Introduction

Many applications rely heavily on natural convection as the dominant mechanism for heat transfer. As a result, it is imperative to gain a comprehensive understanding of the thermal dynamics governing these systems, especially when natural convection is the only influencing factor. Such an understanding paves the way for the development of effective strategies to improve the heat transfer characteristics within these systems.

Typically, the insertion of inserts into the flow channel is used to increase the heat transfer rate, resulting in a reduction in the hydraulic diameter of the channel [1]. Heat transfer enhancement techniques can be broadly divided into two categories: active and passive. Active methods rely on external inputs such as the application of electrostatic fields, mechanical vibration or pulsation to enhance the heat transfer process [2]. Conversely, passive methods involve altering surface geometry or increasing flow turbulence to enhance heat transfer [3, 4]. Passive techniques include various approaches including the use of porous materials, corrugated surfaces, extended surfaces, dimples, wire coils, vortex devices, protrusions and the implementation of nanofluids [5,6,7], among other strategies.

Due to their relatively low thermal conductivity, conventional heat transfer fluids such as oil, water and mixtures of ethylene glycol have inherent limitations in terms of heat transfer efficiency. It is imperative to increase the thermal conductivity of these fluids in order to improve the heat transfer coefficient between the heat transfer medium and the surface. Various methods have been used to achieve this, including the incorporation of suspended particles of nano/micro or larger size into the fluids to increase their thermal conductivity [8,9,10].

Over the past two decades, nanofluids have emerged as an important and attractive class of heat transfer fluids, offering significant potential to improve heat transfer over conventional fluids. Extensive research has been conducted on nanofluids, and several notable studies have contributed to the understanding of their heat transfer properties. Ahuja [11, 12] conducted experiments focused on improving heat transfer in laminar water flow using a suspension of micro-sized polystyrene particles. The results showed a significant increase in both the Nusselt number and the efficiency of the heat exchanger compared to a single-phase liquid. Pak and Cho [13] investigated convective heat transfer in turbulent flow using nanofluids consisting of water with Al2O3 and TiO2 nanoparticles. Their findings revealed that the Nusselt number of the nanofluids increased with higher volume fractions of suspended nanoparticles and Reynolds numbers. Zhaoa et al. [14] conducted a numerical study on the flow of water/Al2O3 nanofluid in a smooth tube under constant temperature and heat flux conditions. The study examined the heat transfer characteristics and demonstrated the influence of nanoparticle addition on heat transfer enhancement. Hashemi et al. [15] performed an experimental investigation concerning the flow of oil/CuO nanofluid inside horizontal coiled tubes under a constant heat flux. The study aimed to analyze the heat transfer and pressure drop characteristics and evaluate the impact of nanofluid flow on heat transfer performance. Ebrahimnia-Bajestana et al. [16] performed a comprehensive analysis by employing a combination of numerical simulations and experimental procedures. The primary focus was to study the behavior of water/TiO2 nanofluid flow within a tube. The research outcomes demonstrated a significant improvement in the heat transfer rate upon introducing nanoparticles into the base fluid, with a notable increase of up to 21%. Sadeghi et al. [17] conducted numerical investigations using nanofluids flowing through a circular tube equipped with a helical tape insert. The results demonstrated that all four types of nanofluids outperformed pure water in terms of the Nusselt number. The Nusselt number increased with higher Reynolds numbers and decreased twist ratios of the helical tape insert.

In their study, Kanti et al. [18] examined the thermophysical characteristics of water-based nanofluids containing alumina (Al2O3), graphene oxide (GO) and their hybrid nanofluids at various mixing ratios. They conducted measurements of properties such as thermal conductivity and viscosity over a range of volume concentrations and temperatures, spanning from 0.1 to 1 vol% and 30–60 °C, respectively. Notably, they observed that at a temperature of 60 °C and a volume concentration of 1 vol%, GO exhibited a substantial thermal conductivity enhancement, which was 43.9% higher than that of the Al2O3 nanofluid. In another study, Wanatasanappan et al. [19] conducted an investigation into the viscosity and rheological characteristics of an Al2O3–Fe2O3 hybrid nanofluid. They experimentally examined five different compositions of Al2O3–Fe2O3 nanoparticles for viscosity and rheological properties across a temperature range of 0–100 °C. The experimental findings revealed that the Al2O3-Fe2O3 composition of 40/60 exhibited the highest viscosity values across all investigated temperatures, whereas the composition of 60/40 exhibited the lowest viscosity values. Azmi et al. [20] conducted experiments aimed at determining the heat transfer coefficients and friction factor of TiO2/water nanofluid under varying volume concentrations and Reynolds numbers. The research results demonstrated a significant increase in heat transfer coefficients when the nanofluid concentration reached 1.0% within the tube. Additionally, the twist ratio of the tapes used in the experiments had an impact on the heat transfer coefficient. These studies collectively contribute to the understanding of nanofluid heat transfer behavior and highlight the potential for enhanced heat transfer performance in various applications.

The second law of thermodynamics provides a fundamental principle stating that energy quality decreases during a process due to the presence of irreversibilities, which can be quantified by the rate of entropy production. When assessing heat transfer systems, it is often more crucial to evaluate them based on the second law of thermodynamics rather than relying solely on the first law. Applying second law analysis to thermal systems aims to determine the optimal operating conditions for practical implementation. One key parameter influencing system efficiency is entropy generation, which arises from irreversibilities caused by thermal and frictional losses. Thermal devices inherently introduce irreversibilities, necessitating the analysis of the second law of thermodynamics to understand the impact of these irreversibilities on the depletion of available energy. Nanofluids exhibit remarkable thermal conductivity along with slightly increased viscosity, which enables them to significantly influence flow irreversibility. In thermal devices, a higher degree of irreversibility results in a greater amount of entropy generation, leading to decreased device efficiency. Minimizing the amount of entropy generated in a thermal device can contribute to improved efficiency. This can be achieved through device design that aims to minimize friction and heat loss. Moreover, the utilization of materials with high thermal conductivity can facilitate more efficient heat transfer.

In the research conducted by Dickson et al. [21], it was found that the concentration of nanoparticles in a nanofluid has a significant impact on the local entropy generation in the nanofluid phase. The presence of internal heat generation was also found to strongly influence the predicted local entropy generation, depending on the interface model used. The research findings revealed a strong dependence of the total entropy generation on the Peclet number and conductivity ratio. Moreover, significant variations were observed in the total entropy generation as a result of changes in the internal heat generation. Bahiraei et al. [22] investigated the thermal, hydraulic and second law characteristics of a hybrid nanofluid composed of silver-decorated graphene nanoparticles within two innovative microchannel heat sinks. The study examined varying volume concentrations of 0.02%, 0.04%, 0.06% and 0.1%. The results revealed that heat transfer plays a more significant role in entropy generation compared to friction. Additionally, the nanofluid exhibited lower irreversibility than pure water, indicating its suitability as a working fluid based on the principles of the second law of thermodynamics. In their study, Bahiraei et al. [23] employed simulations utilizing a two-phase mixture model to investigate the effects of nanoparticle volume fractions ranging from 0.01 to 0.04. The results demonstrated that incorporating the nanofluid can significantly reduce overall exergy destruction and enhance second law efficiency, making it a promising choice for spiral heat exchangers. The study suggests that using a nanofluid with a high-volume fraction can achieve superior performance from the perspective of the second law. Moreover, employing higher flow rates of the nanofluid improves second law efficiency, albeit at the cost of increased exergy destruction. The study also highlights the excellent performance of the spiral heat exchanger in terms of the second law, with a minimum second law efficiency recorded at 0.847. According to Khanmohammadi et al. [24], their results demonstrate that the double twisted tape with a twisted ratio of 2.5 outperforms other types of inserts in terms of convection coefficient, indicating superior heat transfer performance. However, when considering the pressure drop, the single twisted tape with a twisted ratio of 3.5 demonstrates the lowest pressure drop. Analyzing the total entropy generation, it is observed that this parameter decreases significantly for Reynolds numbers ranging from 5000 to 8000, and afterwards, it remains relatively constant. At a Reynolds number of 11,000, the double twisted tape with a twisted ratio of 2.5 exhibits the lowest total entropy generation. These findings suggest that the double twisted tape performs better in terms of second law efficiency at lower Reynolds numbers and lower twisted ratio values. In the study conducted by Sundar et al. [25], the introduction of hybrid nanofluids into a tube resulted in a decrease in thermal entropy generation as the Reynolds number and particle volume loadings increased. The thermal entropy generation decreased as particle loading increased, indicating improved heat transfer efficiency. Dagdevir et al. [26] observed that as the Reynolds number increased, indicating increased turbulence, the thermal boundary layer thickness along the flow path decreased. The utilization of inserts in the heat exchanger tube resulted in a significant reduction in thermal entropy generation rate for the fluid in motion, leading to increased second law efficiency by reducing the rate of exergy destruction. The utilization of CuO nanofluid had a positive impact on the experimental results compared to using water alone, with a decrease in thermal irreversibilities and improved second law efficiency. A study conducted by Moghaddami et al. [27], examined laminar flows of water–Al2O3 nanofluid and conducted a comprehensive analysis to investigate the impact of nanoparticle volume concentration on entropy generation. The experimental results indicated that the addition of nanoparticles at a volume concentration of 1% led to a notable reduction of approximately 3.6% in entropy generation. This suggests that incorporating nanoparticles in the nanofluid can contribute to a decrease in irreversibilities and enhance the efficiency of the system from a second law perspective. Additionally, the study found that at a Reynolds number of 853, entropy generation was minimized for each specified nanoparticle volume concentration. This implies that there is an optimum operating condition in terms of Reynolds number where entropy generation is minimized, indicating improved system performance and efficiency. Marulasiddeshi et al. [28] conducted an investigation into the thermo-hydraulic behavior and the rate of thermodynamic irreversibility in a circular copper tube with water-based Al2O3 and Al2O3 + CuO hybrid nanofluid. The findings revealed that, in comparison with pure water, the maximum enhancement of the Nusselt number was 51%, 59% and 79.7% for 1 vol% of hybrid nanofluid at temperatures of 30 °C, 45 °C and 60 °C, respectively. Additionally, the pressure drop and exergy efficiency of the hybrid nanofluid increased with concentration and Reynolds number, while the total entropy generation of the hybrid nanofluid decreased at higher Reynolds numbers and concentrations. Akbarzadeh et al. [29] utilized the first and second laws of thermodynamics to optimize the positioning of porous inserts within a double-pipe heat exchanger, aiming to enhance heat transfer while minimizing pressure drop and entropy generation. Their conclusion highlighted that the introduction of a porous layer along the walls leads to a higher rate of viscous entropy generation compared to the core region. In another study, Akbarzadeh et al. [30] explored the combined impact of nanofluid, a porous insert, and corrugated walls within a heat exchanger duct, analyzing their effects on heat transfer, pressure drop and entropy generation through numerical simulations. The results demonstrated that in the divergent segments of the wavy duct, the nanofluid temperature was generally higher than that in the convergent sections, and viscous entropy was predominantly generated near the walls. This was also observed around the interface between the porous layer and the clear nanofluid regions due to the strong velocity gradients in these areas.

Traditional heat transfer fluids often have limitations in terms of thermal conductivity, which can affect overall heat transfer efficiency. However, recent advances in nanofluids, particularly hybrid nanofluids, have shown significant potential to improve heat transfer compared to conventional fluids. Furthermore, the incorporation of modified inserts in heat exchanger tubes has been demonstrated to improve heat transfer performance by enhancing flow turbulence. Drawing inspiration from the studies discussed above, there is a compelling motivation to investigate the combined effects of modified coiled wire inserts and hybrid graphene–iron oxide nanofluid in a heat exchanger tube. This study introduces a groundbreaking approach to heat transfer enhancement by integrating a hybrid nanofluid comprising GnP and Fe3O4 nanoparticles with modified coiled wire inserts within a heat exchanger tube. The synergy between these two elements represents a novel concept, exploiting the exceptional thermal conductivity of GnP and the magnetic properties of Fe3O4 to potentially achieve superior heat transfer efficiency. Notably, this research uniquely focuses on evaluating second law efficiency, entropy generation number and Bejan number in the context of this innovative combination, providing advanced insights into heat transfer optimization. Therefore, this research aims to explore the synergistic effects of modified coiled wire inserts and hybrid graphene–iron oxide nanofluid in a heat exchanger tube, providing valuable insights for the development of more efficient heat transfer systems in various industrial applications.

Materials and experimental technique

Preparation of nanofluids

The nanoparticles of GnP and Fe3O4 (Table 1) were procured from Nanografi Nanotechnology Inc. The binary hybrid nanofluids, comprising GnP–Fe3O4 dispersed in a water–ethylene glycol base fluid, were synthesized utilizing a two-step method outlined in a prior publication [31]. The nanofluids were formulated with three distinct mass concentrations, namely, 0.00%, 0.20% and 0.40%, incorporated within a base fluid consisting of 80% distilled water and 20% ethylene glycol. The preparation procedure of these nanofluids encompassed the subsequent stages:

  • Initially, the surfactant was homogenously mixed with the base fluid employing a mechanical stirrer.

  • Subsequently, the GnP–Fe3O4 nanoparticles were methodically added at predetermined mass ratios, followed by thorough re-mixing.

  • Prior to nanoparticle addition, cetyltrimethylammonium bromide (CTAB) was dissolved in pure water [32], after which the GnP–Fe3O4 nanoparticles were systematically integrated into the base fluid at three distinct mass ratios.

  • The resultant mixture underwent mechanical agitation for 30 min to ensure a comprehensive dispersion of the nanoparticles.

  • In order to achieve a uniform suspension, the nanoparticles and surfactant were dispersed within the base fluid through ultrasonication (Bandelin HD3400) at an intensity of 120 W for a duration of 60 min.

  • Additionally, the stability of the nanofluids, prepared with different mixing ratios, was assessed using zeta potential analysis (Table 1).

Table 1 The thermophysical properties of nanoparticles [33]
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Once the hybrid nanofluids have been prepared, the thermal conductivity of the nanofluids is measured using a KD-2 Pro thermal property analyzer and their dynamic viscosities are measured using an MRC VIS-8 rotational viscometer. The density and specific heat of the hybrid nanofluid are determined utilizing well-established correlations extensively cited in scientific literature. These correlations are presented by Eqs. (1) and (2), respectively.

$$ \rho_{{{\text{nf}}}} = (1 - \phi )\rho_{{{\text{bf}}}} + \phi \rho_{{{\text{np}}}} $$
(1)
$$ c_{{{\text{nf}}}} = (1 - \phi )c_{{{\text{bf}}}} + \phi c_{{{\text{np}}}} $$
(2)

Test rig

The experimental setup, as illustrated in Fig. 1, featured a test tube that was divided into three distinct sections: the inlet (1500 mm), the test section (1100 mm) and the outlet (500 mm). The test tube was constructed from SS-304 steel, with inner and outer diameters of 17 mm and 21 mm, respectively. To ensure a uniform heat flux, the outer wall of the test tube was heated using a variac transformer.

Fig. 1
figure 1

Schematic of the test rig [34]

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To minimize convective heat loss, an insulating layer of 6-mm-thick glass wool was applied to the test tube. Temperature measurements from the outer surface were obtained with a precision of 0.4 using 10 K type thermocouples. Additionally, the inlet and outlet temperatures were measured using the same type of thermocouple to ensure uniformity. Fluid supply to the test section was regulated by an inverter-controlled pump, and a flow meter was used to measure the volumetric flow rate. The pressure drop across the test tube was determined with a differential pressure transmitter. For a comprehensive description of the experimental procedure and additional technical details, the previous publication [31] provides in-depth information.

In the context of this study, the preparation of hybrid nanofluid configurations entailed the concurrent fabrication of conical wire inserts, as illustrated in Fig. 2. These inserts were meticulously crafted from stainless steel wire, featuring a circular cross-sectional diameter of 1 mm, and were strategically emplaced at two distinct axial locations: P = 8.5 mm and P = 17 mm. The conical wire inserts possessed precise geometric attributes, as elucidated in Fig. 2, including Le (effective length) = 34 mm, Ded (external diameter) = 17 mm, Dei (internal diameter) = 8.5 mm and De (end tip diameter) = 2 mm.

Fig. 2
figure 2

Technical features of insert types

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Data reduction

Thermal and hydraulic parameters

In this study, the evaluation of the thermal performance is based on the Nusselt number, while the evaluation of the hydraulic performance is based on the friction factor. The dimensionless parameters, Nusselt number and friction factor, are calculated using the procedure outlined below. The expression, which results from equating the heat transferred to the fluid in the tube with the heat absorbed by the fluid, can be represented as shown in Eqs. (3) and (4).

$$ Q_{{{\text{fluid}}}} = Q_{{{\text{conv}}}} $$
(3)
$$ Q_{{{\text{fluid}}}} = \dot{m}C_{{{\text{fluid}}}} (T_{{\text{o}}} - T_{{\text{i}}} ) = \Delta VI - Q_{{{\text{loss}}}} $$
(4)

The dissipation of heat from the test tube to the surrounding environment can be expressed as described in Eq. (5).

$$ Q_{{{\text{loss}}}} = \frac{{(T_{{{\text{ow}}}} - T_{\infty } )}}{{\frac{1}{{h_{{\text{o}}} 2\pi Lr_{{{\text{ins}}}} }} + \frac{{\ln (r_{{{\text{ins}}}} /r_{{\text{o}}} )}}{{2\pi Lk_{{{\text{ins}}}} }}}} $$
(5)

The calculation of the heat flux that uniformly applies to the test tube is accomplished as follows:

$$ q = \frac{{Q_{{{\text{fluid}}}} }}{{\pi LD_{{\text{o}}} }} $$
(6)

The local convective heat transfer coefficient and the corresponding local Nusselt numbers can be expressed as Eqs. (7) and (8), respectively.

$$ h(x) = \frac{q}{{T_{{{\text{iw}}}} (x) - T_{{\text{b}}} (x)}} $$
(7)
$$\dot{m}c\left[{T}_{{\text{b}}}\left(x\right)-{T}_{{\text{b}}}\left(x-\Delta x\right)\right]=\frac{{P}_{{\text{net}}}}{L}\Delta x$$
(7.a)
$${T}_{{\text{b}}}\left(x\right)={T}_{{\text{b}}}\left(x-\Delta x\right)+\frac{{\dot{P}}_{{\text{net}}}\Delta x}{\dot{m}{c}_{{\text{p}}}L}$$
(7.b)

To calculate the average temperature of the fluid \({T}_{{\text{b}}}\left(x\right)\) in a specific section \((x),\) the total energy balance is applied to the fluid flowing through the heated tube of length \(\Delta x\), as indicated by Eq. (7.a). Then, \({T}_{{\text{b}}}\left(x\right)\) is calculated as shown in Eq. (7.b).

$$ {\text{Nu}}(x) = \frac{h(x)D}{k} $$
(8)

The Reynolds number (Re) and the friction factor can be computed using the formulas presented in Eqs. (9) and (10), respectively.

$$ {\text{Re}} = \frac{{{\text{UD}}}}{\nu } $$
(9)
$$ f = \frac{\Delta P}{{\frac{1}{2}\rho .U^{2} \frac{L}{D}}} $$
(10)

Second law analysis

In fact, second law analysis allows losses to be attributed to specific design and operating parameters [35]. As this study is primarily concerned with thermodynamics, heat transfer and fluid mechanics, both entropy generation minimization and exergy analysis are explored.

The entropy generation rate for fluid flow can be determined using the first and second laws of thermodynamics for the passage of length dx [36, 37].

$$ \dot{m}{\text{d}}h = q^{\prime } {\text{d}}x\;\;{\text{and}}\;\;\dot{S}_{{{\text{gen}}}}^{\prime } = \dot{m}\frac{{{\text{d}}s}}{{{\text{d}}h}} - \frac{{q^{\prime}}}{T + \Delta T} $$
(11)

The entropy generation rate (\(\dot{S}^{\prime}_{{{\text{gen}}}}\)) can be obtained as shown in Eq. (11) by incorporating the adaptation of the enthalpy equation per unit length. Consequently, the expression for the entropy generation rate can be written as presented in Eqs. (12) and (13).

$$ \dot{S}^{\prime}_{{{\text{gen}}}} = \frac{{q^{\prime}\Delta T}}{{T^{2} (1 + \Delta T/T)}} + \frac{{\dot{m}}}{\rho T}\left( { - \frac{{{\text{d}}P}}{{{\text{d}}x}}} \right) \cong \frac{{q^{\prime}\Delta T}}{{T^{2} }} + \frac{{\dot{m}}}{\rho T}\left( { - \frac{{{\text{d}}P}}{{{\text{d}}x}}} \right) \ge 0 $$
(12)
$$ \dot{S}^{\prime}_{{{\text{gen}}}} = \frac{{q^{\prime 2} }}{{\pi kT^{2} {\text{Nu}}}} + \frac{{32\dot{m}^{3} f}}{{\pi^{2} \rho^{2} TD^{5} }} $$
(13)

In Eq. (13), the term on the left-hand side represents the entropy generation due to heat transfer (\(\dot{S}^{\prime}_{{{\text{gen}},\Delta {\text{T}}}}\)), while the part on the right-hand side represents the entropy generation due to pressure drop (\(\dot{S}^{\prime}_{{{\text{gen}},\Delta {\text{P}}}}\)).

To facilitate a comparison of the entropy generation rates between a tube with and without heat transfer enhancement techniques, the entropy generation number is defined as depicted in Eq. (14).

$$ N_{{\text{s}}} = \dot{S}^{\prime}_{{{\text{gen}},{\text{e}}}} /\dot{S}^{\prime}_{{{\text{gen}},{\text{s}}}} $$
(14)

The Bejan number [38] is a common dimensionless parameter utilized in entropy generation analysis. It is the heat transfer irreversibility to total irreversibility ratio, as described in Eq. (15).

$$ {\text{Be}} = \frac{{\dot{S}^{\prime}_{{{\text{gen}},\Delta {\text{T}}}} }}{{\dot{S}^{\prime}_{{{\text{gen}},\Delta {\text{T}}}} + \dot{S}^{\prime}_{{{\text{gen}},\Delta {\text{P}}}} }} $$
(15)

Equation (16) expresses the maximum theoretical rate of imported exergy (Ẋq) resulting from heat flux and mass transfer within the tube flow. In Eq. (17), the exergy destruction rate (Ẋd) arising from irreversibilities within the system is computed. The second law efficiency (\({\eta }_{{\text{II}}}\)) is computed using Eq. (18), representing the ratio between the actual thermal efficiency and the maximum achievable efficiency (in the reversible state) of the heat exchanger tube.

$$ \mathop {X_{{\text{q}}} }\limits^{.} = \mathop Q\limits^{.} (1 - \frac{{T_{{\text{i}}} }}{{T_{{{\text{iw}}}} }}) $$
(16)
$$ \mathop {X_{{\text{d}}} }\limits^{.} = T_{{\text{a}}} \mathop {S_{{{\text{gen}}}} }\limits^{.} $$
(17)
$$ \eta_{{{\text{II}}}} = \frac{{\mathop {X_{{\text{q}}} }\limits^{.} - \mathop {X_{{\text{d}}} }\limits^{.} }}{{\mathop {X_{{\text{q}}} }\limits^{.} }} $$
(18)

The most commonly referenced error analysis method in the literature, as advised by Kline and McClintock [39], was applied to determine if the error margins of the data collected in the experimental study met acceptable criteria. Table 2 provides the error values related to the measurement instruments used in the initial study. Based on these values, Table 3 presents the results of the uncertainty analysis for parameters such as Reynolds number, Nusselt number, friction factor, entropy generation number and Bejan number.

Table 2 Uncertainties of measured parameters
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Table 3 Uncertainty analysis values of the experimental data
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Results and discussion

Synthesis and stability of nanofluids

In the study, nanofluids were prepared by incorporating graphene–iron oxide nanoparticles at two different mass ratios (0.2 and 0.4%) into a base fluid consisting of 80% pure water and 20% ethylene glycol. The microstructures and properties of these nanofluid samples were determined by XRD and SEM analyses. In addition, zeta potential analyses were performed to evaluate the stability of the nanofluids.

Figure 3 shows the XRD results for different mass ratios. The graph showed that graphene exhibited similar distributions in the 20–30θ range, while iron oxide exhibited comparable distributions in the 30–40θ range. These results were consistent with previously published research studies by Refs. [40, 41].

Fig. 3
figure 3

XRD distributions of the samples prepared with a 0.2% mass ratio and b 0.4% mass ratio of graphene–iron oxide hybrid nanoparticles

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In Fig. 4, SEM images were taken at different distances: 2 µm (Fig. 4a) and 10 µm (Fig. 4b). The images showed the arrangement of graphene nanosheets in a plate-like morphology with adherent spherical iron oxide nanoparticles. This interaction between graphene and iron oxide resulted in the formation of a nanocomposite structure with a uniform distribution of nanoparticles. In Fig. 4a, the surface of the graphene nanosheet layers was densely populated with iron oxide nanoparticles. The close-up at 2 µm provided a detailed view of this densely packed arrangement. In contrast, Fig. 4b provides a broader view, allowing us to observe the overall distribution of the graphene nanosheets, and how the iron oxide nanoparticles were attached to them. This image provided a broader perspective of the nanocomposite structure.

Fig. 4
figure 4

SEM images of graphene–iron oxide hybrid nanoparticle

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Zeta potential values are used as an indicator of stability in nanofluids. When the stabilization amount exceeds ± 30 mV, the system is considered stable, according to Oflaz et al. [42]. In the analysis of zeta potential results as given in Fig. 5, for the mass ratio of 0.2% (Fig. 5a), the zeta potential value was measured as + 36 mV, and for the mass ratio of 0.4% (Fig. 5b), it reached 34 mV. These positive zeta potential values indicate that the nanofluid samples were stable, as they exceed the ± 30-mV threshold for stability.

Fig. 5
figure 5

Zeta potential analysis results of hybrid nanofluids with different mass fractions

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Validation of experimental methodology

In the validation study, the dimensionless numbers obtained from the experimental tests show approximate values in accordance with the corresponding equations, and their curve characteristics closely match. This conformity between the numerical values and the characteristic behavior provides strong evidence for the accuracy and validity of the experimental methodology. Figure 6 shows the variation of two important dimensionless quantities, the Nusselt number and the friction factor. These results were obtained from experimental tests carried out on a smooth tube using a fluid consisting of 80% pure water and 20% ethylene glycol. The tests take into account the Reynolds number, which is a key parameter in fluid flow analysis. The Nusselt number is related to heat transfer, while the friction factor is related to pressure drop in the flow.

$$ {\text{Nu}} = 0.023{\text{Re}}^{0.8} \Pr^{0.4} $$
(17)
Fig. 6
figure 6

Experimental validation results for Nusselt number and friction factor versus Reynolds number

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$$ f = 0.316{\text{Re}}^{ - 0.25} $$
(18)

The experimental data were compared with the widely used correlations, namely, Dittus and Boelter Eq. (17) [43] and Blasius Eq. (18) [44]. The experiments covered a range of five different Reynolds numbers, approximately ranging from 3000 to 15,000. When comparing the Nusselt number and friction factor results with the literature, it was observed that the deviation values were within ± 11.1% and ± 9.8%, respectively. This confirms the accuracy of the experimental methodology.

Thermal and hydraulic performance

Figure 7 shows the results obtained from the use of modified inserts within the flow area of the hybrid nanofluid at mass ratios of 0.00, 0.20 and 0.40%. The presence of the inserts in the tube caused an expected increase in the Nusselt number. These modified insert configurations disrupted the shapes of the thermal and hydraulic boundary layers within the tube, promoting secondary flow and enhancing convective heat transfer, ultimately leading to an increase in the Nusselt number.

Fig. 7
figure 7

Distribution of Nusselt number versus Reynolds number for all configurations

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When evaluating the performance of the modified inserts in terms of Nusselt number, it was found that the barrel configuration gave the best performance, followed by the hourglass configurations. It can be observed that an increase in the mass ratio of the hybrid nanofluid leads to an upward trend in the Nusselt number for all insert configurations [45]. The highest Nusselt number values were obtained using the barrel-type insert with a P/D ratio of 0.5, regardless of the nanofluid mass ratio. Conversely, the lowest values were recorded for the hourglass-type insert with a P/D ratio of 1. Of the configurations provided, the highest Nusselt number was achieved with a hybrid nanofluid mass ratio of 0.40%, a barrel-type insert with a P/D ratio of 0.5 and a Reynolds number of 15,000, resulting in a value of 345.

Figure 8 shows the relationship between friction factor and Reynolds number. It was found that as the nanofluid mass ratio increased, both the pressure drop and the friction factor increased [45]. Compared to the empty tube experiments, the change in average friction factor was relatively small compared to the increase in Nusselt number. All insert configurations placed inside the tube contributed to an increase in the friction factor. This can be attributed to the modified inserts causing an increase in pressure drop along the tube by disrupting the flow and supporting secondary flow. When the results of the inserts were evaluated based on the friction factor, the barrel-type element showed the highest performance, followed by the hourglass type. The utilizing of hybrid nanofluid slightly increased the fluid friction. The highest results for the smooth tube with different mass fractions from lower to higher obtained as 0.046, 0.047 and 0.048, respectively. The highest friction factor of 0.155 obtained for the configuration of barrel-type P/D = 0.5 with 0.4% mass fraction of GnP–Fe3O4/water–ethylene glycol nanofluid at the lowest Reynolds number of 3000.

Fig. 8
figure 8

Distribution of friction factor versus Reynolds number for all configurations

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The correlations for the hourglass type and barrel type are presented by Eqs. (19) and (20), as well as Eqs. (21) and (22), respectively. These models are applicable to hybrid GnP–Fe3O4 nanofluid with mass ratios ranging from 0.20 to 0.40%, pitch ratios(P/D) of 0.5 and 1, Prandtl numbers within the specified range of 6.11–7.13 and Reynolds numbers ranging from 3000 to 15,000.

$$ {\text{Nu}}_{{{\text{hourglass}}\_{\text{type}}.}} = 0.564{\text{Re}}^{0.809} \Pr^{ - 0.727} \left( {P/D} \right)^{ - 0.231} ({\text{mass}}\% )^{0.161} $$
(19)
$$ f_{{{\text{hourglass}}\_{\text{type}}.}} = 3.055{\text{Re}}^{ - 0.384} \left( {P/D} \right)^{ - 0.303} ({\text{mass}}\% )^{0.130} $$
(20)
$$ {\text{Nu}}_{{{\text{barrel}}\_{\text{type}}.}} = 0.873{\text{Re}}^{0.821} \Pr^{ - 0.987} \left( {P/D} \right)^{ - 0.226} ({\text{mass}}\% )^{0.135} $$
(21)
$$ f_{{{\text{barrel}}\_{\text{type}}{.}}} = 2.494{\text{Re}}^{ - 0.358} \left( {P/D} \right)^{ - 0.356} ({\text{mass}}\% )^{0.123} $$
(22)

Second law performance

The main objective of employing passive techniques is to improve the heat transfer rate. However, a drawback associated with these techniques is the concurrent increase in pressure drop, which is regarded as a negative aspect. The upward trend of the friction factor results in greater irreversibility within the heat exchanger tube, posing a challenge in achieving the ideal method. In order to assess the thermodynamic performance of applied passive techniques in thermal systems, the second law analysis is utilized. This evaluation method involves comparing the results obtained before and after the application of the passive technique, thereby providing valuable insights into whether the employed technique represents the optimal model or not.

Figure 9 shows the entropy generation number for different configurations. As expected, the entropy generation number increases as the Reynolds number increases. In particular, the hourglass-type inserts result in higher entropy generation numbers compared to the barrel-type inserts. Of all the fluid types, the experiment tube with barrel-type wire inserts has the lowest entropy generation numbers, as shown in Fig. 9. In addition, the pitch ratio of the modified inserts also influences the entropy rate generated, with a clear upward trend observed as the pitch ratio increases. It was found that the entropy production tends to decrease significantly with increasing mixing ratio [46]. It was a clear result that irreversibilities in heat transfer were prevented by the use of hybrid nanofluid. In particular, the effect of the combined use of modified internal element and hybrid nanofluid to reduce entropy production was quite successful. In a combined configuration, the use of graphene–iron oxide hybrid nanofluid at a concentration of 0.2% relative to the base fluid resulted in an average 25% reduction in entropy production. In particular, increasing the nanofluid concentration to 0.4% resulted in a significant improvement, leading to a 65% reduction in entropy production. The lowest entropy generation number of 0.118 was obtained with the configuration of the barrel-type P/D = 0.5 with 0.4 mass% GnP–Fe3O4/water–ethylene glycol.

Fig. 9
figure 9

Distribution of entropy generation number versus Reynolds number for all configurations

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Figure 10 illustrates the plotted distribution of the Bejan number as a function of the Reynolds number for all considered configurations. As depicted in the figure, the Bejan number closely approximates unity across all cases, indicating that the dominant factor contributing to the generated entropy rate is the thermal effects for each configuration. The incorporation of modified coiled wire inserts resulted in a reduction in the Bejan number, primarily due to the increased pressure drop observed in the smooth tube flow. As shown from Fig. 10a, the barrel-type P/D = 0.5 configuration was more effective than the other variations in reducing the Bejan number and consequently mitigating the irreversibilities. The inclusion of hybrid nanofluid also played a significant role in maintaining a low Be. In all configurations, when compared to using the base fluid, the inclusion of the mass fractions of 0.2% and 0.4% hybrid nanofluid resulted in lower Be [46]. The results showed that the P/D = 0.5 barrel-type configuration exhibited the lowest Be, specifically recorded as 0.9825, 0.9737 and 0.9303 for 0.0%, 0.2% and 0.4% mass fractions of GnP–Fe3O4/water–ethylene glycol hybrid nanofluid, respectively. These results highlight the improved thermodynamic performance achieved by the use of hybrid nanofluids in this study.

Fig. 10
figure 10

Distribution of Bejan number versus Reynolds number for all configurations

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Figure 11 exhibits the variation of the second law efficiency, a crucial parameter in second law analysis, with respect to the Reynolds number. The implementation of modified coiled wire inserts has demonstrated notable improvements in the second law performance of the heat exchanger tube by reducing the destructed exergy. This indicates that the enhanced thermodynamic efficiency achieved through the incorporation of these internal elements. The results revealed that the second law efficiency achieves higher values as the pitch ratio decreases in barrel-type modified coiled wire insert. Moreover, it was observed that these barrel-type inserts outperform the hourglass-type counterparts, yielding significantly improved second law efficiency results. In addition to the aforementioned findings, it was observed that the second law performance in combined use significantly improved with an increase in the mass ratio of the hybrid nanofluid. This enhancement was particularly prominent when both internal elements and hybrid nanofluid were utilized simultaneously. This successful synergy between internal elements and hybrid nanofluid constitutes one of the most noteworthy achievements of this study. Based on these evaluations, the highest second law efficiency attained was 0.416 for the barrel-type P/D = 0.5 configuration, with a 0.4% mass fraction of GnP–Fe3O4/water–ethylene glycol hybrid nanofluid, at the lowest Reynolds number of 3000. This result showcases the remarkable potential of the combined approach in optimizing the heat exchanger's thermodynamic performance.

Fig. 11
figure 11

Distribution of second law efficiency versus Reynolds number for all configurations

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Conclusions

The study investigated the combined use of a hybrid graphene–iron oxide water–ethylene glycol nanofluid and modified coiled wire inserts in a heat exchanger tube operating under continuous heat flux and turbulent flow conditions. Various performance metrics, including Nusselt number, friction factor, entropy generation number, Bejan number and second law efficiency, were considered to evaluate the system's thermo-hydraulic performance.

  • Among the configurations tested, the barrel-type coiled wire insert configurations demonstrated superior performance compared to the hourglass type, as evidenced by the analyzed parameters. Indeed, based on the evaluations conducted, the barrel-type P/D = 0.5 internal element configuration emerged as the most favorable and optimal choice across all parameters considered.

  • The particle loading in the nanofluid was also found to significantly impact the considered parameters. Absolutely, as observed in the study, the performance indicators, including thermal, hydraulic and second law efficiency, all exhibited improvement with an increase in the mass ratio of the hybrid nanofluid. Specifically, the models incorporating 0.4% graphene–iron oxide hybrid nanofluid demonstrated the most favorable and superior performance among all considered configurations.

  • Examining entropy generation numbers, the study found that the barrel-type wire inserts exhibited the lowest entropy generation among all fluid types. Moreover, the pitch ratio of the modified inserts demonstrated a discernible impact on entropy generation, with a clear upward trend observed as the pitch ratio increased. These findings underscore the role of insert design in minimizing irreversibilities within the system.

  • Results affirm the superior effectiveness of the barrel-type P/D = 0.5 configuration in reducing the Bejan number and mitigating irreversibilities. The study highlights the lowest Be values recorded for this configuration, specifically noted as 0.9825, 0.9737 and 0.9303 for 0.0%, 0.2% and 0.4% mass fractions of GnP–Fe3O4/water–ethylene glycol hybrid nanofluid, respectively. This underscores the enhanced thermodynamic performance achieved through the strategic use of hybrid nanofluids.

  • Notably, the findings suggest that employing nanofluids or coiled wire inserts alone has limitations in enhancing system performance compared to their combined utilization. The second law analyses further supported the advantages of combining both techniques in terms of thermodynamics. A pivotal achievement of this study is the demonstrated synergy between internal elements and hybrid nanofluid in significantly enhancing second law efficiency. The highest recorded second law efficiency of 0.416 was achieved by the barrel-type P/D = 0.5 configuration, coupled with a 0.4% mass fraction of GnP–Fe3O4/water–ethylene glycol hybrid nanofluid at the lowest Reynolds number of 3000. This result underscores the substantial potential of the integrated approach in optimizing the heat exchanger's thermodynamic performance.

  • By leveraging these two techniques in thermal engineering processes, not only can energy conservation be achieved quantitatively, but also the design of systems with qualitative benefits can be enabled. This integrated approach opens up new possibilities for developing more efficient and effective thermal systems.