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Review
Machine Learning in Heat Exchangers: State-of-the-Art ReviewClick to copy article linkArticle link copied!
- Asad AyubAsad AyubSchool of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad 44000, PakistanMore by Asad Ayub
- Iftikhar Ahmad*Iftikhar Ahmad*Email: [email protected]School of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad 44000, PakistanMore by Iftikhar Ahmad
- Ahmed QaziAhmed QaziDepartment of Chemical and Petroleum Engineering, College of Engineering, United Arab Emirates University, Al Ain 1555, United Arab EmiratesMore by Ahmed Qazi
- Hamza SethiHamza SethiSchool of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad 44000, PakistanMore by Hamza Sethi
- Muhammad Zulkefal*Muhammad Zulkefal*Email: [email protected]Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim 7034, NorwayMore by Muhammad Zulkefal
- Aleena ZulfiqarAleena ZulfiqarSchool of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad 44000, PakistanMore by Aleena Zulfiqar
- Wejdan DeebaniWejdan DeebaniDepartment of Mathematics, College of Science and Arts, King Abdul Aziz University, Rabigh 21911, Saudi ArabiaMore by Wejdan Deebani
ACS Engineering Au
Cite this: ACS Eng. Au 2026, XXXX, XXX, XXX-XXX
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Abstract
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Heat exchangers play a key role in energy-efficient and sustainable industrial operations. However, process uncertainties are making realization of efficient and stable heat exchanger operation a challenge. Computational methods have been helpful in designing, operation, and control of heat exchanger. Recently, machine learning (ML) has emerged as a very effective tool in heat exchanger offline design as well as online operation and control. This review focuses on the ML methods reported in the literature on parameter estimation, such as fouling factor and heat transfer coefficient, thermal performance, control strategies, and offline and online optimization of heat exchangers. The more frequently used and effective ML methods are identified, and the gaps in research and the demands of practical implementation are elaborated. This study will provide the state of the art in ML applications in heat exchangers and will help in further studies in realizing the scaled-up digital twin realization for the Industry 4.0 mode of heat exchanger design and operation.
This publication is licensed under
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License Summary*
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License Summary*
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License Summary*
You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
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© 2026 The Authors. Published by American Chemical Society
Special Issue
Published as part of ACS Engineering Au special issue “AI and Machine Learning in Chemical Engineering: Breakthroughs and Applications”.
Introduction
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Heat exchangers are a critical component across process industries. (1−5) Heat exchangers are widely employed to recover heat from hot process streams, thereby reducing overall fuel consumption in various industries. (6) Shell and tube heat exchangers, plate type heat exchangers, (7) spiral heat exchangers, (8) finned heat exchangers, and double pipe heat exchangers (9) are a few of the popular heat exchangers in process industries. Heat exchanger operation is a nonlinear process because fluid properties, flow conditions, and heat transfer coefficients (HTCs) change with time. The laws of thermodynamics are used for analyzing heat exchangers’ performance. (10) Analytical studies often rely on idealized conditions and detailed mathematical models, while experimental investigations are costly because of the expense involved in building and operating the required setups. (1) ML methods are now being deployed to learn from data and help control, monitor performance, and optimize designs.
ML has become an important tool in process industries, supporting a variety of applications such as process automation, (11) protection of industrial control systems against cyberattacks, (12) predictive maintenance, (13) and process optimization. (14) Other studies have applied ML to fault diagnosis (15) and data mining tasks. (16) Considerable research has focused on heat exchanger technologies. This includes studies on the thermal efficiency, (17) the use of nanofluids, (18) design improvements, (19) heat transfer in general, (20,21) modeling and control, (22) and CFD-based design approaches. (23)
Several studies based on ML applications in heat exchangers have been reported in the literature. The applications have evolved from early thermal-performance prediction to the advanced modeling of degradation and multiphase behavior. Initial studies summarized by Ghalandari et al. (7) showed superior performance of artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and support vector machine (SVM) models in the prediction of heat transfer rates, Nusselt numbers, friction factors, and pressure drops across shell-and-tube, plate, microchannel, and nanofluid systems. The ML has been established as a reliable surrogate for empirical and CFD models. The extended studies into more complex operational challenges, particularly fouling, where Villa and Zanini Brusamarello (24) reported the effectiveness of SVM, LSTM, NARX, and GPR models for early fouling detection and predictive maintenance. Zou et al. (25) likewise highlighted ML’s use in tracking fouling resistance and thermal deterioration. More recently, ML has been applied to highly nonlinear boiling processes, with Chu et al. (26) showing how image-assisted models such as CNNs can classify boiling regimes and predict heat flux and critical heat flux, complementing the broader boiling-related performance modeling noted by Zou et al. (25) and earlier ANN applications referenced in Ghalandari et al. (7) Together, these studies illustrate ML’s progression from basic performance prediction to sophisticated modeling of fouling, transients, and multiphase heat transfer.
The review papers by Zou et al. (25) and Ghalandari et al. (7) focus on using machine learning methods for thermal-performance modeling of heat exchangers, including predictions of heat transfer coefficients, pressure drop, Nusselt numbers, and thermophysical properties across various exchanger types. Villa and Zanini Brusamarello (24) provide a systematic review dedicated solely to fouling monitoring and diagnosis, summarizing ML techniques used for early detection, forecasting, and classification in chemical engineering heat exchangers. Meanwhile, Chu et al. (26) concentrated specifically on boiling heat transfer, reviewing ML applications for predicting heat flux between streams and heat transfer coefficient in pool and flow boiling systems.
The novelty of the current paper lies in providing the first unified, cross-domain review that integrates all major machine-learning applications in heat exchangers, including thermal-performance prediction, fouling monitoring, boiling behavior, control strategies, and optimization, into a single, comprehensive framework. Unlike previous reviews, which focus narrowly on performance modeling (Zou et al.; (25) Ghalandari et al. (7)), fouling detection (Villa and Zanini Brusamarello (24)), or boiling heat transfer Chu et al., (26) this paper synthesizes these fragmented research threads to present a holistic, system-level perspective aligned with Industry 4.0 needs. It also advances the field by emphasizing end-to-end workflows, decision guidance, and the foundations for digital twin development, which have not been addressed collectively in earlier literature.
Section “ML Techniques” presents ML methods for thermal systems; Section “Application of ML Models in Heat Exchangers” presents miscellaneous applications for heat exchangers organized by parameter estimation, performance prediction, and control/optimization; Section “Summary and Discussion” summarizes the study comprehensively, and the final section concludes the study.
ML Techniques
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ML is a data-driven approach that uses algorithms to analyze large data sets and learn patterns for accurate prediction without explicit programming. Broadly, there are three general categories of ML algorithms namely supervised ML, unsupervised ML and reinforced ML algorithms (27) as depicted in Figure 1.
Figure 1
Figure 1. Types of ML models. (28)
Supervised learning finds relationships between inputs and labeled outputs by finding a mapping function between them. This approach is very powerful for classification and regression problems, but it can require large labeled input data sets and can result in overfitting. Some of the popular supervised learning algorithms include SVM, logistic/linear regression, and decision trees. (29)
Unsupervised learning exposes models to unlabeled data, allowing them to independently investigate to derive hidden structures and patterns. (30) By quantifying similarity among data points, algorithms perform clustering, dimensionality reduction, or anomaly detection. (31) Although these models are highly effective at analyzing complex data sets without labeled outputs, their results are often more difficult to interpret compared to traditional predictive models.
In reinforcement learning, models are trained to make sequential decisions, where reward is provided for desirable actions while the penalty is applied for undesirable actions. (32) It attempts to find a strategy that maximizes the sum of future rewards, which makes it an interesting algorithm for context-dependent tasks, such as playing games, robotics, and language processing. Reinforcement learning is, therefore, very versatile and finds uses in control, optimization, and various autonomous systems application. (33)
Deep learning employs ANN to tackle knotty research challenges. (34) These ANNs draw inspiration from the human brain’s architecture and exhibit the capacity to learn from extensive data sets. Through this mechanism, deep learning algorithms excel at distinguishing intricate data patterns that may elude human perception. This makes them particularly adept at tasks such as classifying images, translating languages, and recognizing speech. Furthermore, deep learning has achieved cutting-edge effects in tasks involving predictive analysis. (35) ML model development steps are depicted in Figure 2.
Figure 2
Figure 2. ML models development steps.
Application of ML Models in Heat Exchangers
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ML applications in heat exchangers can be categorized into four key areas: the estimation of parameters in heat exchangers, estimation of the operational and thermal performance of heat exchangers, the control of heat exchangers, and the ML algorithms deployed to optimize heat exchanger design. ML models applications in heat exchangers is schematically shown in Figure 3.
Figure 3
Figure 3. ML model applications in heat exchangers.
Estimation of Heat Exchangers Parameters
This subsection reviews the ML models for the estimation of key parameters in heat exchangers.
Fouling Estimation of Heat Exchangers
Heat transfer is reduced and pressure drop is increased when undesirable materials or chemicals are deposited on the heat exchanger surface. (36) The accumulation of deposits that promote fouling significantly increases operating and maintenance costs. (37) Forecasting fouling due to scaling and chemical deposition on the heat exchanger surface could significantly reduce the heat exchangers' overall cost. (38) This section goes into detail about the efficient utilization of ML algorithms to predict fouling on heat exchanger surfaces.
Jardi et al. (39) employed a multilayer feed-forward neural network (MLFFNN) to study fouling resistance in a cross-flow heat exchanger. Steam temperature, density of acid, acid circulation rate, and inlet/outlet acid temperatures were the initial variables in their model, which was tested on 361 data points. The output variable was the fouling resistance. The model performed with high accuracy, producing MSE = 1.811 × 10–11 (m2 C/W)2, RMSE = 4.256 × 10–6 m2 C/W, and R2 = 0.995. In another study, Hosseini et al. (40) used an ML framework to estimate fouling factors over a range of conditions. After testing seven nonlinear transformations and five algorithms, GPR, decision trees, support vector regression (SVR), bagged trees, and linear regression, they concluded that GPR achieved the highest accuracy, with R2 values of 0.98770 (training) and 0.99857 (testing). Based on the findings, it can be said that during both the model training and testing stages, GPR showed the best alignment with the experimental samples. For both the internal and exterior data sets, the trained GPR model obtained R2 values of 0.98770 and 0.99857, respectively. The model’s total predictions are R2 = 0.98999, MAPE = 13.89%, and MSE = 7.02 × 10–4 (m2 C/kW)2. Benyekhlef et al. (41) applied a MLFFNN to forecast fouling resistance in heat exchangers. A model was developed using 375 experimental data sets, with input parameters comprising duration, solute concentration, thermal flux, mass throughput, feed temperature, and thermal conductivity. The outputs estimated by the framework were the product temperature, outlet crude temperature, and resistance to fouling. They were 6.5377 × 10–4 (m2 C/kW)2, 0.99756 for training, 3.9629 × 10–4 (m2 C/kW)2, 0.99835 for testing, and 5.8303 × 10–4 (m2 C/kW)2, 0.99812 for validation. Furthermore, a generic and scalable statistical model for forecasting fouling resistance in cross-flow heat exchangers in waste heat recovery units (WHRUs) was created by Sundar et al. (42) This model utilized commonly measured parameters, and it was built upon a feed-forward ensemble neural network. The R2 value exceeded 99%, indicating the model’s high effectiveness in replicating the actual data. Davoudi and Vaferi (43) proposed an MLFFNN trained on a comprehensive data set containing 11,626 entries to estimate the fouling factor in a single-tube heat exchanger. The predictors incorporated into the model were the fluid density, wall and bulk fluid temperatures, hydraulic diameter, flow velocity, dissolved oxygen content, and operational time. The ANN demonstrated strong predictive accuracy, reproducing experimental fouling factors with an absolute average relative deviation (AARD) of 5.42%, an MSE of 0.0013 (m2 K/kW)2, an RMSE of 0.0355 m2 K/kW, and a coefficient of determination (R2) of 0.977819. The developed model stood out for its simplicity and remarkable accuracy and also for effectively accommodating a large number of experimental data sets.
In another study, Biyanto (44) applied an MLFFNN combined with a nonlinear autoregressive model with exogenous inputs (NARX) to estimate fouling resistance in shell-and-tube heat exchangers. The model incorporated inputs, such as streamflow rates, temperature data, and the physical properties of product and crude blends. It served as a predictive framework to support the optimization of operating conditions and to guide preventive maintenance strategies. During the training and validation stages, the RMSE for fouling resistance between the actual and predicted values was 8.19 × 10–7 and 2.69 × 10–5 m2 C/W, respectively. In another study, Garcia et al. (45) presented a novel approach that combined static and dynamic ANN methods. This method successfully identified issues in a heat exchanger’s closed-loop temperature control system. The three modules of the strategy were one that made sure the supervision system was consistent, another that monitored the heat exchanger’s fouling conditions and identified possible causes, and a third that was connected to decision-making in order to schedule supervisory procedures and forecast the amount of time that it would remain operational under acceptable circumstances. This application of the ANN showed promise for precisely predicting heat exchanger fouling. The fouling factor Rfo in a cross-flow heat exchanger was predicted using the MLFFNN in a study by Lalot and Pálsson. (46) Five input factors were used to create training data using a numerical model in both fouling and clean circumstances. According to the results, ANN modeling helped with predictive maintenance and provided a sensitive and effective forecast of Rfo. To anticipate fouling in double-tube heat exchangers, Sun et al. (47) used a wavelet NN-based optimization. The working fluid’s input and output temperatures, fluid flow velocity, and the three heat exchanger tube wall temperatures were all included in the model’s input variables. The model’s relative fouling prediction error was less than 0.71%. Aminian and Shahhosseini (48) used the MLFFN model to predict the fouling factor of crude oil. The training data sets included surface temperature, Reynolds number, and Prandtl number. The network architecture predicted the fouling factor with an MRE of 26.23%. Aminian and Shahhosseini (49) applied ANN modeling to estimate crude oil fouling in the preheat exchangers. The model inputs were tube inner diameter, crude flow rate, and wall temperature. The MLFFN achieved an MRE of 14.05% and 22.47% for the training and testing, respectively.
Mohanty et al. (50) presented a method for forecasting fouling behavior in a heat exchangers that was based on a local linear wavelet NN approach. This method forecasted fouling behavior in order to enable the best possible cleaning scheduling without interfering with plant operations, and it was based on the cleanliness factor (CF) to measure the exchanger efficiency. The predicted versus actual experimental results showed maximum errors of 0.064% during testing. Radhakrishnan et al. (51) designed a statistical model to forecast fouling in heat exchangers and further employed an MLFNN to estimate outlet temperatures of shell-and-tube units. Their results showed RMSE values of 0.93% for shell-side and 1.83% for tube-side predictions. Kashani et al. (52) later introduced an optimized moving-window neural network for real-time monitoring of crude oil fouling in STHE. Using flow rate and inlet temperatures as inputs, their model predicted fouling resistance (Rf) with an accuracy of 8% up to 2 days ahead, extendable to 10 days with an error of 11%. The summary of all these studies is presented in Tables 1 and 2 with highlights for key information.
Table 1. Summary of ML Applications for Fouling Estimation
| heat exchanger type | ML type | model structure | input variable | output variable | model evaluation | references |
|---|---|---|---|---|---|---|
| cross flow | MLFFNN | 6-X-1 | he considered input variables were elapsed time, acid stream temperatures at the inlet and outlet, steam temperature, acid density, and the volumetric flow rate of the acid | fouling resistance | MSE = 1.811 × 10–11 and R2 = 0.995 | Jaradi et al. (39) |
| cross flow | DLFFNN | 6-2-1 | fluid’s inlet temperature, the flow-rate ratio under fouled and clean conditions, and the outlet temperature of the fluid | fouling resistance | R2 = 0.99% | Sundar et al. (42) |
| MLFFNN | 6-1-1 | elapsed time, volumetric concentration, heat flux rate, mass flow rate, inlet temperature, and thermal conductivity as input parameters | fouling resistance | MSE = 3.9629 × 10–4 and R2 = 0.99835 | Benyekhlef et al. (41) | |
| shell and tube | MLFFNN with NARX | 6-13-3 | flow rates and temperatures of the heat exchanger streams, as well as the physical properties of the product and the crude blend | fouling resistance, product and crude outlet temperature | RMSE = 8.19 × 10–7 | Biyanto (44) |
| cross flow | MLFFNN | 5-5-1 | cold fluid’s inlet and outlet temperatures, the hot fluid inlet temperature, and the mass flow rates of both the hot and cold fluids | fouling factor | NA | Lalot and Pálsson (46) |
| single tube | MLFFNN | 7-10-1 | fluid density, wall temperature, bulk fluid temperature, flow passage diameter, fluid velocity, dissolved oxygen concentration, and elapsed time | fouling factor | MSE = 0.0013 and R2 = 0.977819 | Davoudi and Vaferi (43) |
| double tube | WNN | 4-X-1 | working fluid’s inlet and outlet temperatures, its flow velocity, and three temperature measurements taken along the heat exchanger tube wall | heat exchanger fouling | NA | Sun et al. (47) |
Table 2. Summary of ML Applications for Fouling Estimation (Continued)
| heat exchanger type | ML type | model structure | input variable | output variable | model evaluation | references |
|---|---|---|---|---|---|---|
| cross flow | Gaussian process regression (GPR), decision trees, bagged trees, support vector regression (SVR), and linear regression | NA | fluid velocity, operation time, its temperature and density, the surface temperature, equivalent diameter, and the oxygen level present | fouling factor | MSE = 7.02 × 10–4 and R2 = 0.98999 | Hosseini et al. (40) |
| pre-heat exchangers | MLFFNN | 3-5-6-1 | surface temperature, Reynolds and Prandtl numbers | fouling factor | MRE = 0.2623 | Aminian and Shahhosseini (48) |
| pre-heat exchangers | MLFFNN | 3–8–1 | diameter of the tube, crude velocity, and the temperature at the tube surface | fouling rate | MRE = 15.83% | Aminian and Shahhosseini (49) |
Estimation of HTC of Heat Exchangers
This section illustrates the uses of ML techniques for calculating heat exchanger HTCs. Colak et al. (53) developed two models of ANNs specifically designed for shell and helically coiled tube heat exchangers. For model training, two predictive models were developed. Coil diameter, tube inner diameter, and mass flow rate were used as inputs, while HTC and pressure drop were used as outputs. The second model employed Reynolds number, Dean number, coil diameter, and curvature ratio as inputs with the Nusselt number and performance evaluation criteria as outputs. Both models demonstrated high predictive accuracy, achieving MSE and R values of 3.94 × 10–4 and 0.99673 for the first model and 2.79 × 10–7 and 0.99999 for the second. Bahiraei et al. (54) proposed a multilayer perceptron (MLP) framework that was enhanced using four bioinspired optimization strategies, namely biogeography-based optimization (BBO), ant colony optimization (ACO), ant lion optimizer (ALO), and artificial bee colony (ABC). According to the results, the BBO algorithm is the most effective way to forecast the overall HTC, with R2 values of 0.998 and 0.989 for the testing data and RMSE values of 0.030 and 0.025 for the training data, respectively. Zheng et al. (55) tested RF and GRNN approaches for predicting HTCs in channels with six bulges of different heights (0.001, 0.1, and 1 mm) from 729 CFD simulations. Using 143 validation cases, both models achieved R2 values above 0.97, far exceeding classical heat transfer correlations, with GRNN consistently outperforming RF in accuracy, generalization, and applicability for sensitivity and optimization tasks.
Abd Elaziz et al. (56) applied the Crow Search Algorithm (CSA) to enhance the ANFIS. The model was specifically designed to predict the oscillatory HTC. In this framework, mean pressure and oscillation frequency served as the input variables, while OHTC was the output variable. The ANFIS-CSA model was assessed by benchmarking it against the traditional ANFIS and a genetic-algorithm-enhanced version. The findings showed that the ANFIS-CSA model outperformed the other models. Colak et al. (57) developed two ANN models to estimate the total cost, pressure drop on the tube and annulus sides, and the overall HTC. Input parameters such as density, number of parallel tubes, thermal conductivity of tube side, Reynolds number of tube side, inside friction factor, Reynolds number of annulus side, outside friction factor, series pipe number, tube side pumping power, and annulus side pumping power were used in Model 1, which had a configuration of 10-15-4-4. Density, number of parallel tubes, tube-side thermal conductivity, tube-side Reynolds number, inside friction factor, annulus-side Reynolds number, outside friction factor, and series pipe number were used as input parameters for Model 2, which had an 8-15-4-4 configuration. According to the results, the MSE and R for the overall HTC from model-1 were 2.19 × 10–3 and 0.98197, while the MSE for the pressure drop on the tube and annulus sides and the overall cost were 9.14 × 10–3, 2.54 × 10–4, and 1.93 × 10–4, respectively. The MSE and R for the overall HTC from model-2 were 1.11 × 10–4 and 0.98453, respectively, while the MSE for the pressure drop on the tube and annulus sides and the overall cost are 1.90 × 10–4, 6.44 × 10–2, and 5.59 × 10–2. Dheenamma et al. (58) developed ANN models to forecast plate heat exchanger characteristics. Water served as the hot fluid, while two non-Newtonian fluids, carboxymethyl cellulose (CMC) and xanthan gum (XG), were used in varying concentrations. For each cold fluid, a separate model was developed, taking the fluid concentration, Reynolds number, and Prandtl number as input parameters. According to the data, the configurations of 4-5-5-5-4 and 5-5-5-5-4 provide the best performance for XG, with MAREs of 4.03 and 6.792, respectively. Likewise, the most successful configurations for the CMC were 4-6-4 and 5-5-4, which yielded MAREs of 5.85 and 5.392, respectively.
Rahman and Zhang (59) used the backpropagation (BP) technique to build a three-layer feed-forward network. With oscillation frequency and mean pressure as input variables, the model was created to predict oscillatory HTCs in finned-tube heat exchangers. The average percentage of error between the experimental and anticipated oscillatory convective HTCs was 3.2%. Colorado et al. (60) developed an empirical model based on MLFFNNs to forecast heat transfer rates in helical coil systems with various working fluids. They used the helical diameter, number of coil turns, Prandtl number, and Rayleigh number as input parameters. The Nusselt number was the output variable. According to the outcome, when compared with experimental data, the model with a 4-4-1 configuration predicted the Nusselt number with an R-value of 0.98. Mehrabi et al. (61) developed a model based on the ANFIS to forecast the annular and inner pressure drops in helicoidal double pipe heat exchangers in addition to the overall HTC. The input variables included the pitch of the coil, Prandtl numbers, and inner and annular Dean numbers. With R2 values of 0.994, 0.995, and 0.951 for the overall HTC, inner pressure drop, and annular pressure drop, respectively, and corresponding RMSE errors of 13.61, 5.08, and 13.81%, the model showed a great capacity for prediction. Ghasemi et al. (62) used a BP neural network to estimate pressure drops, Nusselt numbers, and total HTCs in a modified twisted tape double pipe heat exchanger. With input variables such as fluid temperatures, nanofluid volume fractions, twisted tape parameters, fluid Reynolds numbers, nanofluid viscosity, and thermal conductivity, the model architecture made use of a multilayered perceptron structure. For the model with a 9-33-1 topology, the mean squared errors (MSEs) for the Nusselt number, overall HTC, and pressure drop were 0.66535, 4547.68, and 0.008768, respectively. While most studies rely on neural or Gaussian process surrogates, fuzzy-logic systems have likewise been exploited for noniterative estimation of the bed-to-wall heat transfer coefficient in circulating fluidized-bed combustors, delivering rapid estimates without repeated CFD runs. (63) Evolutionary symbolic-regression techniques, such as Gene Expression Programming, have likewise been deployed to derive closed-form correlations for the bed-to-wall heat transfer coefficient in fluidized adsorption beds, yielding accuracies superior to traditional empirical equations. (64) The summary of this section is presented in Tables 3 and 4.
Table 3. Summary of ML Applications for HTC Estimation
| heat exchanger type | ML type | model structure | input variable | output variable | model evaluation | references |
|---|---|---|---|---|---|---|
| shell and helically coiled tube | MLFFNN | 3-8-2-2 | tube inner diameter, coil diameter and mass flow rate | HTC and pressure drop | MSE = 3.94 × 10–4 and R = 0.99673 | Colak et al. (53) |
| shell and helically coiled tube | MLFFNN | 4-9-1-1 | Reynolds and Dean numbers, coil diameter and curvature ratio | Nusselt number and performance evaluation criteria values | MSE = 2.79 × 10–7 and R = 0.99999 | Colak et al. (53) |
| ribbed triple tube | MLFFNN with BBO | 3-3-1 | nanoparticle concentration, rib pitch and rib height | overall HTC | R2 = 0.998 and RMSE = 0.030 | Bahiraei et al. (54) |
| finned-tube heat exchanger | ANFIS-CSA | 3-4-2-2-1 | frequency of the oscillations and the mean pressure | oscillatory HTC | MSE = 4.25 × 10–5 and R2 = 0.9835 | Abd Elaziz et al. (56) |
| double pipe | MLFFNN | 10-15-4-4 | density, number of parallel tubes, thermal conductivity of tube side, Reynolds number of tube side, inside friction factor, Reynolds number of annulus side, outside friction factor, series pipe number, tube side pumping power and annulus side pumping power | overall HTC | MSE = 2.19 × 10–3 and R = 0.98197 | Colak et al. (57) |
| tube sides pressure drop | MSE = 9.14 × 10–3 | |||||
| annulus sides pressure drop | MSE = 2.54 × 10–4 | |||||
| overall cost | MSE = 1.93 × 10–4 | |||||
| double pipe | MLFFNN | 8-15-4-4 | density, number of parallel tubes, thermal conductivity of tube side, Reynolds number of tube side, inside friction factor, Reynolds number of annulus side, outside friction factor and series pipe number | overall HTC | MSE = 1.11 × 10–4 and R = 0.98453 | Colak et al. (57) |
| tube sides pressure drop | MSE = 1.90 × 10–4 | |||||
| annulus sides pressure drop | MSE = 6.44 × 10–2 | |||||
| overall cost | MSE = 5.59 × 10–2 |
Table 4. Summary of ML Applications for HTC Estimation (Continued)
| heat exchanger type | ML type | model structure | input variable | output variable | model evaluation | references |
|---|---|---|---|---|---|---|
| finned-tube heat exchanger | MLFFNN | 2-10-1 | oscillating frequency and mean pressure | oscillatory HTC | R = 0.94696 | Rahman and Zhang (59) |
| helical heat exchanger | MLFFNN | 4-4-1 | Prandtl number, Rayleigh number, helical diameter and number of coils turn | Nusselt number | R = 0.98 | Colorado et al. (60) |
| helicoidal double pipe | ANFIS | inner and annular dean number, inner and annular Prandtl number and pitch of the coil | overall HTC | RMSE = 13.61% and R2 = 0.994 | Mehrabi et al. (61) | |
| inner pressure drop | RMSE = 5.08% and R2 = 0.995 | |||||
| annular pressure drop | RMSE = 13.81% and R2 = 0.951 |
Performance Prediction of Heat Exchangers
This section examines the use of ML techniques to forecast heat exchanger performance. Islamoglu et al. (65) developed an ANN using the BP algorithm to predict the performance of a nonadiabatic capillary tube suction line heat exchanger. The study examined the model’s capability to estimate both the mass flow rate and the suction line outlet temperature. The network’s input variables included subcooling, suction line inlet temperature, capillary tube internal diameter, suction line internal diameter, capillary tube length, heat exchanger length, and adiabatic inlet length. According to the study’s findings, the mean relative errors (MREs) for estimating the mass flow rate and the outlet temperature of refrigerant suction lines are 2.26 × 10–2 and 1.94 × 10–2, respectively. Ramasamy et al. (66) create and contrast NARX-type NN models using feed-forward BP. The models were used to predict how the heat exchanger outlet temperatures would fluctuate over time. The refinery’s plant historian provided the information needed to develop the models. Two data sets were created for the model’s input variables: the first contained 25 variables with 933 observations, including calculated variables, and the second contained 23 variables without calculated variables. In the case of models with calculated variables, network structures of 25-32-2 and 25-35-2 were employed for the feed-forward network. In contrast, in models without calculated variables, network structures of 23-17-2 and 23-17-2 were used for the feed-forward and NARX network models, respectively. From the results, it is observed that an NARX neural network model has superior prediction capabilities with an RMSE of less than 2.5 °C in the outlet temperatures and possesses a correct directional change index of more than 90%.
Xie et al. (67) created an ANN model to establish correlations between friction factors and Nusselt numbers in fin-and-tube heat exchangers that span three different types of fin-and-tube configurations that were established experimentally and numerically. The ANN model featured two outputs that corresponded to the fluid flow friction factor and heat transfer Nusselt number, and it included 12 input features that represented geometrical factors. The findings showed that when it came to forecasting the output variables, the 12-9-5-2 feed-forward neural network design had the best accuracy. To forecast the thermal-hydraulic performance of small heat exchangers, Peng and Ling (68) developed a modeling approach based on SVR. In the study, the ANN model was used to compare and assess the produced models. Colburn factor (j) and friction factor (f) were the output variables for both models, while fin height, fin pitch, fin thickness, fin length, and Reynolds number at the air side were the input variables. According to the results, SVR outperformed the ANN model in terms of prediction, with lower MSEs of 2.645 × 10–4 for the j factor and 1.231 × 10–3 for the f factor. Additionally, the SVR model computes faster than the ANN model.
An ANN model was used in a study by Du et al. (69) to forecast the friction factor () and Nusselt number (Nu) in a finned oval-tube heat exchanger. Performance comparisons between the ANN models and experimental correlations were carried out in the study. Air inlet angles, air side and water side Reynolds numbers, inlet air and water temperatures, the number of tube rows and tube passes, the major and minor axes’ outer lengths, and the fin collar’s outside diameter were among the model’s input variables. The findings suggested that ANN models are more effective than experimental correlations at forecasting heat transfer and flow resistance properties in the unknown heat exchanger scenarios. In another work, El-Said et al. (70) investigated how ML methods could be used to forecast how air injection would affect a shell and tube heat exchanger’s thermohydraulic performance. They compared the effectiveness of the k-nearest neighbors (KNN), SVM, social media optimization (SMO), and random vector functional link (RVFL) algorithms. Both the hot fluid’s volume flow rate and the cold and hot fluid’s intake temperatures were maintained at constant levels. The RVFL algorithm provided the highest prediction accuracy among all of the methods tested.
The cold fluid temperature and the injected air volume flow rates were the input variables for the algorithms, and the pressure drop across the heat exchanger and the hot and cold fluids’ outlet temperatures were the output variables. When compared with all other algorithms, the results demonstrated that RVFL generated the most accurate results. The equivalent root mean squared errors (RMSE) for RVFL, SMO, SVM, and KNN were 0.719167, 2.477069, 1.741808, and 1.855635, respectively. The related MREs for RVFL, SMO, SVM, and KNN were 0.016167, 0.061746, 0.043366, and 0.041383.
In another study, Gupta et al. (71) developed predictive models for predicting plate fin heat exchanger performance characteristics based on ANNs and ANFIS. For optimization, the study used simulated annealing and a straightforward genetic method. The plate fin heat exchanger’s performance characteristics were determined by the temperatures of the hot and cold fluid outlets. Flow rate, pressure at cold and hot inlets, inlet temperature of cold and hot fluids, and pressure drop of cold and hot fluids were among the input factors in their investigation. Their research showed that in comparison to ANN, ANFIS produced more accurate outcomes. Baghban et al. (72) used a CNT/water nanofluid to examine the heat transfer efficiency of a helically coiled tube heat exchanger. Three different ANNs were used in their analysis: Least Squares Support Vector Machine (LSSVM), ANFIS, and MLP-ANN. The study’s goal was to forecast the Nusselt number, helical number, volumetric concentration, and Prandtl number were the input variables used to do so. MREs for LSSVM, ANFIS, and MLP-ANN were 0.11, 5.94, and 5.17%, respectively, indicating that LSSVM performed better in terms of prediction accuracy than the other applied models. Furthermore, a sensitivity analysis was conducted to assess the influence of each factor on the model’s output, revealing that among the input variables, the helical number had the most significant impact on the Nusselt number. The summary of all these studies is presented in Table 5 with all the key details.
Table 5. Summary of ML Applications for Performance Prediction
| heat exchanger type | ML type | model structure | input variable | output variable | model evaluation | references |
|---|---|---|---|---|---|---|
| nonadiabatic capillary tube suction line heat exchanger | MLFFNN | 7-7-2 | suction line inlet temperature, internal diameter of a capillary tube and suction line, length of the capillary tube, subcooling and heat exchanger and adiabatic inlet length | suction line outlet temperature | MRE = 1.94 × 10–2 | lslamoglu et al. (65) |
| mass flow rate | MRE = 2.26 × 10–2 | |||||
| performance prediction of heat exchangers Compact heat exchanger | SVR | NA | fin height, fin pitch, fin thickness, fin length and Reynolds number at the air side | Colburn factor and friction factor | MSE = 2.645 × 10–4 and MSE = 1.231 × 10–3 | Peng and Ling (68) |
| compact heat exchanger | BPNN | 5-6-4-2 | fin height, fin pitch, fin thickness, fin length and Reynolds number at the air side | Colburn factor and friction factor | MSE = 7.471 × 10–4 and MSE = 2.591 × 10–3 | Peng and Ling (68) |
| finned oval-tube | MLFFNN | 10-8-5-2 and 10-8-5-1 | air inlet angles, Reynolds number of the air side and water side, temperature of inlet air and inlet water, number of tube rows and tube-passes, outer length of major axis and minor axis, and fin collar outside diameter | Nusselt number and friction factor | Du et al. (69) | |
| shell and tube | RVFL, SMO, SVM and KNN | NA | cold fluid temperature and injected air volume flow rates | outlet temperature of hot and cold fluids and pressure drop | RMSE = 0.719167, 2.477069, 1.741808, and 1.855635 | El-Said et al. (70) |
| helically coiled tube heat exchanger | LSSVM, ANFIS, and MLP-ANN | Prandtl number, volumetric concentration and helical number | Nusselt number | MRE = 0.11, 5.94, and 5.17% | Baghban et al. (72) |
Control of Heat Exchanger
The successful implementation of the ML approach to heat exchanger control is reviewed and demonstrated in this section.
García-Morales et al. (73) introduced a nonlinear control approach for a double-tube heat exchanger using an inverse ANN with integral control (ICANNI). ICANNI was employed to control the cold water’s exit temperature, using cold water flow as a baseline. The temperature of the hot and cold water as well as the water’s flow were the model’s input parameters, while the output variables were the temperatures of the hot and cold water. The results showed that ICANNI showed good reference tracking with an RMSE of 0.2025, a standard deviation (SD) of 0.0410, an establishment time of 23 s, and overshoots smaller than 2.7 °C. Furthermore, when compared to PID and ANNi controllers, ICANNI showed a 1.91-fold faster settling time than PID and a 1.5-fold faster settling time than ANNi. In another paper, Carvalho et al. (74) proposed an enhanced control strategy based on neural network model predictive control (NNMPC). They employed NNMPC to control the exit stream temperature of the heat exchanger network. Their findings demonstrated that NNMPC outperformed both conventional PID and linear model predictive controllers (MPCs) in a complex heat exchanger network scenario. When compared to conventional control techniques, NNMPC showed better set-point tracking and disturbance rejection capabilities.
In a separate study, Bakosova et al. (75) employed neural-network-based predictive control (NNPC) and robust model-based predictive control (robust-MPC) as two control strategies to regulate the output stream temperature of a tubular heat exchanger. Their results showed that NNPC provided the best closed-loop control performance in terms of set-point tracking and energy consumption reduction when compared with conventional PID controllers. The primary disadvantage of NNPC was its small offset. Compared to the PID control, both advanced control systems reduced energy consumption. In a study, Vasičkaninová and Bakošová (76) proposed an intelligent control approach that maintains the outlet temperature of a tubular heat exchanger used for hot water preheating of petroleum using a fuzzy controller and a neural network predictive controller. Their results showed that the auxiliary control input produced the best control performance and that the suggested control techniques, with their intricate control structures, produced more precise and quick control responses.
An NNPC structure was used by Vasičkaninová et al. (77) in another study to forecast the behavior of a tubular heat exchanger that was regarded as a system with dispersed parameters. The neural network model was trained offline and had a single hidden layer of six neurons. To guarantee that the heated outlet stream had the appropriate temperature, NNPC was used to calculate the best control inputs. The study also monitored the amount of energy used to heat the water. PID control and the heat exchanger’s NNPC were contrasted. The findings show that, in comparison to the PID control, NNPC efficiently regulated the temperature of the heated output stream, displaying less oscillation and shorter settling times. Díaz et al. (81) created an ANN model to forecast heat exchanger dynamic performance and contrasted its results with those of PI and PID controllers. As part of their contribution, two ANN models were used to build the internal model system for controlling the overtube air temperature. One is utilized for modeling, while the other is employed for heat exchanger control. According to the findings, the ANN-based control approach performed better at regulating the overtube air temperature than the traditional PI and PID controllers.
Varshney et al. (78) applied ANN and PID controllers to manage the temperature of a heat exchanger within a closed-flow air circuit. The control strategy involved varying the air flow over the tube surface and the water flow inside the tubes to maintain the test section at a specified temperature. Controller effectiveness was assessed for different set point values. According to their findings, the ANN-based control outperformed the PID control in terms of response times, steady-state errors, and oscillation. Hu et al. (79) used ANN models in another study to forecast the dynamic behavior of a heat ventilation and air conditioning (HVAC) heat exchanger. Two multilayerfeedforward neural network (MLFFN) models were used in the study to forecast the HVAC system’s heat exchanger’s static and dynamic reactions. For static response prediction, five input variables were considered: air mass flow rate, inlet and outlet chilled water temperatures, and the inlet temperatures of both hot air and chilled water. The heat transfer rate was chosen as the output parameter. An ANN model configured with a 5-10-1 structure predicted the heat transfer rate, with an accuracy deviation of ±4.87%. To capture the dynamic response of the heat exchanger, another ANN model was developed with ten input neurons and two output neurons, resulting in a 10-20-2 architecture. The maximum relative errors were 11.42% for the chilled water outlet temperature and 6.94% for the outlet air temperature. Jahedi et al. (80) applied a wavelet neural network (WNN) with infinite impulse response (IIR) to regulate outlet air temperature and humidity in an HVAC heat exchanger. Their results indicated that WNN-IIR achieved a better energy efficiency compared with conventional PD controllers. For ML applications in the control of a heat exchanger, the summary of key details is given in Table 6.
Table 6. Summary of ML Applications for Control of Heat Exchanger
| heat exchanger type | ML type | model structure | input variable | output variable | model evaluation | references |
|---|---|---|---|---|---|---|
| double tube | ICANNI | 4-1-2 | input temperature of cold, and hot water, and cold and hot water flow | output temperature of hot and cold water | RMSE = 0.2025 | García-Morales et al. (73) |
| water-to-air fin-tube | MLFFNN | 4-5-5-1 | air and water mass flow rate, and air and water inlet temperatures | heat transfer rate | NA | Díaz et al. (81) |
| fin tube heat exchanger | MLFFNN | 5-3-1 | the predictive framework is based on dynamic inputs consisting of temperature and voltage from the last two time steps, in addition to the instantaneous voltage at the current step | present temperature | NA | Varshney et al. (78) |
| HVAC heat exchangers | MLFFNN | 5-10-1 | inlet and outlet chill water temperature, inlet temperature of hot air and chilled water and air mass flow rate | heat transfer rate | MRE = 1.38 × 10–2 | Hu et al. (79) |
Application of Optimization Techniques in Heat Exchangers
Various studies have explored the design optimization of heat exchangers with several objective functions.
Design Optimization of STHEs
Sai and Rao (82) suggested a hybrid optimization method to reduce STHX design costs. The hybrid approach combines particle swarm optimization (PSO) and nondominated sorting genetic algorithm II (NSGA-II) to maximize heat transfer and decrease total cost. The results reveal that the hybrid approach reduces the overall cost by 4.85%. Cao et al. (83) analyzed the performance of helical baffle heat exchangers through a combination of numerical modeling and experimental investigation. Their optimization framework employed a Multi-Objective Genetic Algorithms (MOGAs), where the updated entropy generation number and total cost were used as objective functions. Design variables included the number and diameter of tubes, tube length, helix angle, and axial overlap ratio. The MOGA generated a Pareto front of solutions, allowing trade-offs between thermodynamic performance and economic cost to be effectively assessed. The findings showed that thermal enhancement and the axial velocity were greatly impacted by the helix angle and axial overlapped ratio. The results of this investigation showed that the multiobjective optimization method outperformed the single-objective optimization technique.
Saijal et al. (84) used a thorough method for the multiobjective optimization and parametric analysis of STHEs with staggered baffles. Using CFD-generated data set, an ANN model was first trained and then applied in combination with NSGA-II to perform multiobjective optimization. The optimization framework focused on two goals: lowering the pressure drop and increasing the heat transfer rate. Design factors examined included the baffle cut, baffle spacing, baffle orientation, shell inner diameter, and tube outer diameter. The outcomes revealed that staggered baffle arrangements achieved better comprehensive performance than either segmented or helical baffle designs. Furthermore, a lower baffle cut increases heat transfer in the heat exchanger and decreases pressure loss. 75.6 mm shell diameter, 17.2 mm tube diameter, 54.3 mm baffle spacing, 0.38 baffle cut, and a baffle orientation angle of 121.33° were the ideal design characteristics determined by the study. The ideal pressure drop is 88,083.86 Pa, and the ideal heat transfer rate is 154,555 W. Jamil et al. (85) evaluated design and operational parameters to optimize STHEs exergoeconomically. The paper critically evaluates several design approaches for the thermal-hydraulic design of STHX. To determine flow exergy and exergy destruction in the heat exchanger setup, exergy analysis was also carried out. Sensitivity analysis was used to evaluate the effect of changing input parameters on the operating cost of heat exchangers, while economic analysis was used to calculate various cost aspects associated with the current system. Ultimately, the use of GA resulted in a configuration that is cost-optimal. Due to the exponential growth in pressure drops, the results showed that the heat exchanger’s running costs rise as the mass flow rate and baffle count increase. Heat transfer area, capital cost, operating cost, and total cost were all lowered by 26.4, 20, 50, and 22%, respectively, following GA optimization.
The Adaptive Range Genetic Algorithm (ARGA) was used by Lyer et al. (86) to optimize STHEs economically. Across several case studies, ARGA showed notable cost reductions by minimizing the overall cost. Three distinct test cases related to STHX design were resolved in this work and contrasted with current approaches. The results show that the total cost is lower in Case 1, Case 2, and Case 3 by 34.99, 28.95, and 52.71%, respectively. Wang et al. (87) explored the optimization of shell-and-tube heat exchangers equipped with staggered baffles by combining CFD simulations, ANN modeling, and GA-based optimization. The ANN was utilized to derive objective functions more effectively than traditional statistical methods. Wen et al. (88) found that MOGA was used to improve the exchanger design. The optimization process identified three configurations with superior thermal-hydraulic characteristics, resulting in reduced shell-side pressure drop by 19.37% while enhancing the overall HTC by 28.3%.
Wang et al. (89) optimized the shell-and-tube heat exchanger’s (STHE) helical baffle configuration. Their method integrated a multiobjective GA with a second-order polynomial regression response surface. Maximizing the HTC per unit pressure drop and minimizing the maximum shear stress while remaining within allowable stress limits were the main optimization goals. According to the findings, the HTC per unit pressure drop generally declined as the overlapping degrees increased, but it first increased and subsequently decreased with increasing helical angles. The study also found that, in comparison to the overlapped degree, the helical angle had a greater impact on flow and heat transfer performance. The ideal setup resulted in a 4.1% decrease in the maximum shear stress and a 14.1% increase in HTC per unit pressure drop. Tharakeshwar et al. (90) used a Bat Algorithm (BA) and GA to carry out multiobjective optimization for STHEs. Total cost and efficacy were the study’s optimization goals, and the design variables included pitch, tube length, tube layout pattern, baffle cuts, and baffle spacing. According to the data, a 45° tube layout has better efficacy and HTC than 30° and 90° layouts. Furthermore, as the baffle spacing, baffle cut, and pitch increase, both efficacy and overall cost decrease. The study came to the conclusion that BA is more efficient than GA since it reduces costs by up to 13.7% and at least 9.2%, while cost minimization reduces effectiveness by roughly 3%. Rao and Saroj (91) optimized the economics of STHEs using Jaya’s Algorithm (JA). This study’s objective was to reduce the total yearly cost while accounting for 11 configurational features related to the STHE configuration. The researchers employed three different algorithms, GA, PSO, and CSO, to evaluate optimization outcomes across two case studies. The analysis revealed that the GA proved to be the most effective approach, showing stronger suitability for addressing complex optimization tasks, regardless of whether the problems were constrained or unconstrained. In comparison to GA, PSO, and CSO, JA’s improvements in total yearly cost reduction in cases 1 and 2 were 10.59, 2.5, and 1.24%, respectively, and 16.89, 13.83, and 13.40%.
Wen et al. (92) introduced a new approach for the design improvement of STHEs using Helical Baffles (STHXsHB). The approach coupled a Kriging response surface with a MOGA. Helix angles, baffle overlap ratios, and inlet volumetric flow rates were among the design variables, and heat transfer rates and the overall cost were the optimization objectives. The study showed that the Kriging metamodel allowed for an enhanced optimization process with fewer design points when compared to the MOGA approach alone. The results showed that a tiny helical angle of 15° and a baffle overlap proportion of less than 0.3° were advantageous for maximizing the heat transfer rate and minimizing the total cost. Similarly, Khosravi et al. (93) evaluated the optimization capabilities of the Cuckoo Search (CS) method, Frefly Algorithm (FA), and GA for STHX design. In this analysis, the optimization of STHX aims to maximize its thermal efficiency. During the optimization process, seven design elements are considered: length, diameter, quantity, pitch ratio, baffle spacing rate, baffle cut propotion, and tube layout. The findings showed that GA typically falls short of identifying workable and optimal solutions. On the other hand, the design parameters that FA and CS found consistently produce the maximum STHX efficiency. Furthermore, compared with the FA approach, the CS method requires a lot less processing. The optimization results indicate that 83.8% is the greatest efficiency that can be attained with different design options. Guo et al. (94) presented a new optimization method for STHEs. Their approach combined the second law of thermodynamics with evolutionary algorithms for optimization. The tube outer diameter, tube quantity, baffle spacing ratio to shell diameter, baffle cut angle, and cold fluid outlet temperature were all design aspects taken into account during the optimization process. The entropy generation number served as the optimization’s goal function. Three case studies of heat exchanger designs were presented in the paper identified configurations that significantly raised heat exchanger efficiency while lowering overall costs. The summary of all these studies is presented in Tables 7, 8, 9.
Table 7. Application of ML for STHEs Design Optimization
| heat exchanger type | design variables | objective function(s) | optimization technique(s) | key findings | references |
|---|---|---|---|---|---|
| STHX | tube outside diameter, shell inside diameter and baffle spacing | total cost and overall HTC | NSGA-II-PSO | good convergence and strong exploitation to escape from local optima were two advantages of NSGA II-PSO; it was used in two cases and had a total cost that was 4.85% lower in case 1 and 1.51% lower in case 2 | Sai and Rao (82) |
| STHX with helical baffle heat exchanger | number, outer diameter and length of tube, helix angle and axial overlapped ratio | total cost and entropy generation number | MOGA | helix angle and axial overlapped ratio will decrease thermal enhancement and axial velocity, and multiobjective optimization is a better approach than single-objective optimization | Cao et al. (83) |
| STHX | shell inner and tube outer diameter, baffle cut, baffle spacing and baffle orientation angle | heat transfer rate and Pressure drop | NSGA-II and staggered baffles perform significantly better than segmented or helical baffles; heat transmission improves and pressure drop decreases with a lower baffle cut; the maximum heat transfer rate is 154,555 W, and the minimum pressure drop is 88,083.86 Pa | Saijal and Danish (84) | |
| STHX | tube layout, tube outside diameter, number of tubes, tube passes, shell diameter, baffle cut and baffle spacing | total cost | GA | the heat exchanger’s operating costs will rise as the mass flow rate and baffle count increase due to the exponential growth in pressure drops; however, by optimizing the heat transfer area with GA, the capital, operating, and total costs are reduced by 26.4, 20, 50, and 22%, respectively | Jamil et al. (85) |
| STHEs | tube outside diameter, shell inside diameter, baffle spacing and number of tube passes | total cost | ARGA | three cases associated with design were solved and compared with existing methodologies, total cost is reduced by 34.99, 28.95, and 52.71% in Case 1, Case 2 and Case 3 respectively | Iyer et al. (86) |
Table 8. Application of ML for STHEs Design Optimization (Continued)
| heat exchanger type | design variables | objective function(s) | optimization technique(s) | key findings | references |
|---|---|---|---|---|---|
| STHX with SG, CH, and ST baffles | baffle cut, staggered angle and number of baffles | heat transfer rate and pressure drop | MOGA | STHX-ST performed better than STHX-SG and STHX-CH. If you want to improve heat transfer, a special STHX-ST at a staggered angle = 180° is not necessarily the greatest option. The ideal STHX-ST configuration is baffle cut = 0.45, staggered angle = 79°, and number of bags = 11 | Wang et al. (87) |
| STHX | helix angle, overlapped degree and inlet flow rate | overall HTC and shell-side pressure drop | MOGA | using MOGA, three configurations were optimized to decrease shell-side pressure drop and increase the overall heat transfer coefficient; the optimized configuration showed a 19.37% reduction in pressure drop and a 28.3% gain in overall HTC relative to the original design | Wen et al. (88) |
| STHX | helical angle and overlapped degree | heat transfer coefficient, pressure drop on the shell side, HTC per pressure drop and maximum shear stress | MOGA | the HTC per unit pressure drop of STHE-HB initially increases and then falls as the helical angle increases, and decreases with greater baffle overlap; flow and heat transfer respond more strongly to changes in helical angle than in baffle overlap; following optimization, the HTC per unit pressure drop improved by 14.1%, and the maximum shear stress was reduced by 4.1% | Wang et al. (89) |
| STHX | baffle cuts, baffle spacing, tube pitch, tube length and tube layout pattern | total cost and effectiveness | GA + BA | the most efficient of the 30° and 90° tube layouts is the 45° tube architecture, which also has the lowest overall cost. GA is not as efficient as BA; by increasing baffle spacing, baffle cut, and pitch, BA can reduce expenses by up to 13.7% and boost efficacy by up to 3% | Tharakeshwar et al. (90) |
Table 9. Application of ML for STHEs Design Optimization (Continued)
| heat exchanger type | design variables | objective function(s) | optimization technique(s) | key findings | references |
|---|---|---|---|---|---|
| STHX | shell diameter, outer diameter of tube and tube bundle, tube pitch and layout angle, number of tube passes, percentage baffle cut, baffle spacing at inlet and outlet, baffle spacing at center and diametrical clearance of shell-to-baffle and tube-to-baffle | total annual cost | JA, GA, PSO and CSO | comparison of JA with GA, PSO, and CSO across two case studies indicates that JA is more suitable for handling complex constrained and unconstrained problems; in case 1, JA improved total annual cost reduction by 10.59, 2.5, and 1.24% relative to GA, PSO, and CSO; in case 2, the improvements were 16.89, 13.83, and 13.40%, respectively | Rao and Saroj (91) |
| STHX with helical baffles | helical angles, baffle overlap proportion, and inlet volume flow rate | total cost and heat transfer rate | MOGA with Kriging response surface | by employing the Kriging metamodel, the number of design points is minimized, and the optimization process is expedited; a helical angle of 15° combined with a baffle overlap fraction under 0.3 allows for a favorable balance between heat transfer rate and total cost | Wen et al. (92) |
| STHX | tube layout, pitch ratio, tube dimensions (diameter and length), number of tubes, baffle spacing ratio, and baffle cut ratio | maximize thermal efficiency | GA, FA and CS | while design factors identified by FA and CS always result in maximum STHX efficiency, GA is typically unable to identify acceptable and ideal solutions; after optimization, the maximum efficiency that can be attained using many design configurations is 83.8% | Khosravi et al. (93) |
Design Optimization of Other Types of Heat Exchangers
This section surveys effective optimization techniques applied to a range of heat exchanger designs. Design optimization studies have often relied on CFD or experimental analysis to assess the influence of geometry and construction on thermal performance (e.g., ref (95)). ML surrogates now provide an efficient alternative to evaluate such impacts while reducing the computational cost. For plate-fin heat exchangers (PFHEs), do Nascimento et al. (96) developed a surrogate-assisted optimization framework that coupled a random vector functional link (RVFL) network with NSGA-III. CFD simulations provided data sets for training and testing the RVFL network, which improved computational efficiency and predictive accuracy. The multiobjective optimization targeted the reduction of hot and cold side pressure drops, minimization of exchanger volume, and enhancement of effectiveness. Experimental verification was carried out using the shear stress transport turbulence model with modeling errors limited to 3.27% for HTCs and 4.36% for pressure drops. Compared with earlier results, the optimized designs achieved notable improvements, with cutting pressure drops by roughly 55.4% on the hot side and 72.3% on the cold side. Wang et al. (97) performed optimization of a shell and helically coiled tube heat exchanger using GA, defining the objective function as the maximization of heat transfer rate per unit thermal surface area. According to the study’s findings, changes to the tube diameter, coiled pitch, and coiled diameter could have a big effect on the heat transfer mechanism. In comparison to the experimental data, the heat exchanger with the best construction had an 110% increase in heat flow and a 101% increase in heat transfer rate. The study also highlighted the importance of pressure drop considerations in heat exchanger design and found that applying a pressure drop limitation marginally increased the optimal heat flux value by 3.6%.
Jilak et al. (98) presented a multiobjective optimization method in another study that combines ANN in a synergistic manner for the best plate heat exchanger design. A Multi-Objective Evolutionary Algorithm (MOEA) was used in this methodology to produce a design that maximizes efficiency while minimizing expenditures. Fin gradient, fin height, fin curvature length, linear cold flow length, nonflow length, linear warm flow length, fin thickness, and plate thickness were among the design elements taken into account throughout the optimization process. The analysis showed a 9.533% cost decrease and a 19.962% increase in efficiency rate. Using orthogonal design methodologies and GAs, Du et al. (99) optimized plate-fin heat exchangers (PFHEs). Maximizing the overall heat transfer rate and minimizing the overall pressure drop were the optimization goals. The decision variables for multiobjective optimization in that study are corrugation angle, offset, length, fin height, and fin width. Numerical results showed that the optimized design had considerable benefits over the original design: a 6.2% increase in the total heat transfer rate, a major 40% reduction in the total pressure drop, and a roughly 2.7% decrease in the overall volume.
Another study used a GA to optimize the size of a shell and double concentric tube heat exchanger (Baadache and Bougriou (100)). Their method simultaneously identified the ideal values of several design parameters, which directly addressed the heat exchanger’s sizing and layout. This study’s goal was to determine the overall cost, which included both capital and operational expenses. The results showed that the heat exchanger’s overall cost dropped by roughly 13.16% when GA was used. Najafi et al. (101) used GA to perform multiobjective optimization for a plate and fin heat exchanger in a different study. By treating these variables as objective functions for the multiobjective GA, the optimization sought to maximize both the overall heat transfer rate and minimizing the overall yearly cost. The heat exchanger’s hot and cold sides’ combined length, fin height, fin frequency, fin lance length, fin thickness, and number of fin layers were among the design variables. To evaluate the impact of these design choices on the objective functions, a sensitivity analysis was also conducted. The results provide a wide range of optimal solutions, allowing for the selection of the best design parameters based on the application and total annual cost of the system.
A GA-based optimization method for cross-flow plate-fin heat exchangers was developed by Mishra et al. (102) By taking into account variables like fin height, fin pitch, and flow lengths for hot and cold fluids, their optimization aimed to reduce entropy generation units. This paper highlighted GA’s capacity to solve engineering optimization challenges and showed how second-law-based design might offer valuable insights. Han et al. (103) used both GA and particle swarm optimization (PSO) for rolling fin tube heat exchangers. Their study concluded that at Re = 541 and an ellipticity of 0.34, the TFHE achieved a 20% reduction in pressure drop while maintaining nearly the same HTC. Likewise, Zeng et al. (104) investigated the optimization and sensitivity of heat exchanger tubes fitted with conical strip vortex generators. Using NSGA-II, their study showed that while the heat transfer rate and pressure drop reduced with a decrease in the pitch ratio, they both increased with larger conical strip filling ratios and Reynolds numbers. Following optimization, the values of the design variables were P* = 3.97, Re = 1468, and C = 0.35. The corresponding friction factor ratio and Nusselt number ratio for this optimized solution were 7.07 and 6.56, respectively. The key details for the paper reviewed here are given in Tables 10 and 11.
Table 10. Application of ML for Design Optimization of Other Types of Heat Exchangers
| heat exchanger type | design variables | objective function(s) | optimization technique(s) | key findings | references |
|---|---|---|---|---|---|
| plate fin compact heat exchanger | heat transfer rate, height of fins, number of fin layers at cold stream, transverse length of fins and spacing of fins | heat exchanger volume, pressure drop for hot side and cold side and effectiveness | NSGA-III | for experimental validation, the shear stress transport turbulence model was employed, yielding errors of 4.36% in pressure drop and 3.27% in heat transfer coefficient; following optimization, the pressure drops on the hot and cold sides decreased by approximately 55.4% and 72.3%, respectively, compared with values reported in the literature | do Nascimento et al. (96) |
| shell and helically coiled tube heat exchanger | coiled pitch and diameter, tube diameter and inlet flow rates on the tube side and shell side | heat transfer rate | GA | variations in coil pitch and tube diameter significantly influence the heat transfer rate; with constant inlet flow rates and no pressure drop constraint, the optimal structure enhanced heat flux by 110%; when the pressure drop constraint was applied, the improvement in heat flux was 3.6% | Wang et al. (97) |
| flat plate heat exchanger | fin gradient, height and thickness of fin, fin curvature length, linear cold and warm flow length, nonflow length and plate thickness. | thermal efficiency and manufacturing cost | MOEA | the MOEA-based optimization yielded a 19.962% enhancement in efficiency along with a 9.533% decrease in cost | Jilak et al. (98) |
| plate fin heat exchanger | fin height, fin width, fin length, fin offset, and fin corrugation angle | heat transfer rate and pressure drop | MOGA | optimization led to a 6.2% improvement in heat transfer rate, a 40% reduction in total pressure drop, and a 2.7% decrease in volume relative to the original design | Du et al. (99) |
| shell and double concentric tube heat exchanger | shell internal diameter, outside diameter of the outer tubes, outside diameter of the internal tubes and distance between baffles | total cost | GA | using GA, the total cost of the heat exchanger decreased by approximately 13.16%, while the heat transfer area per unit volume increased from 133.8 to 473.8 m2/m3 | Baadache and Bougriou (100) |
Table 11. Application of ML for Design Optimization of Other Types of Heat Exchangers (Continued)
| heat exchanger type | design variables | objective function(s) | optimization technique(s) | key findings | references |
|---|---|---|---|---|---|
| rolling fin and tube heat exchanger | tube bundle length, number of tube rows, core width of heat exchanger, fin pitch | volume, weight and pressure drop | PSO and GA | relative to GA, PSO optimization yielded improvements, lowering the minimum volume by 3.34%, the weight by 4.31%, and the pressure drop by 14.04% | Han et al. (103) |
| tube fin heat exchanger | Reynolds number and tube ellipticity | HTC and pressure drop | NSGA-II | different Reynolds numbers and tube ellipticities were analyzed through CFD simulations; these data were applied to train and validate an ANN model for predicting HTC and pressure drop; optimization was performed using the NSGA-II algorithm; under conditions of Re = 541 and ellipticity = 0.34, the TFHE pressure drop decreased by 20% | Zeng et al. (104) |
Summary and Discussion
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In the area of fouling prediction and parameter estimation, the most frequently used methods were MLFFNN, GPR, SVR, NARX, and wavelet networks. GPR and MLFFNN outperformed the rest of the methods and achieved a higher correlation coefficient R2 value of up to 0.98 and demonstrated higher generalization in both cross-flow and shell-and-tube heat exchangers. The dominant input parameters for the fouling model included inlet–outlet temperatures, flow rates, fluid physical properties, wall temperature, and chemical concentration, while the output was the fouling resistance and fouling factor. A common recommendation for these studies was that increasing the size of data sets improved the robustness of the model, and methods such as GPR, which is uncertainty aware, were preferred over the others in the case of high operational variability. The time-varying fouling behavior was best captured by hybrid or dynamic models such as NARX and wavelet neural networks, especially when the fouling was very nonlinear and exhibited transient characteristics. In the case of HTC prediction, dominant methods included ANN/MLP, ANFIS, GRNN, GPR, and bioinspired optimized neural networks such as BBO-ANN and CSA-ANFIS. The hybrid NN-based optimization method and GRNN that reduced the prediction error significantly were effective methods. The input variables used in this model development were the Reynolds number, Prandtl number, Dean number, coil geometry, fin characteristic, nanoparticle concentration, and fluid thermophysical property, while the outputs were the Nusselt number, overall HTC, and pressure drop. The hybrid optimization methods using ML as a core method were more recommended for complex geometries such as helically coiled, ribbed, or finned heat exchangers. Surrogate models were also recommended as a replacement for CFD simulation, where they drastically reduce the computational time while maintaining higher prediction accuracy. In the performance prediction, the dominant methods were SVR, ANN, LSSVM, RVFL network, and deep feed-forward architecture. SVR and RVFL models outperform the neural network approach in small- and medium-sized databases due to their regularization and reduced overfitting tendency, while the neural network model outperforms in large data set cases. The common input variables were fin geometry, flow rates, temperature, Rynolds numbers, and fluid properties, while friction factors, the Colburn factor, the Nusselt number, and outlet temperatures were the dominant outputs. It was recommended that ML should be selected based on size, such as SVR or LSSVM for limited data, neural networks and deep learning for large data. It also emphasized that ML models can capture the thermal-hydraulic behavior more accurately than the empirical correlation, making the ML model in general very suitable for offline condition application. In control-related applications, the most frequently adopted methods were neural network predictive control (NNMPC), inverse ANN controllers (ICANNI), fuzzy-logic-ANN hybrids (ANFIS), and wavelet neural network controllers. The high performers were NNMPC and ICANNI, which delivered faster settling time, reduction in overshoot, and higher energy efficiency in comparison to the conventional PID and PI controllers. The control model used dynamic inputs such as past temperature, mass flow rates, voltage, and inductive condition, with the control output typically being the outlet temperature or heat transfer rate. It was recommended that ANN-based predictive control is good for nonlinear and time-delayed systems, as traditional PID controllers are insufficient under strong disturbance or nonlinear dynamics. Several studies suggested ML-based control integrated with the online monitoring system to enable real-time adaptation to fouling and load variation. In heat exchanger optimization, frequently used methods were the GA, particle swarm optimization, NSGA-II, MOGA, Bat Algorithm, Kriging-enhanced GA, and Cuckoo Search. Hybrid GA-based and PSO-based methods were most effective, achieving cost-effective reduction of 20–50%, improving the HTC and pressure drop balance. Optimization variables included baffle cut, baffle spacing, tube diameter, pitch, helix angle, overlap ratio, and fluid velocity, with the objective function focused on cost, pressure drop, transfer rate, entropy generation, and mechanical stress. A common recommendation was that a staged baffle, smaller baffle cuts, and a low helix angle provide superior performance and should be explored earlier in the design space.
The current applications are confined to specific types, conditions, or geometrical structures of heat exchangers, but future applications may develop a universal or geometry-adaptive ML framework that can perform well across heat exchanger types. The reported data sets are small or confined to specific cases, so a generalized database can also be developed by merging the available data sets across different studies or doing a simulated study of different heat exchangers to develop a unified ML model. Uncertainty quantification is a very important area in modeling and simulation, but not much has been investigated in reported studies that can be a future area of research. The integration of the physical model and the data-driven model to form a hybrid model will be helpful to improve the intuitiveness and robustness of the model. In the case of control, the reported work is still not upscaled, and the online application of ML needs a robust and adaptive framework. This area may be investigated further to address the gap between the laboratory-scale model development and real-time applications. The optimization study mostly relies on single-output optimization or single-case geometry, but more dimensions in terms of design and operation can be explored. Cross-comparison for a wide range of models can be investigated to help the designer and practitioner select the best-suited model for the context. Predictive maintenance is a very important area of investigation for the current digital twin application in heat exchangers, but more studies on real-time sensor data collection and performance evaluation and optimization can be explored. This includes the physical model development at a laboratory scale and their digital counterpart to start with and proceed to real-time implementation.
Conclusions
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This review paper investigated the ML applications as a powerful tool for addressing the challenges in the analysis, design, operation, and control of heat exchangers across process industries. The ML methods reported in the studies consistently outperformed the traditional empirical and analytical correlation in estimating critical heat exchanger parameters such as fouling resistance, HTC, pressure drop, and thermal-hydraulic performances. The neural networks, Gaussian regression, support vector machine, and hybrid optimization-assisted by ML model were the most widely applied and effective approaches across different heat exchanger configurations. The study was performed in four key domains, such as parameter estimation, performance prediction, process control, and design optimization, where a wide range of ML applications were analyzed. The ML enables accurate prediction even in complex geometries such as helically coiled, finned, ribbed, and multipass challenging heat exchanger, demonstrating strong capability to capture nonlinear dynamics of the heat exchanger. ML-based control study, particularly ANN-based predictive control, have shown significant improvement over the conventional PID system by providing faster response, reduction in overshoot, and superior performance under nonlinear and time-varying operating conditions. The regression method assisted by ML reduced the exchanger cost, operation cost, energy consumption, and pressure drop, while improving heat transfer efficiency, highlighting the importance of ML potential in high-performance engineering design and operation. Several limitations of the current studies were found such as small data set, fragmented studies confined to specific geometry or context, lack of uncertainty quantification studies, and real-time implementation of the area that can be explored in future. Overall, this review underscored the ML central role in next-generation heat exchanger technologies, enabling predictive maintenance, adaptive control, digital twin, data-driven optimization, supporting the transition toward smarter efficient and sustainable thermal management systems.
Author Information
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- Iftikhar Ahmad - School of Chemical and Materials Engineering, National University of Sciences and Technology, Islamabad 44000, Pakistan;
https://orcid.org/0000-0003-0997-2175;
- Ahmed Qazi - Department of Chemical and Petroleum Engineering, College of Engineering, United Arab Emirates University, Al Ain 1555, United Arab Emirates;https://orcid.org/0009-0002-1467-2935
Acknowledgments
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This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. (GPIP: 2019-665-2024). The authors, therefore, acknowledge with thanks DSR for technical and financial support.
References
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Figure 1
Figure 1. Types of ML models. (28)
Figure 2
Figure 2. ML models development steps.
Figure 3
Figure 3. ML model applications in heat exchangers.
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