Thermal performance investigation of N‐shape double‐pipe heat exchanger using Al2O3, TiO2, and Fe3O4‐based nanofluids

Researchers and engineers are actively working on enhancing the efficiency of heat exchangers in engineering applications by developing novel designs, exploring new materials, and utilizing nanofluids. Three kinds of nanofluids with varying concentrations are investigated in this paper. The objective is to assess the performance of N‐shaped double‐pipe heat exchanger used in thermoelectric power plants. The performance has been evaluated using COMSOL Multiphysics software. The findings show that higher nanofluid concentrations resulted in elevated heat transfer coefficients and improved efficiency of N‐shape double pipe heat exchanger. The analysis revealed that a mere 1% rise in the volume fraction of nanofluids enhanced the efficiency of the heat exchanger on average 23% when compared to the base fluid (water). In comparison to the N‐shape double pipe (Inconel 625) heat exchangers, the N‐shape double pipe (copper) heat exchangers appear to be more efficient. The introduction of nanoparticles has a notable impact on the heat transfer coefficients. Specifically, within an N‐shaped double pipe (copper) heat exchanger, the inclusion of a 1% volume fraction results in a 2.09% enhancement in the heat transfer coefficient for Al2O3/water, a 1.3% improvement for Fe3O4/water, and a 1.15% increase for TiO2/water. It also exposed that adding 1% Al2O3/water led to a significant 0.623% increase in effectiveness, while TiO2/water showed a 0.259% rise, and Fe3O4/water exhibited a 0.375% improvement. Moreover, increasing the Reynolds number enhances the Nusselt number for Al2O3/water and Fe3O4/water nanofluids by 55.22%, and for TiO2/water by 54.60% at a 6% volume concentration, leading to additional increases in exchanger efficiency. Therefore, the augmentation in nanofluid concentration leads to a reduction in the temperature pinch points both at the intake and outflow. This observation suggests that nanofluids exhibit a superior ability compared to conventional fluids when it comes to effectively lowering temperatures.


K E Y W O R D S
exchanger's efficiency, heat exchanger, heat transfer coefficient, nanofluid, N-shape, volume fraction

| INTRODUCTION
Heat exchanger is employed to transfer heat from one variable-temperature fluid to another in a variety of industries, including petroleum, gasoline, chemical industries, power generation, heating, air conditioning, heat recovery, and chemical processes. 1However, their limited thermal conductivity prompts the use of methods like fin insertion, geometry alteration, and enhanced thermophysical characteristics in working fluids to improve performance. 2To address this, nanofluids, consisting of nanometer-sized particles suspended in base fluids like water or oil, are employed due to their excellent physical properties. 3Nanoparticles, typically metals, oxides, or carbides, enhance thermal conductivity, positively impacting the heat transfer coefficient between surfaces and the working fluid. 4Nanofluids surpass conventional heat transfer fluids with improved stability, physical properties, high thermal conductivity, and minimal pressure drop.This superiority makes nanofluids integral to widely used heat exchangers, prompting researchers to focus on diverse methods to enhance thermal performance and overall efficiency.To exemplify this, Akhtari et al. 5 explored α-Al 2 O 3 /water nanofluid in heat exchangers, revealing improved heat transfer efficiency with increased flow rates, particle concentrations, and nanofluid inlet temperature.Heat transfer coefficients rose by 13.2% and 21.3%, respectively, compared to water.Another study 6 on γ-Al 2 O 3 nanoparticles showed a 19%-24% boost in heat transfer coefficients and Nusselt numbers at 0.1%-0.3%volume fractions.Javadi et al. 7 compared three nanofluids in a plate heat exchanger, revealing a 30% improvement in overall heat transfer coefficients at 2% volume concentration for Al 2 O 3 and TiO 2 were compared to SiO 2 .Pattanayak et al. 8 experimentally studied Al 2 O 3 , CuO, TiO 2 , and ZnO nanofluids in a double-pipe counter-flow heat exchanger.The most effective performance (0.085%) was achieved with TiO 2 /water at a 0.075% volume concentration.Similarly, Jalili et al. 9 observed a 12% enhancement in convection heat transfer coefficient in a countercurrent double-pipe heat exchanger with fins when using water-aluminum oxide and water-titanium dioxide nanofluids at concentrations ranging from 0.4% to 6%.In addition, Fe 3 O 4 nanoparticles with diameters of 15-20 nm were dispersed in water at a volume fraction of 0.08%-0.1%,which significantly increased the convection heat transfer coefficient and Nusselt number by approximately 12%-26%. 10 It was suggested that Fe 3 O 4 nanoparticles generate a maximum heat transfer enhancement of 14.7% at a 0.06% volume fraction in a double-pipe heat exchanger with a return bend. 11As a result, the nanofluid's convective heat transfer coefficient increased along with the nanoparticle concentration and nanofluid temperature. 12n particular, enhancing the heat exchanger's overall performance using nanofluids would depend on numerous aspects such as temperature, thermal conductivity, flow rate, particle size, concentration, and so on. 13,14beroumand et al. 15 conducted experiments on Cu/ engine oil, revealing that nanoparticles at 0.2%-1% weight concentrations improved thermal conductivity by 27%-49%.Another study on Fe 3 O 4 nanofluid in an ethylene glycol/water mix (20%:80%) showed a 46% increase in thermal conductivity with 2.0 vol.% nanoparticles. 16Hasan et al. 17 enhanced heat transfer in a double pipe heat exchanger by adding an extended surface to the inner tube's outer part, using a 5% volume concentration of "Alumina nanofluid."This resulted in a 20% increase in heat transfer coefficient and a 4.7% rise in thermal conductivity.Ajeeb et al. 18 experimentally improved energy efficiency in a compact gasket plate heat exchanger using Al 2 O 3 nanofluids at various low concentrations, reaching peak efficiency at the highest particle concentration of 1.3.Dharmakkan et al. 19 evaluated the microplate heat exchanger performance, achieving the highest Nusselt number of 35.8 with a hybrid nanofluid (TiO 2 -ZnO/ethylene glycol) at 4% volume concentration and a temperature of 50°C.Ghazanfari et al. 20 studied twisted tubes and Al 2 O 3 nanofluid's impact on a shell and tube heat exchanger, resulting in an 8% increase in heat transfer coefficient and a 40% reduction in pressure drop.Hamza et al. 21xplored a hybrid nanofluid's influence on tube heat exchangers, reporting a 47.17% maximum increase in Nusselt number with plain twisted tape inserts, achieving an overall 29% heat transfer enhancement.Alklaibi et al. 22 investigated a shell and helical coil heat exchanger, finding a slight improvement in effectiveness beyond a 1.0% volume fraction of Fe O 3 4 nanofluid. 20jeeb et al. 23 conducted a comparative study on a compact plate heat exchanger using Al 2 O 3 and TiO 2 nanofluids.Results showed a substantial thermal performance improvement of about 7.30% with 2% volume concentration for Al 2 O 3 nanoparticles and 4.20% for TiO 2 nanoparticles.Investigating the impact of flow rates on smooth and corrugated double-tube heat exchangers, Zheng et al. 24 found that the use of nanofluids and thread structures can enhance their thermal performance.Similarly, a study by Hasan et al. 25 analyzed the heat transfer performance of a helical heat exchanger with different water-based nanofluids, and found that Al 2 O 3 exhibited the highest heat transfer rate while SiO 2 performed the least efficiently.Another study by Gugulothu et al. 26 focused on shell-and-tube heat exchangers and found that using Al 2 O 3 nanofluid as the working fluid resulted in superior heat transfer rates compared to other nanofluids and base fluid.Azeez et al. 27 conducted a numerical analysis on a hybrid nanofluid consisting of 4% volume fraction AlN-water in a four-channel laminar FC flow heat exchanger, and observed a 30% improvement in HT in the trapezoidal channel compared to water.Moreover, further investigation on the subject matter can be located in Abay et al. 28 and Saha et al. 29 Upon reviewing existing literature, it was noted that there is limited reporting on the heat transfer coefficients, as well as the effectiveness and thermal performances of an N-shape double-pipe heat exchanger employing various nanofluid compositions (Al 2 O 3 , TiO 2 , and Fe 3 O 4 ).This study employs COMSOL Multiphysics to assess the thermophysical properties and performance of an N-shape double-pipe heat exchanger.The choice of this design is based on its moderate size, ease of manufacturing, and compactness, contributing to favorable outcomes.The N-shape configuration reduces the overall volume compared to a straight-tube model, allowing for consideration of heat stress consequences.Furthermore, it's noteworthy that N-tube heat exchangers typically exhibited a slight reduction in operational pressure.The adoption of stainless-steel construction played a crucial role in preventing corrosion and the accumulation of deposits.In light of this investigation, a recommendation is made for the utilization of nanofluids with varying concentrations as cooling fluids.This strategic approach has shown the potential to notably enhance the performance of the heat exchanger.

| MATERIALS AND METHODS
This research focuses on a copper double-pipe heat exchanger with concentric pipes (16 and 10 cm radii) used in a thermoelectric power plant to cool the turbine shaft's lubrication system.The aim is to deliver lubricant at the right temperature for efficient plant operation.This is achieved through a counterflow arrangement of fluids.The ultimate objective is to maintain the lubricant at an optimal temperature for ideal operating conditions.Figure 1 illustrates the three-dimensional design of the N-shaped heat exchanger.It is approximately 5 m in length and constructed from high thermal conductivity copper.

| Governing equations
The steady-state conservation equations governing mass, momentum, and energy for the nanofluid can be formulated as follows 30 : where ρ nf represents the density of nanofluids, P is the pressure, V is the velocity vector, τ is the stress tensor, T is the temperature, and k nf presents thermal conductivity of nanofluids.Utilizing the finite element method in COMSOL Multiphysics showcases its adaptability for effectively addressing and resolving the Navier-Stokes equations.

| Boundary conditions
The initial step in applying the finite element technique to address a problem is the design of an appropriate mesh tailored to the specific domain.
While this task may initially appear formidable, it holds paramount importance as the mesh structure significantly influences the accuracy of the finite element method's approximations.Striking a balance between mesh size and computational costs is crucial, necessitating careful consideration to avoid overly refining the mesh.Developing an effective meshing strategy can be intricate, entailing a trade-off between employing a regular mesh in specific contact areas and a finer mesh in others.In this endeavor, the COMSOL Multiphysics program proves invaluable, allowing for the evaluation of mesh quality through various geometric criteria, such as simple, triangular, diamond, or quadratic shapes.In our approach, we have opted for a freely structured triangular mesh with edge tightening for its suitability to our problem.
Figure 2 provides a visual representation of the double-pipe configuration within our heat exchanger.Particular emphasis has been placed on regions where diverse thermal phenomena originate.Notably, in zones like the inner tube contact region with the outer tube fluid, where both thermal conduction of the inner tube and thermal convection between the inner and outer tubes occur, maintaining a thin mesh is imperative.This ensures that our calculation process receives comprehensive data, ultimately leading to accurate results.Given the high aspect ratio in this area, special care is required in handling the mesh.Moreover, it's worth noting that the material properties of both oils are temperature-dependent.Consequently, we have employed a nonisothermal flow predefined Multiphysics coupling to accurately account for this variation in our simulations.Table 1 illustrates the specific boundary conditions selected for the analyzed problem.
To ascertain whether the flow exhibits laminar or turbulent characteristics, an initial estimation of the Reynolds number is conducted.This parameter is defined as follows: Here ρ represents the fluid density, v stands for the typical velocity, μ signifies the viscosity, and D H denotes the hydraulic diameter for the inner pipe.Specifically, for the inner pipe, D H equates to the diameter of the pipe, whereas for the outer pipe, it corresponds to the difference between the pipe's radius.The values corresponding to these parameters are provided in Table 2.
The inner and outer pipes exhibit Reynolds numbers of approximately 152.487 and 297.906, respectively.With this approximation, a nonisothermal flow Multiphysics coupling is employed in the laminar regime.Additionally, due to minimal temperature fluctuations in both pipes, the densities of the separated fluids can be regarded as constant, allowing for the utilization of incompressible formulations to model the fluid flows in both cases.Table 3 illustrates several experimental observations conducted on a double-pipe heat exchanger.Upon close examination, it is evident from both experimental and computational studies that the overall heat transfer effectiveness of the double pipe heat exchanger can be significantly enhanced by strategically adjusting its geometric configurations.The efficacy of nanofluids in this context is contingent on their physical properties and volume concentrations.Notably, among the nanofluids assessed, Al 2 O 3 emerges as the top performer, surpassing both TiO 2 and Fe 3 O 4 in terms of heat transfer efficiency.

| Mathematical modeling
The determinants of convective heat transfer depend on a range of thermophysical characteristics inherent to the nanofluid.To ascertain these factors, calculations involving density, thermal conductivity, and specific heat capacity are essential, as well as the viscosity.The density of nanofluids can be computed using conventional formulas established for a two-phase mixture.
The effective density of the nanofluid is expressed as follows 35,36 : The specific heat of the nanofluid is determined through the following calculation 37 : To compute the thermal conductivity of a nanofluid, the Maxwell model is employed 38 : The Einstein model is utilized to estimate the viscosity of the nanofluid 39 : nf bf (8)   In recent thermophysical characterization studies, as detailed in Table 4, the emphasis has been on discerning parameters over a wide spectrum of temperatures.This section scrutinizes how properties change with varying temperatures, with a special focus on the correlation between density and temperature for the base fluid, which is water in this context. 42: The specific heat, thermal conductivity, and viscosity of the base fluid as functions of temperature are determined according to the methods outlined in Vajjha and colleagues [42][43][44] Additional investigations have been carried out to comprehensively understand how the thermophysical properties of nanofluids evolve with varying temperatures and volume fractions.These studies have provided valuable insights into the behavior of these nanofluids under different thermodynamic conditions.Figures 3, 4, and 5 represent the relationship of density versus temperature of Al 2 O 3 , TiO 2 , and Fe O 3 4 nanofluids with 1%-6% volume fractions, respectively.Observing Figure 3, it becomes evident that the density of the A l2 O 3 /water nanofluid decreases as temperature rises.Conversely, when the volume fraction is increased, there is an observed increase in density.It has also been observed that the water has minimum density and decreases with the increasing temperature.In addition, the behaviors of nanofluids are generally similar to that of water, although there is a notable increase in density when combined with water.However, when considering the overall density of the nanofluid, it decreases as the volume fraction increases.This observation can be seen in Figure 4, where it has been determined that the density of TiO 2nanofluid decreases as the temperature increases.Conversely, the density of this nanofluid increases when the volume fraction is increased.Furthermore, Figure 5 reveals that the density of Fe 3 O 4 nanofluids decreases as the temperature increases.These findings provide valuable insights into the density variations of different nanofluids under varying conditions.
Similarly, Figures 6, 7, and 8 have illustrated the range of the specific heat versus the function of temperature of Al 2 O 3 , TiO 2 , and Fe 3 O 4 nanofluids with 1%-6% of volume fractions.The presence of nanoparticles in the nanofluid modifies its thermal properties.As temperature rises, specific heat capacity increases due to enhanced nanoparticle Brownian motion, facilitating better energy transfer.However, at higher temperatures, nanoparticle aggregation may reduce effective surface area, leading to a decrease in specific heat capacity.| 1077 Figure 6 illustrates that water consistently possesses the highest specific heat capacity.It's worth noting that this property exhibits an exponential evolution, directly proportional to temperature increase.However, the introduction of nanoparticles has an inverse effect, causing a reduction in this behavior.Figures 7 and 8 indicate an upswing in the specific heat capacity of the nanofluid with higher temperatures.It's noteworthy that at lower temperatures, the nanofluid's specific heat capacity is marginally less than that of pure water.The heat exchange between the hot fluid (lubricant) and the cold fluid (nanofluids) is crucial for assessing the effectiveness of the heat exchanger.This evaluation allows for the determination of the amount of heat transferred between these two fluids.The effectiveness, expressed as a dimensionless value between 0 and 1, is calculated in a counter-flow configuration.The initial step involves conducting an efficiency analysis to quantify the thermal flow rate.q C = mṫ p which is provided in Bendaraa et al. 45 For the hot fluid (lubricant): For the cold fluid (nanofluid): The nondimensionalized Nusselt and Reynolds numbers are calculated by, respectively 45 The Prandtl number is characterized as follows 45 : nf pnf nf (16)   Hence, the convection heat exchange coefficient is determined by the following equation 45 : To calculate the effectiveness of the heat exchanger, use the following formula 46 : The log mean temperature difference (LMTD) is defined as 45 : For counter flow, ( ) After incorporating these parameters into the COMSOL Multiphysics application, a validation simulation was conducted.In Table 5, we intricately compare the research outcomes from Bendaraa et al. 45 with the results derived from our own research endeavors.This tabular representation serves to highlight the nuanced differences and similarities, offering a comprehensive overview of the findings between the two studies.This confirms the precision of the model.In addition, Figure 9, a comprehensive comparison is presented, illustrating the Nusselt Number and Reynolds Number between the work conducted by Bendaraa et al. 45 and our present study.
The data reveals a noteworthy agreement between our current findings and those of the prior work, demonstrating consistent and comparable results.In this validation process, we have employed Al 2 O 3 nanofluid with a 0% volume fraction.Copper materials have been utilized for both scenarios, providing compelling evidence of the acceptable accuracy achieved by our present code.

| RESULTS AND DISCUSSION
In this investigation, the effect of nanoparticle volume fraction on the hydrodynamic behavior and heat transmission of nanofluid flow was studied in an Nshape double pipe heat exchanger operating under countercurrent regimes, employing two distinct materials.A numerical simulation was performed using the COMSOL Multiphysics platform, leading to several conclusions regarding the process parameters.The lubricant oil, upon entering the outer tube, has a temperature of 360 K. Inside the internal tube, the mixture of nanofluid and water commences at 300 K. Additionally, various nanofluid volume fractions ranging from 0% to 10% were considered.The findings of the investigation revealed that the N-shaped double-pipe heat exchanger (DPHE), made of copper, demonstrates superior effectiveness compared to the N-shaped DPHE constructed with Inconel 625.Furthermore, it has been observed that the incorporation of nanoparticles has a substantial impact on heat transfer coefficients.In the case of an N-shape double pipe (copper) heat exchanger, when 1% particle concentrations of Al 2 O 3 are introduced into the base fluid (water), the heat transfer coefficient experiences a 2.08077% increase, while Fe 3 O 4 demonstrates a 1.3027% enhancement, and TiO 2 exhibits a 1.1457% rise.Thus, the investigation concludes that among the nanofluids examined, Al 2 O 3 /water emerges as the most efficient option.

| Impacts on the heat exchanger effectiveness
Figure 10 illustrates the relationship between the effectiveness versus nanofluids (Al 2 O 3 , Fe 3 O 4 , and TiO 2 ) with 1%-10% volume fractions where pipe material has been chosen copper.The study found that utilizing the volume fraction leads to an average increase of 1.60494% in exchanger efficiency for the single loop N-shape double pipe heat exchanger, in comparison to the conventional fluid, water (Figure 10).Conversely, the efficiency of the exchanger showed only marginal shifts with regard to the average volume fraction of TiO 2 mixed with water.Additionally, it was noted that an increase in the efficiency of the exchanger resulted from the average volume fraction of Fe 3 O 4 combined with water, generating a 0.37037% increase in exchanger efficiency.Elevating the volume fraction of the nanofluid plays a significant role in influencing the thermal properties within our system.In this configuration, the inner pipe carries the heated lubricant fluid, while the outer pipe facilitates the flow of the cooling fluid.Similarly, Figure 11 illustrates the impact on the efficiency of the countercurrent double pipe heat exchanger when transitioning from copper to Inconel 625 (a Nickel-based alloy).This change was assessed across various volume fractions of the nanofluids employed in previous experiments.It has been investigated that there was an average 12.4615% decrease in Al 2 O 3 +water nanofluid efficiency (Figure 11) compared to conventional fluid (water) that it has been used in N-shape double pipe heat exchanger.Under identical conditions for TiO 2 +water and Fe 3 O 4 + water nanofluids, the efficiency is anticipated to decrease, averaging at 15.6923% and 14.9231%, respectively, in comparison to the countercurrent N-shape  double pipe heat exchanger where copper was employed as the pipe material.

| Nanofluid effects on nusselt number
The Nusselt number (Nu) and Reynolds number (Re) are essential dimensionless parameters in fluid mechanics, with significant roles in describing heat transfer and fluid flow, respectively.Figure 12 illustrates how the Nu varies with Reynolds number for different concentrations of nanofluids, as compared to the base fluid.With an escalating Nu in a nanofluid, there is an observed upswing in both the Re and particle concentrations.The dispersion of nanoparticles makes it feasible for nanofluid to have a higher Nusselt number than water at the same mass flowrate.When compared to water data, the Nu enhancement for the Al 2 O 3 /water nanofluid at a particle concentration of 3% is roughly 16.77% at a Reynolds number of 25,485.Comparable to the findings for water, at a particle concentration of 0.06%, there is an observed enhancement of approximately 55.22% in the Nu when the Re is at 25,485.The Nu enhancement is around 1.45%, 8.87%, 26.58%, and 39.25% for 1%, 2%, 4%, and 5% volume concentrations, respectively, within the observed Re range from 3282 through 25,485.Additionally, the Nu enhancement is around 1.45%, 8.87%, 26.58%, and 39.25% for 1%, 2%, 4%, and 5% volume concentrations, respectively, within the observed Re range from 3282 through 25,485.The illustration presented in Figure 13 serves as a demonstration of the Nu improvement that can be observed in the TiO 2 /water nanofluid.Specifically, it is evident that this improvement amounts to approximately 1.65%, 8.29%, 25.70%, and 54.60% for volume concentrations of 1%, 2%, 4%, and 6% respectively.It is important to note that these results were obtained under the condition of a constant Re value of 25,485.Furthermore, at a constant Reynolds number of 25,485, the Nusselt number (Nu) exhibits a noticeable increase with varying volume concentrations of Fe 3 O 4 /water nanofluid.Specifically, the Nu values rise by approximately 1.47%, 8.93%, 26.66%, and 55.22% for volume concentrations of 1%, 2%, 4%, and 6%, respectively, as depicted in Figure 14.This suggests a significant augmentation in heat transfer efficiency as the concentration of Fe 3 O 4 nanoparticles in the water medium increases.The observed trends underscore the potential of nanofluids to enhance thermal performance, with higher concentrations leading to more substantial improvements in heat transfer characteristics.

| Effect of nanofluids on LMTD
The effectiveness of heat transfer greatly depends on the LMTD, which is a crucial factor in assessing the overall efficiency of the heat exchange process.The investigation primarily involved the analysis of exit temperatures in a countercurrent N-shape DPHE with the incorporation of nanofluids, aiming to evaluate the LMTD.The cooling fluid, represented by the outlet temperature of cold nanofluids flowing through the inner pipe, interacted with the hot fluid, engine oil passing through the engine and subsequently cooling down in the N-shape double pipe heat exchangers.As observed, the outlet temperature of cold nanofluids gradually increased due to their heat absorption from the engine oil, effectively cooling it down.Conversely, the temperature at the outlet of the hot fluid (engine oil) showed a continuous decrease as it lowered its temperature.Utilizing nanofluids with different volume fractions resulted in reduced inlet and outlet pinches, which is mostly due to a decrease in the LMTD. Figure 15 has been displayed the relationship between the LMTD versus nanofluids (Al 2 O 3 , Fe 3 O 4 , and TiO 2 ) with 1%-10% volume fractions where pipe material has been chosen copper.Additionally, nanofluids have displayed an elevated capability for energy absorption when contrasted with standard fluids.This has resulted in substantial average decreases of 12.6687%, 5.72993%, and 5.45888% for the average volume fraction of Al 2 O 3 +water, TiO 2 +water, and Fe 3 O 4 +water (Figure 15), respectively, in comparison to water as the cooling fluid in the N-shape DPHE.
On the other hand, Figure 16 illustrates the correlation between LMTD and nanofluids (specifically Al 2 O 3 , Fe 3 O 4 , and TiO 2 ) across a range of volume fractions from 1% to 10%.The pipe material considered for this analysis is Inconel 625.This graphical representation provides insights into how LMTD varies with different nanofluids and concentrations when Inconel 625 is employed as the pipe material.It has been observed the behavior of LMTD on countercurrent Nshape double pipe (Inconel 625) heat exchanger and got that on average 33.6261% increasing in LMTD on Al 2 O 3 +water nanofluid, 42.4622% increase in TiO 2 +water, 42.9501% increase in Fe 3 O 4 +water (Figure 16) compared to N-shape double pipe (copper) heat exchanger using conventional cooling fluid.

| Nanofluid effects on HT coefficient
In this investigation, the research focused on analyzing the influence of nanofluids on the HT coefficient within a  Similarly, Figure 18 illustrates the correlation between the HT coefficient and nanofluids (Al 2 O 3 , Fe 3 O 4 , and TiO 2 ) with 1% to 10% volume fractions where pipe material has been chosen Inconel 625.According to Figure 18, it has been observed that for the HT coefficient of the countercurrent N-shape DPHE (Inconel 625), there is a significant enhancement in exchanger efficiency.Specifically, the use of an Al 2 O 3 +water-based nanofluid, as opposed to the base fluid (water), led to a 4.39399% increase in exchanger efficiency.Conversely, 1.01021% decrease by average volume fraction of TiO 2 +water nanofluid.Furthermore, there is an observed increase in the HT coefficient of about 0.38979% when using a mixture of Fe 3 O 4 +water compared to the cooling fluid (water) in the inner pipe of the Countercurrent Heat Exchanger (Inconel 625).

| Outlet temperature of lubricant
The investigation of nanofluid outlet temperatures provided valuable insight into the configuration's inlet and outlet pinch profiles.As a result of utilizing nanofluid for cooling purposes in this system, its elevated thermal conductivity allows it to effectively capture and manage the temperature of the hot fluids, making the outlet temperature a pivotal parameter in evaluating the exchanger's performance.Opting for nanofluids in lieu of conventional cooling fluids results in a decrease in outlet temperature, as evidenced by observations in both Figures 19 and 20.Notably, it has been noted that the use of Al 2 O 3 +water nanofluid proves more effective in reducing lubricant temperature for both materials when compared to Fe 3 O 4 +water and TiO 2 +water nanofluids.Furthermore, the trend indicates that an increase in volume concentrations of nanofluids leads to a significant reduction in outlet temperature for both materials.

| CONCLUSIONS
This research rigorously investigated the thermal efficiency of a purpose-designed N-shaped doublepipe heat exchanger for effective lubricating oil cooling.Nanofluids were proposed as a potential coolant enhancement.Employing numerical analyses in COMSOL Multiphysics, the study thoroughly examined heat transfer characteristics, efficiency, and temperature variations, with a key emphasis on escalating nanofluid volume fractions.Results highlighted substantial temperature differences between the outlet and inlet ports, showcasing the superior cooling capabilities of nanofluids compared to the base fluid.This underscores the potential for enhanced heat exchange in practical applications.
The study emphasizes the efficacy of Al In general, the N-shape double pipe (copper) heat exchanger proves more effective than its Inconel 625 counterpart.Incorporating nanoparticles significantly influences heat transfer coefficients, with 1% Al 2 O 3 in the copper heat exchanger yielding a 2.08077% increase, while Fe 3 O 4 and TiO 2 exhibit improvements of 1.3027% and 1.1457%, respectively.This study recommends utilizing Al 2 O 3 /water nanofluid in the N-shaped double-pipe heat exchanger for enhanced thermal efficiency in cooling lubricating oil across diverse systems.These findings provide valuable insights for optimizing heat exchanger designs, particularly in the selection of nanofluids and materials for specific applications.

2 3 ,
Representation of the mesh used.T A B L E 1 Boundary Condition characteristic.TiO 2 , and Fe 3 O 4 Lubricant oil --Laminar -

F I G U R E 4
Density variation of TiO 2 /water nanofluid.F I G U R E 5 Density variation of Fe 3 O 4 /water nanofluid.F I G U R E 6 Specific heat evolutions of Al 2 O 3 /water nanofluid.

7
Specific heat evolutions of TiO 2 /water nanofluid.F I G U R E 8 Specific heat evolutions of Fe 3 O 4 /water nanofluid.

F I G U R E 10
Variation in the effectiveness of countercurrent N-shape DPHE (copper).F I G U R E 11 Variation in the effectiveness of countercurrent N-shape DPHE (Inconel 625).F I G U R E 12 Variation of Nu with particle concentrations and Reynolds number for Al 2 O 3 /water nanofluid.

F
I G U R E 13 Variation of Nu with particle concentrations and Reynolds number for TiO 2 + water nanofluid.SALIM ET AL. | 1083 F I G U R E 14 Variation of Nu with particle concentrations and Reynolds number for Fe O 3 4 + water nanofluid.F I G U R E 15 LMTD of countercurrent N-shape double pipe (Copper) heat exchanger.
16 LMTD of countercurrent Nshape double pipe (Inconel 625) heat exchanger.SALIM ET AL. | 1085 counter-current N-shaped DPHE, which was fabricated using both copper and Inconel 625 materials.This dualmaterial composition enabled a thorough evaluation of the nanofluid's influence on heat transfer performance across various material qualities and attributes.Therefore, Figure 17 depicts the correlation between the heat transfer coefficient and nanofluids (specifically Al 2 O 3 , Fe 3 O 4 , and TiO 2 ) across volume F I G U R E 17 HT Coefficient analysis of Countercurrent N-shape DPHE with Copper.F I G U R E 18 HT coefficient analysis of Countercurrent N-shape DPHE with Inconel 625.fractions ranging from 1% to 10%.In this context, the chosen pipe material is copper.The research findings indicate a significant enhancement in exchanger efficiency, specifically a 5.56036% increase, with the utilization of an Al 2 O 3 +water-based nanofluid in place of the base fluid (water).On the other hand, 0.523724% increase by average volume fraction of TiO 2 +water nanofluid.There is also an increase in HT coefficient Fe 3 O 4 +water about 1.77843% compared to conventional cooling fluid(water).

F
I G U R E 19 Outlet temperature of countercurrent N-shape double pipe (copper) heat exchanger.F I G U R E 20 Outlet temperature of N-shape double pipe (Inconel 625) heat exchanger.
Experimental studies on double pipe heat exchanger.
34A B L E 2 Typical scales of the Reynolds number. 2 -H 2 O nanofluids (0.1%, 0.3%, and 0.5%) enhance heat transfer by 14.8% but increase pressure drop (up to 51.9%) in double-tube heat exchangers compared to water.El-Maghlany et al.33Cu/water Cu-water nanofluid boosts heat transfer coefficient and exchanger performance significantly compared to the base fluid.NTU increases by 23.4% and effectiveness by 16.5%.Lotfi et al.34MWNT-water Multiwalled carbon nanotube (MWNT)/water nanofluid improves heat transfer in a horizontal shell and tube exchanger compared to the base fluid. : 40,41 L E 4 Thermophysical properties of fluids and (Al 2 O 3 , TiO 2 , and Fe 3 O 4 ) nanofluids.40,41 F I G U R E 3 Density variation of Al 2 O 3 /water nanofluid.SALIM ET AL.
45A B L E 5 Comparison between Bendaraa et al.45results and present work.Comparision of the Nusselt number and Reynolds number between Bendaraa et al.'s 45 work and the present work.
2 O 3 /water nanofluid, showcasing a significant 1.60494% improvement in heat exchanger effectiveness.Fe 3 O 4 /water nanofluid exhibits a more modest enhancement of 0.37037%, while TiO 2 /water has minimal impact with copper pipes and reduced effectiveness with Inconel 625 pipes.Both Al 2 O 3 /water and Fe 3 O 4 /water nanofluids demonstrate identical Nusselt number enhancements at 6% volume concentration (55.22%), with TiO 2 /water slightly lower at 54.60%.In Inconel 625, there are notable increases in LMTD: 33.6261% with Al 2 O 3 nanofluid, 42.4622% with TiO 2 , and 42.9501% with Fe 3 O 4 nanofluid, while improvements are relatively lower with copper material.Analyzing HT coefficients, Al 2 O 3 shows a 5.56036% increase for copper materials, TiO 2 exhibits a 0.523724% increase, and Fe 3 O 4 demonstrates a 1.177843% improvement.In Inconel 625, the heat transfer coefficient exhibits a marginal decrease with Al 2 O 3 .Additionally, Al 2 O 3 nanofluid effectively decreases lubricant temperature in both materials compared to Fe 3 O 4 and TiO 2 nanofluids.
C p lub specific heat of lubricant (J/kg.°C)C pnf specific heat of nanofluid (J/kg.°C)C min minimum value of heat capacities (J/kg.°C) C pbfspecific heat of Base fluid (J/kg.°C)C pnp specific heat of nanoparticles (J/kg.°C)