The Performance of Compact Heat Exchangers in Different Configurations Utilising MWCNT/H₂O Nanofluid: A Numerical Study

A heat exchanger is a specialized thermal device designed to enable efficient heat transfer across various industrial applications. The most important part is the configuration of the tubes, which are carefully coiled into a smooth, tight structure. This helical structure makes heat transfer more efficient by causing fluid turbulence, which helps with mixing, and by maximizing the surface area accessible for heat exchange. Using helical coil configurations in heat exchangers is exceptionally helpful since they boost heat transfer and take up less space than straight tube configurations [1]. The Dean number (De) quantifies the intensity of the secondary flow in curved tubes [2, 3].

For more than a decade, research on the applications of nanomaterials has been gaining traction among scientists. In 1995, a novel category of classic heat transfer fluids was presented, containing suspended nanoparticles ranging from 1 to 100 nm in size inside the base fluids [4]. Using nanofluids in coil heat exchangers could save energy, reduce operating costs, and improve the performance of the system. Nevertheless, difficulties including nanoparticle stability, erosion of heat exchanger surfaces, and cost-effectiveness need to be fixed in order to secure widespread adoption. Shirejini et al. [5] observed a 10.3% increase in the heat transfer rate following the incorporation of Al₂O₃ nanoparticles into the base fluid. Wu et al. [6] found that the Nusselt number (Nu) increases with a corresponding rise in alumina nanoparticle concentration. Under turbulent flow, Fotukian and Esfahany [7] documented an improvement in the hydrodynamic and thermal properties of nanofluids by around 20% and 25%, respectively.

Numerous investigations have shown that nanofluids can greatly improve heat transfer in heat exchangers. Initiatives are being implemented to reduce the costs related to the production of highly efficient heat exchangers. Bouselsal et al. [8] investigated innovations in tube and shell heat exchangers by modifications in tube designs and the incorporation of nanoparticles. The research shows that employing of 2% Al₂O₃-multi-walled carbon nanotube (MWCNT) nanofluid with high flow rates improves heat transfer efficiency by 103.07%. Suresh et al. [9] examined the heat transfer and friction factor (f) for both smooth and helical surfaces using CuO/water nanofluid. The heat transfer rate increases at high volume concentration. Wang et al. [10] studied the thermal properties of CNT/water nanofluids in a horizontal smooth tube. They found that the improvement in average Nusselt number (Nu_av.) rises with the augmentation of nanoparticle concentrations. Similarly, Kumar et al. [11] reported that rising heat transfer coefficients and pressure drop (ΔP) were augmented by an increase in Al₂O₃ particle concentration through a helical tube.

Kahani et al. [12] studied the influence of MWCNT/H₂O nanofluid inside a helical tube. The highest Nu can be reached by changing the curvature ratio only a little and making the pitch spacing bigger. Jassim et al. [13] examined the impact of a swirl generator on the hydro-thermal efficiency of a double helical tube. Results demonstrated that better thermal performance is achieved with a smaller swirl generator.

Geometrical change represents a highly effective method for improving thermal performance. Hasan et al. [14] conducted a computational analysis on the efficiency of a helical heat exchanger utilizing (Al₂O₃, CuO, SiO₂, and ZnO)/H₂O nanofluids, examining several head rib designs with distinct coil revolutions. The helical tube with two head ribs and thirty coil revolutions was found effective for all tested nanofluids. Using two rib head geometries enhanced the performance by 20%–80%, and by 17%–66% utilizing thirty coil revolutions. Xu et al. [15] found that the 4-head rib tube improved the performance by 5%–35% compared to the plain tube. Likewise, Pourhedayat et al. [16] studied the hydrothermal properties of a helical tube made of spring wire. It was discovered that an increase in wire diameter corresponds to an increase in friction. Also, the exergy destruction decreased as the wire diameter increased. Luo et al. [17] concluded that employing the helical corrugation increased the performance by 19%.

Vahidifar and Kahrom [18] conducted an experimental investigation on the augmentation of heat transfer in a twin tube heat exchanger utilizing an insert composed of wire and rings. Employing wire coils and rings to augment the heat transfer ratio resulted in an increase of 2.30 to 2.40 for rings, compared to the absence of inserts, yielding an overall performance of 128.0% in the ring insert. Prabhanjan et al. [19] examined the performance rate of helical and smooth tubes, finding a superior performance in the helical tube relative to the smooth tube. Wu et al. [6] noted a 0.37% to 3.43% enhancement in the performance for Al₂O₃/H₂O nanofluid relative to the conventional fluid in the helical heat exchanger. Chen et al. [20] evaluated the heat transfer performance of a corrugated helical tube. They found that the f increases substantially with the corrugation geometry. Moradi et al. [21] conducted an experimental evaluation of the heat and entropy in a vertical helical tube. The outcomes indicate that the flow system enhances the performance by 35% and boosts entropy generation by 26%. Gao et al. [22] examined the thermal performance of a heat recovery system featuring a spring blade while altering the Reynolds number (Re). Results indicated that employing the mixed spring-blade resulted in increased performance by 35% to 45% compared to the insets standalone. The ΔP also increased markedly as the performance evaluation criterion (PEC) increased.

Based on the aforementioned literature survey, it is observed that many studies have attempted to enhance the hydrothermal performance by incorporating nanofluids, rib profiles, etc. Therefore, the present study concentrated on a detailed analysis of heat transfer and ΔP in shell and helical coil heat exchangers (SHCHE), taking into account various head rib geometries (three and four ribs), and using MWCNT/water nanofluids as the target fluid. The rib design geometry and nanoparticle concentrations enhance heat transfer by promoting fluid mixing. This research will also provide benefits to heat transfer, nanofluids, process industries, and other related fields. The effective heat exchanger can be used in industries to save power consumption because it works better than traditional heat exchangers.

The precision of the single-phase model is predominantly contingent upon the exact evaluation of the thermo-physical properties of nanofluids. The mixture is thought to be homogeneous, with very little slip movement between the pure fluid and the particles. The liquid and nanoparticles are in a state of hydrodynamic and thermal equilibrium, which means that there is very little exchange of momentum and interactions between the two phases. It has been suggested to use a single-phase model since it is accurate enough and costs less to compute for moderate concentrations of nanoparticles [27]. The governing equations are presented below:

Continuity equation:

$\nabla .~\left( {{\rho }_{nf}}{{u}_{nf}} \right)=0$     (1)

Momentum equation:

$\nabla .~\left( {{\rho }_{nf}}{{u}_{nf}}{{u}_{nf}} \right)=-\nabla \text{p}+\nabla .\text{ }\!\!~\!\!\text{ }\left( {{\text{ }\!\!\mu\!\!\text{ }}_{nf}}\nabla {{u}_{nf}} \right)+{{\rho }_{nf}}g$           (2)

Energy equation:

$\nabla .~\left( {{\rho }_{nf}}{{c}_{p,nf}}{{u}_{nf}}{{T}_{nf}} \right)=\nabla .\text{ }\!\!~\!\!\text{ }({{\text{k}}_{nf}}\nabla {{T}_{nf}}$)             (3)

Other characteristics of nanofluids are expressed as:

Density:

${{\rho }_{nf}}=\left( 1-\sum {{\varphi }_{np}} \right){{\rho }_{f}}+\sum {{\varphi }_{np}}{{\rho }_{np}}$          (4)

Specific heat:

${{c}_{p,nf}}=\frac{\left( 1-\sum {{\varphi }_{np}} \right){{\left( \rho {{C}_{p}} \right)}_{f}}+\sum {{\varphi }_{np}}{{\left( \rho {{C}_{p}} \right)}_{np}}}{{{\rho }_{nf}}}$          (5)

Viscosity:

$\frac{{{\text{ }\!\!\mu\!\!\text{ }}_{nf}}}{{{\text{ }\!\!\mu\!\!\text{ }}_{f}}}={{\left( 1-\sum {{\varphi }_{np}} \right)}^{-2.5}}$          (6)

Thermal conductivity:

$\frac{{{\text{k}}_{nf}}}{{{k}_{f}}}=\frac{{{k}_{np}}+2{{k}_{f}}-2\sum {{\varphi }_{np}}\left( {{k}_{f}}-{{k}_{np}} \right)}{{{k}_{np}}+2{{k}_{f}}+\sum {{\varphi }_{np}}\left( {{k}_{f}}-{{k}_{np}} \right)}$         (7)

The expression for the critical Re in the helical coil is as follows [28]:

$\text{R}{{\text{e}}_{cr}}=2100\left[ 1+12\sqrt{\frac{d}{D}} \right]$        (8)

Furthermore, De is stated as follows [29]:

$De=Re\sqrt{\frac{d}{D}}$         (9)

where, $Re=\frac{\rho vd}{\mu }$.

The (k-ε) model was utilised and presented in Eqs. (10) and (11). A number of comparative studies have indicated the stability and computational efficiency of this model; therefore, it was selected for the numerical calculations [30-33].

$\nabla .({{\rho }_{m}}{{\text{v}}_{k}})=\nabla .(\frac{{{\mu }_{t,m}}}{{{\sigma }_{k}}}\nabla \text{k})+{{\text{G}}_{m}}-{{\rho }_{m}}\varepsilon $          (10)

$\nabla .({{\rho }_{m}}{{\text{v}}_{\varepsilon }})=\nabla .\left( \frac{{{\mu }_{t,m}}}{{{\sigma }_{\varepsilon }}}\nabla \text{ }\!\!\varepsilon\!\!\text{ })+\frac{\varepsilon }{k}({{C}_{1}}{{\text{G}}_{m}}-{{C}_{1}}{{\rho }_{m}}\varepsilon  \right)$         (11)

where, ${{\mu }_{t,m}}={{\rho }_{m}}{{C}_{\mu }}\frac{{{k}^{2}}}{\varepsilon }$, and the constants are$~{{C}_{1}}=1.44,~{{C}_{2}}=1.92,\text{ }\!\!~\!\!\text{ }~{{\sigma }_{\varepsilon }}=1.3\text{ }\!\!~\!\!\text{ and }\!\!~\!\!\text{ }{{\sigma }_{k}}=1.0$.

In the following section, the effects of geometrical variations were assessed and compared with the findings of previous researchers. The present study was performed on a 6% MWCNT/H₂O nanofluid in a SHCHE for various cross sections (circular, 3 ribs, and 4 ribs), with De varying from 4000 to 9000.

5.1 Validation

The numerical findings from this study were validated through comparisons with the numerical simulations and experimental data of previously published research. Thereby, Nu values with various De were validated against the experimental study conducted by Chen et al. [20] and Tuncer et al. [34] and with the numerical correlations of Shchukin [35] for the turbulent flow, as illustrated in Figure 5. It can be noticed that the computed values of the Nusselt number (Nu) for water align with the predictions of the above-mentioned studies, indicating a maximum relative variance of less than ±7.0%. Meanwhile, the f across various De is validated against the correlations of Ito [36], Srinivasan et al. [37], and Mishra and Gupta [38] as presented in Figure 6. The findings indicate robust alignment with previous correlations, with a maximum deviation of about ±2.87%. This agreement validates the computational methodology utilized in the current work and supports its applicability for further investigation of heat transfer and flow characteristics.

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Figure 5. Validation of the Nusselt number (Nu) with experimental studies

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Figure 6. Validation of the friction factor (f) with experimental correlation studies

•Shchukin [35] correlation:

$\begin{gathered}\mathrm{Nu}=0.0316 \operatorname{Re}^{0.8} \operatorname{Pr}^{0.4}\left(\frac{d}{D}\right)^{0.05} \\ \text { for } 0.63<\operatorname{Re}\left(\frac{d}{D}\right)^2<20 \\ \mathrm{Nu}=0.0266 \operatorname{Re}^{0.85} \operatorname{Pr}^{0.4}\left(\frac{d}{D}\right)^{0.15} \\ \text { for } 20<\operatorname{Re}\left(\frac{d}{D}\right)^2<700\end{gathered}$         (12)

•Ito correlation [36]:

$f=0.076R{{e}^{-0.25}}+0.00725{{\left( \frac{d}{D} \right)}^{0.5}}$          (13)

•Srinivasan et al. [37] correlation:

$f=\frac{0.084{{\left( \frac{d}{D} \right)}^{0.2}}}{\text{D}{{\text{e}}^{0.2}}}$      (14)

•Mishra and Gupta [38] correlation:

$f=0.0791R{{e}^{-1/4}}+0.0075\sqrt{\frac{d}{D}}$        (15)

5.2 Thermal and hydrodynamic characteristics

The impact of adding the nanoparticles was studied and depicted in Figure 7, which shows the findings of the Nu of (1%, 3%, and 6%) MWCNT/H₂O nanofluid employing a single-phase model through the coil heat exchanger at De ranging from 4000-9000. The average enhancement in Nu was observed as (7.1%, 14.6%, and 28.5%) at volume fractions (1%, 3%, and 6%), respectively, along the considered circular pipe of SHCHE. It can be seen that Nu is overestimated at $\varphi ~$= 6%. The main reasons for enhancing Nu could be attributed to the improved efficiency of heat transfer and the thermal conductivity of MWCNT-H₂O nanofluids. Furthermore, the chaotic motion of MWCNT nanoparticles is predicted to enhance heat transfer and increase turbulence intensity due to the adoption of effective properties and the flow field, thereby improving overall heat transfer [4, 30, 34].

Figure 8 represents the outcomes of the Nu of 6% MWCNT/H₂O nanofluid employing various geometries of SHCHE. The average improvement in Nu was observed as (28.5%, 41.4%, and 34.9%) along the circular, three-head ribs, and four-head ribbed pipes of SHCHE, respectively. Implementing a ribbed geometry is highly significant for increasing the heat transfer rate of helical pipes [15], which is in agreement with the results of the current study. Curvatures in the ribbed profile boost mixing in the SHCHE. Curvature increases mixing, which augments heat dissipation. Three-head ribs have the largest Nu compared to circular and four-head ribs. Smaller rib head numbers mean greater Nu for helical heat exchangers.

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Figure 7. Average Nusselt number (Nu_av.) of water and multi-walled carbon nanotube (MWCNT)/H₂O nanofluid at $\varphi $ (1%, 3%, and 6%) versus Dean number (De)

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Figure 8. Average Nusselt number (Nu_av.) of water and multi-walled carbon nanotube (MWCNT)/H₂O nanofluid at $\varphi $ (6%) with circular, three, and four ribs versus Dean number (De)

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Figure 9. Friction factor (f) of water and multi-walled carbon nanotubes (MWCNT)/H₂O nanofluid at $\varphi $ (1%, 3%, and 6%) versus Dean number (De)

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Figure 10. Friction factor (f) of water and multi-walled carbon nanotube (MWCNT)/H₂O nanofluid at $\varphi $ (6%) with circular, four, and three ribs versus Dean number (De)

Greater energy consumption is required for pumping when there is increased pressure loss. Hence, to improve heat transfer, it is vital to consider pressure loss because it significantly influences the efficiency of SHCHE [13]. Figure 9 displays the predicted f values along the coil heat exchanger at De (4000-9000). Also, Figure 10 illustrates the variation of f for a 6% concentration with three configurations: three head ribs, four head ribs, and a smooth tube. The outcomes indicate that f rises with increasing volume fractions and decreases as De rises throughout the employed SHCHE. This trend arises from a slight rise in the viscosity ratio and the thinness of the small velocity boundary layer [39]. Moreover, the maximum penalty of f values for MWCNT nanofluid in circular geometry was 0.82%, 2.4%, and 5.7% at concentrations of 1%, 3%, and 6%, respectively. From Figure 10, it was observed that the highest values of f at 6% MWCNT-based water nanofluid were (5.7%, 7.5%, and 6.7%) for smooth, three- and four-head ribs of SHCHE, respectively. The observation reveals that f is significantly increased because of the influence of turn areas, resulting in a ΔP that subsequently raises the consumption of pumping power [2, 40, 41].

Figure 11 depicts the velocity vectors at 6% and De (4704) velocity vector of turbulence strength, indicating that the velocity vector of turbulence strength is increased in the turn regions due to eddy formation. This phenomenon boosts the thermal performance, as centrifugal forces lead to a great velocity gradient near the curvature of the coil wall. The eddy formation in the recirculation areas is considered a crucial merit of the coil structure in comparison to the traditional one in improving heat transfer.

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Figure 11. Velocity vector for multi-walled carbon nanotube (MWCNT)/H₂O nanofluid at $\varphi $ (6%) and Dean number (De) (4704), (a) longitudinal section, (b) inlet shell cold side, (c) outlet shell cold side

5.3 Temperature contour

The longitudinal sections of temperature contours are illustrated in Figure 12, which presents the thermal behavior of SHCHE using 6% MWCNT nanofluid and De = 8684. At the inlet Figure 12(a), a highly non-uniform temperature distribution, with more intense temperatures at the top than at the bottom. This reveals that thermal boundary layers are starting to emerge and that coil curvature is causing flow effects that are not symmetrical. In the middle section of Figure 12(b), the temperature contour becomes more homogenized at the top and bottom regions. This indicates strong secondary flow due to the enhanced mixing. At the outlet part in Figure 12(c), the distribution of temperature becomes almost uniform, reflecting the effective dissipation of heat along the coil length [42-45].

The temperature contours of four head ribs for MWCNT volume fraction at φ = 6% and De = 8684 are illustrated in Figure 13. At the inlet Figure 13(a), the temperature distribution is not uniform, with higher temperatures concentrated near the top. This reveals the impact of secondary flow in curvature zones on the production of thermal boundary layers. In the middle area Figure 13(b), the ribs significantly elevate fluid mixing, resulting in higher temperatures through the top and bottom zones of the pipe than in the circular layout. This is because the ribs disturb the boundary layer and make Dean vortices stronger. The temperature distribution becomes almost uniform by the outlet section Figure 13(c), revealing effective heat dissipation and enhanced energy transfer.

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Figure 12. Temperature contours of the longitudinal section for shell and helical coil heat exchanger (SHCHE) of multi-walled carbon nanotube (MWCNT) volume fraction at $\varphi $ = 6% and Dean number (De) = 8684

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Figure 13. Temperature contours of four head ribs for multi-walled carbon nanotube (MWCNT) volume fraction at $\varphi $ = 6% and Dean number (De) = 8684

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Figure 14. Temperature contours of three head ribs for multi-walled carbon nanotube (MWCNT) volume fraction at $\varphi $ = 6% and Dean number (De) = 8684

In Figure 14, the temperature contours of the three-head ribs in the SHCHE utilizing MWCNT nanofluid at a volume fraction of φ = 6% and De = 8684 demonstrate a considerable improvement in thermal performance along the tube length. The temperature distribution at the outlet section in Figure 14(a) is clearly non-uniform, with high temperatures observed at the top. This indicates that secondary flow is generated due to the curvature configuration, resulting in the formation of thermal boundary layers. Moving to the middle Figure 14(b), the temperature distribution and mixing become higher than at the inlet due to the three-head ribs' geometry. The outlet in Figure 14(c) shows a more uniform and less extreme temperature, indicating effective heat distribution.

When comparing the three configurations (smooth tube, three-head, and four-head ribs) at φ = 6% and De = 8684, the three-rib layout reveals the best thermal performance. This is because the temperature is most evenly distributed along the length of the tube, especially in the middle and outlet areas, where thermal gradients are minimized more efficiently than in the other cases. The enhanced uniformity means that the mixing is effective and the secondary flow is heightened because of rib-induced disturbances, which greatly disrupt the thermal boundary layer.

5.4 Performance evaluation criteria

PEC is an effective engineering method to assess the overall thermal efficiency of engineering systems, including heat exchangers, while incorporating enhancements like nanofluids or extended surfaces, and can be given by the following expression [46]:

$PEC=\left( \frac{{{\overline{Nu}}_{nf}}}{{{\overline{Nu}}_{f}}} \right).{{\left( \frac{{{f}_{nf}}}{{{f}_{f}}} \right)}^{-1/3}}$      (16)

Figure 15 demonstrates the influence of a 6% MWCNT-based water nanofluid on the PEC across various geometries of a coil heat exchanger (circular, three head ribs, and four head ribs) at De ranging from 4000 to 9000. PEC values decreased slightly with increasing De throughout the whole range. Overall, all three configurations exhibit higher PEC values, achieving the highest PEC at lower De. These were reported as (1.262, 1.380, and 1.320) for the circular, three ribs, and four ribs, respectively. The values of PEC then fluctuated slightly with increasing De. In contrast, the lowest values of PEC were reported at the highest De as (1.224, 1.329, and 1.264) for all tested configurations, respectively.

Hence, the findings reveal that the highest obtainable PEC of 6% MWCNT-based water nanofluid is 1.380 circulating within three ribs helical coil heat exchanger. Consequently, the incorporation of three head ribs in SHCHE appears to be the most favorable option for designers seeking to enhance heat transfer.

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Figure 15. Performance evaluation criteria (PEC) of multi-walled carbon nanotube (MWCNT)-based water nanofluid at various volume fractions and Dean numbers (De)