cases considered for mesh independence analysis. The percentage of the difference between two consecutive grids are also presented. Case 5 is chosen for all the simulations, since using finer meshing leads to relative errors less than two percent.

Validation
To verify the code, the experimental results of Qi et al. [35] for the average Nusselt number for laminar nanofluid flow in a circular tube made of stainless steel using stationary and rotating twisted tapes were used. They used a motor to drive the rotation of the twisted tape which was set to 5 RPM. They experimentally examined different concentrations of TiO 2 /water nanofluid (0.1%, 0.3%, and 0.5%) at different Reynolds numbers (600-7000) in a circular tube, with inner diameter, thickness and length of 22, 2, and 1400 mm (only the middle section (1000 mm) was used as the test section), respectively, equipped with twisted tape inserts with the length, pitch size, width, and thickness of 1600, 100, 16, and 2 mm, respectively. They chose relatively low mass concentrations of nanoparticles to reach a better stability for the nanofluid. They discussed the results based on the line relationship between the shear stress and shear rate that TiO 2 nanofluids can be approximately regarded as a kind of Newtonian fluid, and the non-Newtonian effects can be ignored. Figure 3 displays the average Nusselt number for the stationary twisted tape with nanofluid volume concentration of 0.5% at different Reynolds numbers ranging from 600 to 2200. As shown, the results are in excellent agreement with the experimental data of Qi et al. [35] where the maximum difference is less than 3.5%, as displayed in Table 3.
Grids with different numbers of mesh elements are examined considering the average Nusselt number as the criteria to examine the grid independency. Table 2 presents the cases considered for mesh independence analysis. The percentage of the difference between two consecutive grids are also presented. Case 5 is chosen for all the simulations, since using finer meshing leads to relative errors less than two percent.

Validation
To verify the code, the experimental results of Qi et al. [35] for the average Nusselt number for laminar nanofluid flow in a circular tube made of stainless steel using stationary and rotating twisted tapes were used. They used a motor to drive the rotation of the twisted tape which was set to 5 RPM. They experimentally examined different concentrations of TiO2/water nanofluid (0.1%, 0.3%, and 0.5%) at different Reynolds numbers (600-7000) in a circular tube, with inner diameter, thickness and length of 22, 2, and 1400 mm (only the middle section (1000 mm) was used as the test section), respectively, equipped with twisted tape inserts with the length, pitch size, width, and thickness of 1600, 100, 16, and 2 mm, respectively. They chose relatively low mass concentrations of nanoparticles to reach a better stability for the nanofluid. They discussed the results based on the line relationship between the shear stress and shear rate that TiO2 nanofluids can be approximately regarded as a kind of Newtonian fluid, and the non-Newtonian effects can be ignored. Figure 3 displays the average Nusselt number for the stationary twisted tape with nanofluid volume concentration of 0.5% at different Reynolds numbers ranging from 600 to 2200. As shown, the results are in excellent agreement with the experimental data of Qi et al. [35] where the maximum difference is less than 3.5%, as displayed in Table 3. Experimental data [35] Present numerical results

Results
Two models for embedding the overlapped twisted tapes were considered: in the first model, the inner and outer twisted tapes swirl in the same angular direction (Co-STT), and, in the second, model, the inner and outer twisted tapes swirl in an opposite angular direction (Counter-STT). The proposed models were analyzed for four Reynolds numbers (250, 500, 750, and 1000) employing Al 2 O 3 nanofluid at four concentrations (0, 1, 2, and 3%). It should be noted that, in the following, first, the different cases shown in Figure 1 are examined using pure water as the HTF to find the best configuration. Then, for the best system, the effects of nanoparticle concentration are assessed.

Effect of Double-Pipe Configurations
The distribution of bulk temperature in the heat exchanger inner and outer tubes throughout the channel length for water as the working fluid at various Reynolds numbers is displayed in Figure 4. The fluid temperature from the inlet to outlet is different for inner and outer tubes so that the fluid flowing through the outer tube experiences fewer changes than that for the inner tube. The reason is because of the difference in mass flow rate values of inner and outer tubes since the higher mass flow rate at the outer tube causes fewer changes in the fluid temperature along the heat exchanger length. It is also visible that the fluid temperature undergoes more changes in lower Reynolds numbers due to the lower fluid velocity resulting in more time for fluids flowing through the inner and outer tubes from the heat exchanger's inlet to outlet to exchange heat. Another point that is visible in this figure is that, at a given Reynolds number, the fluid outlet temperature in PHE is different compared with Co-STT and Counter-STT cases so that the twisted tape cases show a higher temperature difference between the heat exchanger inlet and outlet in comparison with the PHE. In fact, at a given Reynolds number, higher variation in fluid temperature from inlet to outlet implies higher heat transferring between the fluid flowing through inner and outer tubes resulting in higher heat exchanger efficiency. As a result, applying twisted tapes in both tubes of the heat exchanger causes a thermal enhancement. The reason is that in the twisted tape cases, secondary flow is created as a result of flow swirling, which consequently improves the flow mixing, disturbs the thermal boundary layer and enhances the heat transfer rate. In other words, the twisted tape redirects the colder core fluid with a better cooling capability to the heat exchanger interface wall causing higher thermal performance of the system.
For a better comparison between the bulk temperature distributions of the proposed cases along the heat exchanger length at a given Reynolds number, Figure 5 illustrates the local bulk temperature at the Re = 250. It is visible that the temperature difference of the heat exchanger's inlet and outlet is higher in Co-STT and Counter-STT cases in comparison with the PHE. Comparing the two cases of Co-STT and Counter-STT, a slightly higher fluid temperature difference of the heat exchanger's inlet and outlet is visible in the Counter-STT case due to the opposite angular direction of the twisted tapes in the inner and outer tubes.  For a better comparison between the bulk temperature distributions of the proposed cases along the heat exchanger length at a given Reynolds number, Figure 5 illustrates the local bulk temperature at the Re = 250. It is visible that the temperature difference of the heat exchanger's inlet and outlet is higher in Co-STT and Counter-STT cases in comparison with the PHE. Comparing the two cases of Co-STT and Counter-STT, a slightly higher fluid temperature difference of the heat exchanger's inlet and outlet is visible in the Counter-STT case due to the opposite angular direction of the twisted tapes in the inner and outer tubes.   Figure 6 displays the heat flux between the inner and outer tubes for different proposed cases. As shown, the transferred heats for the double-pipe inserts (Cases 2 and 3) are much higher than that for Case 1. Besides, Case 3 has a slight advantage compared with Case 2 according to the transferred heat flux between the pipes. For example, for the Reynolds number of 250 and = 0, the heat flux for Case 3 is 6.67 W, which is 29.62 and 4.82% higher than Cases 1 and 2, respectively.  Figure 6 displays the heat flux between the inner and outer tubes for different proposed cases. As shown, the transferred heats for the double-pipe inserts (Cases 2 and 3) are much higher than that for Case 1. Besides, Case 3 has a slight advantage compared with Case 2 according to the transferred heat flux between the pipes. For example, for the Reynolds number of 250 and φ = 0, the heat flux for Case 3 is 6.67 W, which is 29.62 and 4.82% higher than Cases 1 and 2, respectively.  Figure 6 displays the heat flux between the inner and outer tubes for different proposed cases. As shown, the transferred heats for the double-pipe inserts (Cases 2 and 3) are much higher than that for Case 1. Besides, Case 3 has a slight advantage compared with Case 2 according to the transferred heat flux between the pipes. For example, for the Reynolds number of 250 and = 0, the heat flux for Case 3 is 6.67 W, which is 29.62 and 4.82% higher than Cases 1 and 2, respectively.    Figure 8 demonstrates the friction coefficient variations for the cases of PHE, Co-STT, and Counter-STT at different Reynolds numbers. Applying twisted tape increases the friction coefficient due to the added surface area and flow blockage created by the twisted tape inserted in the tube. Furthermore, there is no difference between the friction coefficient values of the Co-STT and Counter-STT cases as the secondary flow intensity, added surface area, and flow blockage effects are the same in both cases. Moreover, the friction coefficient decreases at higher Reynolds numbers. This can be explained using Equation (17) in which there exists velocity to the power of two in the denominator of friction coefficient correlation.  Counter-STT at different Reynolds numbers. Applying twisted tape increases the friction coefficient due to the added surface area and flow blockage created by the twisted tape inserted in the tube. Furthermore, there is no difference between the friction coefficient values of the Co-STT and Counter-STT cases as the secondary flow intensity, added surface area, and flow blockage effects are the same in both cases. Moreover, the friction coefficient decreases at higher Reynolds numbers. This can be explained using Equation (17) in which there exists velocity to the power of two in the denominator of friction coefficient correlation.  Figure 9 shows the cross-sectional velocity contours for PHE, Co-STT, and Counter-STT at Re = 250. It is visible that applying the twisted tapes at both inner and outer tubes redirects the core fluid with higher velocity and heat transfer capacity to the vicinity of the interface wall causing higher thermal performance. There is no difference between the velocity contours of Co-STT and Counter-STT cases since the direction of the twisted tape does not affect the velocity distribution. In addition,  Figure 9 shows the cross-sectional velocity contours for PHE, Co-STT, and Counter-STT at Re = 250. It is visible that applying the twisted tapes at both inner and outer tubes redirects the core fluid with higher velocity and heat transfer capacity to the vicinity of the interface wall causing higher thermal performance. There is no difference between the velocity contours of Co-STT and Counter-STT cases since the direction of the twisted tape does not affect the velocity distribution. In addition, comparing the red colors of different cases, showing higher velocity at the fluid core, it can be implied that the twisted tapes create a secondary flow and better mixing causing higher velocity and advection phenomenon near the interface wall, and, as a result, a higher heat transfer rate is obtained. Nanomaterials 2020, 10, x FOR PEER REVIEW 12 of 18 comparing the red colors of different cases, showing higher velocity at the fluid core, it can be implied that the twisted tapes create a secondary flow and better mixing causing higher velocity and advection phenomenon near the interface wall, and, as a result, a higher heat transfer rate is obtained.
(a) (b) (c)  Figure 10 displays the cross-sectional temperature contours for PHE, Co-STT, and Counter-STT at the Reynolds number of 250. The PHE temperature contours show the normal development of thermal boundary layer in both inner and outer tubes as the fluid flows through the unit; however, the temperature contours at the cases of Co-STT and Counter-STT are different so that the thermal boundary layer disturbance occurs and secondary flow and better flow mixing affect the boundary layer causing higher heat exchanger efficiency. Moreover, looking at the temperature distributions at  Figure 10 displays the cross-sectional temperature contours for PHE, Co-STT, and Counter-STT at the Reynolds number of 250. The PHE temperature contours show the normal development of thermal boundary layer in both inner and outer tubes as the fluid flows through the unit; however, the temperature contours at the cases of Co-STT and Counter-STT are different so that the thermal boundary layer disturbance occurs and secondary flow and better flow mixing affect the boundary layer causing higher heat exchanger efficiency. Moreover, looking at the temperature distributions at the tubes' outlet implies the fact that using twisted tape causes a higher amount of fluid to participate in the heat transfer process between the tubes due to the presence of secondary flow and better flow mixing by substituting the fluid near the interface wall with the core fluid and vice versa. Comparing the temperature distribution for the two cases of Co-STT and Counter-STT shows that, in the Counter-STT case, the secondary flow at both tubes causes the regions with thinnest thermal boundary layer in both tubes to be in direct contact with each other and are placed in the same angular direction, resulting in higher thermal performance in comparison with Co-STT case. Thus, the regions in the outer tube with the thinnest thermal boundary layer are in direct contact with the regions in the inner tube with the thickest thermal boundary layer.  Figure 11 illustrates the temperature contour at the interface wall of the heat exchanger for PHE, Co-STT, and Counter-STT at the Reynolds number of 250. The temperature distribution on the interface wall implies the intensity of the secondary flow affecting the interface wall. In the PHE, the temperature enhances uniformly as the fluid flows along the heat exchanger length showing the thermal boundary layer development. In contrast, in the presence of twisted tapes in the inner and outer tubes, the disturbance in the thermal boundary layer increases, which is enhanced in Counter-STT compared with Co-STT, implying higher thermal performance.  Figure 11 illustrates the temperature contour at the interface wall of the heat exchanger for PHE, Co-STT, and Counter-STT at the Reynolds number of 250. The temperature distribution on the interface wall implies the intensity of the secondary flow affecting the interface wall. In the PHE, the temperature enhances uniformly as the fluid flows along the heat exchanger length showing the thermal boundary layer development. In contrast, in the presence of twisted tapes in the inner and outer tubes, the disturbance in the thermal boundary layer increases, which is enhanced in Counter-STT compared with Co-STT, implying higher thermal performance. Figure 11 illustrates the temperature contour at the interface wall of the heat exchanger for PHE, Co-STT, and Counter-STT at the Reynolds number of 250. The temperature distribution on the interface wall implies the intensity of the secondary flow affecting the interface wall. In the PHE, the temperature enhances uniformly as the fluid flows along the heat exchanger length showing the thermal boundary layer development. In contrast, in the presence of twisted tapes in the inner and outer tubes, the disturbance in the thermal boundary layer increases, which is enhanced in Counter-STT compared with Co-STT, implying higher thermal performance.

Effect of Nanoparticle Concentration on the Performance of Counter-STT Compared with Co-STT
To investigate the effects of Al2O3 nanofluid in the case of Counter-STT, Figure 12 depicts the variations of Nusselt number at the inner and outer tubes in terms of Reynolds number at various

Effect of Nanoparticle Concentration on the Performance of Counter-STT Compared with Co-STT
To investigate the effects of Al 2 O 3 nanofluid in the case of Counter-STT, Figure 12     Using nanoparticles enhances the viscosity of the fluid, causing higher friction coefficient magnitudes. Moreover, using nanofluids in such geometries, including twisted tape inserts causing intense flow mixing and secondary flow, seems to be beneficial as it prevents undesirable phenomena, including the possible agglomeration and sedimentation of nanoparticles. Figure 13 depicts the variations of friction factor at the inner and outer tubes in terms of Reynolds number at various volume concentrations of the nanofluid in the case of Counter-STT. Using nanoparticles enhances the viscosity of the fluid, causing higher friction coefficient magnitudes. Moreover, using nanofluids in such geometries, including twisted tape inserts causing intense flow mixing and secondary flow, seems to be beneficial as it prevents undesirable phenomena, including the possible agglomeration and sedimentation of nanoparticles. As discussed above, the twisted tape inserts augment both the heat transfer rate as a desirable objective and friction coefficient as an undesirable parameter. Therefore, there is a trade-off between the benefits of using twisted tape in thermal performance enhancement and the side effects in forcing more pumping power to the system. To analyze this issue, the dimensionless PEC introduced in As discussed above, the twisted tape inserts augment both the heat transfer rate as a desirable objective and friction coefficient as an undesirable parameter. Therefore, there is a trade-off between the benefits of using twisted tape in thermal performance enhancement and the side effects in forcing more pumping power to the system. To analyze this issue, the dimensionless PEC introduced in Equation (21) is discussed here. In fact, this number is employed to evaluate the practical use of any enhancement techniques in the viewpoint of energy-saving potential. Generally, higher values of PEC imply superior energy saving. Figure 14 illustrates the PEC parameter for PHE, Co-SST, and Counter-SST at the inner and outer tubes. Using nanofluid and increasing its volume concentration results in higher PEC values showing more enhanced heat transfer than enhanced friction coefficient in such configurations. In addition, it can be observed that, for a higher Reynolds number, the PEC number enhances as well, implying better energy saving in higher velocities of the inlet fluid flowing through both inner and outer tubes. Moreover, the figure shows that the Counter-STT model yields higher PEC values compared with that for the Co-STT model in all Reynolds numbers and nanofluid volume concentrations. Ultimately, the highest value of PEC number is equal to 1.40 and 1.26 in the inner and outer tubes, which are found at Re = 1000, the volume fraction of 3%, and Counter-STT model. Equation (21) is discussed here. In fact, this number is employed to evaluate the practical use of any enhancement techniques in the viewpoint of energy-saving potential. Generally, higher values of PEC imply superior energy saving. Figure 14 illustrates the PEC parameter for PHE, Co-SST, and Counter-SST at the inner and outer tubes. Using nanofluid and increasing its volume concentration results in higher PEC values showing more enhanced heat transfer than enhanced friction coefficient in such configurations. In addition, it can be observed that, for a higher Reynolds number, the PEC number enhances as well, implying better energy saving in higher velocities of the inlet fluid flowing through both inner and outer tubes. Moreover, the figure shows that the Counter-STT model yields higher PEC values compared with that for the Co-STT model in all Reynolds numbers and nanofluid volume concentrations. Ultimately, the highest value of PEC number is equal to 1.40 and 1.26 in the inner and outer tubes, which are found at Re = 1000, the volume fraction of 3%, and Counter-STT model.

Conclusions
Benefiting from the compound heat transfer enhancement techniques of overlapped twisted tape and nanofluid, this study numerically investigated the flow of Al2O3 nanofluid through a counter flow double pipe in which both inner and outer tubes are equipped with overlapped twisted tape inserts in two models of the same (Co-STT) and opposite (Counter-STT) angular directions. A

Conclusions
Benefiting from the compound heat transfer enhancement techniques of overlapped twisted tape and nanofluid, this study numerically investigated the flow of Al 2 O 3 nanofluid through a counter flow double pipe in which both inner and outer tubes are equipped with overlapped twisted tape inserts in two models of the same (Co-STT) and opposite (Counter-STT) angular directions. A parametric study was conducted to evaluate the effect of key design variables, including the angular direction, Reynolds number, and nanofluid volume fraction on the thermo-hydraulic characteristics of such a configuration. Dimensionless number of PEC was employed to assess the trade-off between enhancement in heat transfer and pressure drop. The following outcomes are obtained from this study:

Conflicts of Interest:
The authors declare no conflict of interest.