Renewable and Sustainable Energy Reviews xxx (xxxx) xxx

Contents lists available at ScienceDirect

Renewable and Sustainable Energy Reviews

journal homepage: http://www.elsevier.com/locate/rser

Recent trends on nanofluid heat transfer machine learning research applied

to renewable energy
Ting Ma a, Zhixiong Guo b, *, Mei Lin c, Qiuwang Wang a
a
Key Laboratory of Thermo-Fluid Science and Engineering, MOE, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China
b
Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA
c
Department of Fluid Machinery and Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

A R T I C L E I N F O A B S T R A C T

Keywords: Nanofluids have received increasing attention in research and development in the area of renewable and sus­
Machine learning tainable energy systems. The addition of a small amount of high thermal conductivity solid nanoparticles could
Nanofluid improve the thermophysical properties of a base fluid and lead to heat transfer augmentation. Various
Heat transfer enhancement
enhancement mechanisms and flow conditions result in nonlinear effects on the thermodynamics, heat transfer,
Heat exchanger
Renewable energy
fluid flow, and thermo-optical performance of nanofluids. A large amount of research data have been reported in
Solar energy the literature, yet some contradictory results exist. Many affecting factors as well as the nonlinearity and refu­
Nanoparticle tations make nanofluid research very complicated and impede its potentially practical applications. Nonetheless,
Thermal property machine learning methods would be essentially useful in nanofluid research concerning the prediction of ther­
Optical property mophysical properties, the evaluation of thermo-hydrodynamic performance, and the radiative-optical perfor­
mance applied to heat exchangers and solar energy systems. The present review aims at revealing the recent
trends of machine learning research in nanofluids and scrutinizing the features and applicability of various
machine learning methods. The potentials and challenges of machine learning approaches for nanofluid heat
transfer research in renewable and sustainable energy systems are discussed. According to the Web of Science
database, about 3% of nanofluid research papers published in 2019 involved in machine learning and such a
tendency is increasing.

efficiency was enhanced by 78% using 6 ppm aqueous gold nanofluid

[15].
1. Introduction
Since the term “nanofluid” was first used in 1995, numerous studies
have been conducted to investigate the thermophysical properties,
In the most recent decade, nanofluids have received considerable
synthesis, preparation, thermal fluid characteristics, and applications of
attention in research and development in the areas of heat transfer
nanofluids. A recent literature survey conducted by Guo [16] found that
enhancement techniques [1,2] and renewable and sustainable energy
research papers on nanofluids had increased by 827.8% from 2009 to
systems [3,4]. Studies with nanofluids span a wide spectrum including
2018 in just ten years. Over 4300 archival papers on nanofluids are
hydrodynamics [5], thermodynamics [6,7], solar collectors [8,9], hy­
collected in the Web of Science database in the single year 2019. Various
droelectric rotors [10], wind turbines [4], geothermal heat exchangers
property-enhancement mechanisms, models for heat transfer charac­
[11], and ocean power plants [12], to name a few. A nanofluid with the
terization, and methods for suspension preparation and stability have
addition of nanoparticles (NPs) into a base fluid exhibits improved
been extensively reviewed. Thus, some selection in the present review
thermophysical properties for enhancing heat transfer or for increasing
article is inevitable.
energy absorption and storage as compared with only the use of base
Table 1 lists some representative review papers on nanofluid heat
fluid. For example, the effective thermal conductivity of a 0.75 vol%
transfer and energy applications in the recent five years. It shows that
MWCNTs-SiC/Water-EG nanofluid was increased by up to 33% [13].
most review papers are dedicated to the measurements and evaluation
The ternary carbonate salts (Na2CO3-Li2CO3-K2CO3) containing SiO2
of thermophysical properties (e.g., thermal conductivity, viscosity,
nanoparticles of 5–30 nm in diameter showed specific heat capacity
specific heat, and optical properties) that influence the performance of
enhancement by 78–116.8% [14]. The photothermal conversion

* Corresponding author.
E-mail addresses: mating715@mail.xjtu.edu.cn (T. Ma), zguo@rutgers.edu (Z. Guo), janeylinm@mail.xjtu.edu.cn (M. Lin), wangqw@mail.xjtu.edu.cn (Q. Wang).

https://doi.org/10.1016/j.rser.2020.110494
Received 28 January 2020; Received in revised form 23 July 2020; Accepted 18 October 2020
1364-0321/© 2020 Elsevier Ltd. All rights reserved.

Please cite this article as: Ting Ma, Renewable and Sustainable Energy Reviews, https://doi.org/10.1016/j.rser.2020.110494
T. Ma et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx

Nomenclature EG ethylene glycol

GA genetic algorithm
D diameter, m GMDH group method of data handling
h heat transfer coefficient, W/(m2⋅K) IANN intelligence algorithms based ANN
k thermal conductivity, W/(m⋅K) ICA imperialist competitive algorithm
Nu Nusselt number LS-SVM least-square support vector machine
Pr Prandtl number MAPE mean absolute percent error
Re Reynolds number ML machine learning
R2 goodness fit MLP multi-layer perceptron
MSE mean square error
Greek MWCNT multi-wall carbon nanotubes
Φ concentration NP nanoparticle
Δp pressure drop, Pa NTU Number of Transfer Units
Abbreviations PCM phase change material
AC ant colony PHE plate heat exchanger
AI artificial intelligent PSO particle swarm optimization
ANFIS adaptive neuro-fuzzy inference system PV/T photovoltaic/thermal
ANN artificial neural network RBF radial basis function
CART category and regression tree RF random forest
CNT carbon nanotube SA simulate anneal
CSP concentrated solar power SSE sum squared error
DASC direct absorption solar collector SVM support vector machine
DDA discrete dipole approximation

nanofluid heat transfer and fluid dynamics. The influential factors such To this end, the present review is in time and will focus on the ma­
as temperature, nanoparticle volume or mass fraction, nanoparticle chine learning research and development of heat transfer with nano­
type, size, and shape, as well as type of base fluid have been discussed. It fluids for renewable and sustainable energy systems. It covers machine
is also noticed that interests in nanofluid research and development in learning for the prediction of thermophysical properties of nanofluids,
renewable and sustainable energy systems have increased substantially evaluation of thermal-hydrodynamic performance of heat exchangers
[17]. with the use of nanofluids, and radiative and optical performance of
Nanofluids have very complicated thermophysical properties and are nanofluids in solar energy systems. The potentials and challenges of the
used in complex heat exchange processes and energy systems. Their use of machine learning methods on nanofluid heat transfer and
effects on heat transfer, fluid flow, optical and radiative performance are renewable and sustainable energy research are also discussed.
nonlinear. Thus, machine learning (ML) could be employed in the
research of nanofluids. Table 1 also identifies a few review articles 2. Machine learning of thermal properties and characteristics
involving machine learning in nanofluid research. Machine learning
methods include artificial neural network (ANN), such as the multi-layer Accurate measurement and prediction of nanofluid thermophysical
perceptron artificial neural network (MLP-ANN) and radial basis func­ properties are critical as the thermal and hydrodynamic performance of
tion artificial neural network (RBF-ANN), group method of data heat transport processes or a heat exchange device or equipment de­
handling (GMDH), adaptive neuro-fuzzy inference system (ANFIS), pends on the properties of the heat transfer medium. Yet the thermo­
category and regression tree (CART), random forest (RF), and support physical properties of a nanofluid are influenced by many factors,
vector machine (SVM), such as least-square support vector machine (LS- including the nanoparticle concentration, type, size and shape, the
SVM), etc. Such machine learning methods can also be combined with suspension temperature, shear rate and pH value, and the preparation
genetic algorithm (GA), particle swarm optimization (PSO), and impe­ procedure as well as the type of base fluid [26], the flow condition, etc.
rialist competitive algorithm (ICA) to further improve the prediction By the example of the nanoparticle type, dozens of high thermal con­
accuracy and computational efficiency. ductivity nanoparticles have been examined for fabricating nanofluids,
Fig. 1 presents the data of the number of publications on nanofluid such as CNTs [21], Al2O3 [28], Ag [29], CeO2 [30], CuO [31], Cu [32],
(NF) and machine learning research, respectively, acquired from topic Fe3O4 [33], graphene [34], MgO [35], SiO2 [36], SiC [37], TiO2 [38]
searches in the Web of Science conducted on July 8, 2020 for the decade and Ni [39], to name a few. Therefore, the determination of the ther­
from 2010 to 2019. The data on NF resulted from topic search using key mophysical properties of a nanofluid is extremely complicated and still a
words “nanofluid” or “nanofluids”. The data on ML resulted from a wide major task in the pursuit of nanofluid research. Experimental measure­
range of search using topic words “machine learning” or “artificial ment of properties is costly and has a limited parametric data range.
neural network” or “category and regression tree” or “random forest” or Analytical approaches or numerical simulations require known property
“support vector machine”. The figure shows that the publications on values and relationships between nanoparticles and base fluids.
both research areas are soaring in recent years and the research papers Regardless, an emerging approach that has a promising future is ma­
are an order of magnitude more on machine learning than on nanofluid. chine learning.
However, nanofluid publications involving machine learning (i.e., a Machine learning is paramount in artificial intelligent (AI) research.
combination of the above two searches) are scarce, slowly climbing from It mainly includes ANN [40–49], CART [50], RF [50], and SVM [50,51].
single digit annually in the period of 2010–2014 to about 129 in the year Fig. 2 illuminates the general classification of machine learning pre­
of 2019, which occupied about 3% of nanofluid research publications in diction and regression algorithms. Figs. 3–5 display the schematic
that year. Therefore, it demands more attention to machine learning structures for a typical ANN, the algorithm flows of CART and RF, and
research in the nanofluid research community. the schematic diagram of SVM, respectively.

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Table 1 Table 1 (continued )

Representative review papers on nanofluid heat transfer research in recent five Reference/Year Review foci ML involvement
years.
and optimization of thermal
Reference/Year Review foci ML involvement properties of nanofluids.
Verma et al. [18], Experimental and numerical No Goel et al. [17], 2020 Review on nanofluid direct No
2015 results of nanofluid properties absorption solar collectors and
and heat transfer coefficients; applications for direct steam
variable performance of the generation and hybrid PV/T
solar systems with or w/o use of systems.
nanofluids. Guo et al. [16], 2020 Overview on measured thermal ANN for thermal
Raja et al. [7], 2016 Different parameters governing No properties, enhancement property prediction
nanofluid characteristics, heat mechanisms, models for
transfer performance, and properties and heat transfer
applications in heat exchangers. characteristics, and applications
Zhao et al. [19], Prediction of thermal ANN data-driven of nanofluids to cooling,
2016 conductivity and viscosity based modeling renewable energy and energy,
on ANN, and applications in and building technologies
automotive radiators.
Ganvir et al. [6], Nanofluid preparation, stability, No
2017 thermophysical properties,
convective heat transfer
performance, and applications
in automobile radiators,
electronic cooling, space and
defense.
Ibrahim et al. [20], Various techniques on heat No
2017 transfer enhancement for latent
thermal energy storage
including phase change
materials with NPs.
Sidik et al. [21], Preparation methods of CNT No
2017 nanofluids, thermal
conductivity, and applications in
solar collectors.
Gorji et al. [22], Optical performance of No
2017 nanofluids and applications in
direct absorption solar thermal
collectors.
Elsheikh et al. [3], Applications of nanofluids in No
2018 different solar energy systems Fig. 1. Archival publications on nanofluids and machine learning research
including solar collectors, acquired from topic search in the Web of Science.
photovoltaic/thermal (PV/T)
systems, thermoelectric devices,
water heaters, solar-geothermal
combined systems, evaporative
cooling for greenhouse and
water desalination.
Akbarzadeh and Techniques for enhancing No
Valipour [23], thermal efficiency in solar
2018 parabolic trough collectors.
Raj and Subudhi [9], Nanofluid preparation and No
2018 applications in flat-plate and
direct absorption solar
collectors.
Said et al. [24], 2018 Effects of nanofluids on the No
performance and environment
safety level of PV/T systems.
Khanafer and Vafai Applications of nanofluids in No
[25], 2018 different types of solar thermal Fig. 2. Categories of prediction and regression algorithms.
systems, i.e., thermal energy
storage, solar collectors, solar
stills, PV/T systems. Challenges
on safety and cost.
Ramezanizadeh et al. Characteristics of different Machine learning for
[26], 2019 machine learning methods viscosity prediction
including MLP-ANN, GMDH,
ANFIS, RBF, and LS-SVM
combined with GA, PSO and
ICA. Applications of machine
learning methods to dynamic
viscosity modeling of
nanofluids.
Bahiraei et al. [27], AI algorithms including ANNs, Machine learning
2019 fuzzy logic optimization algorithms for
methods and hybrid AI prediction and
algorithms used for prediction optimization
Fig. 3. Schematic structure of ANN topology.

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Table 2 summarizes the features of some typical machine learning

algorithms. Since the internal learning mechanism of the ANN is stan­
dardized, the ANN has been widely applied to many research fields in
recent years. The ANN has also been employed to predict nanofluid
thermophysical properties. As shown in Fig. 3, the input variables for the
nanofluid ANN could be temperature, volume fraction or mass fraction,
concentration, pressure, type of nanoparticles or base fluid, etc. The
output variables, such as thermal conductivity, dynamic viscosity, and
specific heat, are calculated using the internal learning algorithms.
Large samples size is the pre-condition for using ANN. Sometimes,
samples from experiments are not sufficient for training and testing
models for ANN. Therefore, the ANN is recommended to cases with
available large sample size of data. Furthermore, the ANN has the ability
to combine with other intelligence algorithms such as particle swarm
optimization (PSO), simulate anneal (SA), and ant colony (AC), which
are attributed in Table 2 as the intelligence algorithms based ANN
(IANN). Via integration, the ANN can be established to meet the high
standard of accuracy demand with optimal prediction performance.
Fig. 4. Schematic algorithm flows of category and regression tree (CART) and
As aforementioned, the sampling data size is important in machine
random forest (RF).
learning approaches [52–54]. If the sample size is too small, random or
systematic errors from measurements may obscure the original regu­
larity of the research subject; any mode fit to the data will be highly
undetermined. On the other side, large sample size will incur high ex­
penses in data production, collection, and storage. Researchers are often
faced with the dilemma of finding a balance of compromise between
sample size and acquisition cost. To ease this issue, the present authors
recommend carrying out the probably approximately correct (PAC)
learning, which can test the learnability of a certain machine learning
algorithm for a specific number of samples [55,56]. The PAC learning
research ensures the realization assumption of a machine learning al­
gorithm and checks whether the sample size is sufficient through
empirical risk minimization.
The CART shown in Fig. 4 is an intuitive model that traverses the
branches of the tree and selects the next branch based on the node’s
decision. This method uses a decision tree as a predictive model and
takes a group of training data as the input variables to determine which
properties are most suitable for segmentation. It loops on the data set
after segmentation until all the training data are classified. As the name
implies, the random forest (RF) is composed of multiple CARTs, i.e., the
RF is a set of decision trees in which the input variables run on the
multiple decision trees. The CART and RF methods have a clear structure
which is easy to understand. However, the risk of overfitting limits their
Fig. 5. Schematic diagram of support vector machine (SVM). applicability.
The support vector machine (SVM) schematically sketched in Fig. 5
is a supervised learning model, which is useful for classification,
Table 2 regression analysis, and pattern recognition. The key point of the SVM
Features of different machine learning algorithms. algorithm is to establish a hyperplane of classification to maximize the
Method Advantages Disadvantages Applicability boundary edges between the positive and negative cases. The SVM is
ANN Ability to model Large samples Cases with available applicable for cases with small sample size or high-dimensional data.
complex nonlinear required and high large samples. However, its performance mainly depends on the kernel function, which
relationship and demand for should be carefully determined. The difficulty to deal with large sample
generalization. computing resource. size is another limitation of the SVM.
CART Clear structure and Easy to overfit. Cases with limited
easy to understand. computing resources.
Longo et al. [40] predicted the thermal conductivity of oxide-water
IANN Optimized network Large samples Cases with available nanofluids using the ANN with a 3-input model and a 4-input model,
structures and required and high large samples and respectively. It concluded that the goodness fit (R2) of the testing model
parameters of ANNs by demand for requiring for better with the 3-input was 0.1862, which is not a satisfactory result. The
intelligence computing resource. prediction
validity of the neural network structure and the accuracy of the ANN
algorithms. performance.
RF Ability to model Risk of overfitting Cases with limited prediction should be further verified. Toghraie et al. [43] used an ANN
complex nonlinear with high-noise computing resources. model to predict the viscosity of Ag/ethylene glycol (EG) nanofluid at
relationship; stable data. different temperatures and with various nanoparticle volume fractions,
performance; reducing taken as the input variables. The neural network structure of the ANN
risk of overfitting.
SVM Acceptable with small Sensitive to kernel Cases with small
contained -one hidden layer-. The tangent sigmoid function and purelin
samples; nonlinear function; difficult to samples. function were used as training functions for the hidden layer and output,
regression; high- deal with large respectively. The mean square error (MSE), the sum squared error (SSE),
dimensional pattern samples and the maximum error in the ANN prediction were 6.9456 × 10− 5,
recognition.
0.0030, and 0.0314, respectively. For comparison, the dynamic viscosity

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was also obtained from a correlation, in which the MSE, SSE, and Hamilton Crosser model, the feed-forward ANN model had a better
maximum errors were 0.0012, 0.0512, and 0.0858, respectively. Thus, agreement with the experimental data. Esfe et al. [42] designed a
the ANN had better accuracy than the correlation. Unfortunately, there structure of ANN including 3 input variables, 2 hidden layers, and 2
were only 42 samples used for training in the ANN; and the requirement output variables to predict the thermal conductivity and dynamic vis­
of lager sample size was not met. Hojjat et al. [41] proposed a cosity of ferromagnetic nanofluids. The maximum prediction error was
feed-forward ANN model to predict the thermal conductivity of three 2% for the thermal conductivity and 2.5% for the dynamic viscosity.
non-Newtonian nanofluids. In this ANN model, the temperature, the Several other machine learning algorithms have also been adopted to
nanoparticle concentration, and the thermal conductivity of the base predict the thermal properties of nanofluids [57–62]. From the limited
fluid were considered as the input variables. Compared with the machine learning studies in nanofluids, it seems that even a simple

Table 3
Machine learning research in nanofluid property evaluation and heat transfer characterization.
Reference Method Nanofluid Input variables Output R2 MAPE
variables

Longo et al. [40], ANN Oxide–water temperature, thermal 0.9910 0.6310

2012 volume fraction, conductivity
cluster average size,
NP thermal
conductivity
Hojjat et al. [41], ANN TiO2, Al2O3, CuO in temperature, thermal / 1.60
2011 carboxymethyl concentration conductivity
cellulose water
Esfe et al. [42], ANN, Fe/EG temperature, thermal / 2.25
2015 Correlation diameter of conductivity,
particles, volume dynamic
fraction viscosity
Toghraie et al. ANN; Ag/EG temperature, dynamic / /
[43], 2019 Correlation volume fraction viscosity
Akhgar et al. ANN; MWCNT-TiO2/ temperature, thermal / 1.845; 2.415
[44], 2019 Correlation Water-EG volume fraction conductivity
Hassan et al. ANN Molten salt temperature, mass specific heat 0.9992 /
[45], 2019 fraction, size
Hassanpour et al. ANN Al2O3-water diameter, pressure, heat transfer 0.9929 9.530
[46], 2018 weight percent, coefficient
excess temperature
Esfe et al. [47], ANN; Al2O3-MWCNT/ temperature, viscosity 0.998; 0.982 0.07; 7.30
2018 Correlation 5W50 volume fraction,
share rate
Baghban et al. ANN; CNT/water Prandtl number, Nusselt number 0.981; 0.972; 1 /
[48], 2019 ANFIS; LS- number of helical,
SVM volumetric
concentration
Kalani et al. ANN; RBF; ZnO/water ambient fluid outlet 0.98979;0.9923;0.9934/ 0.7777;0.7481;0.8110/
[49], 2017 ANFIS temperature, temperature, 0.9363;0.9906;0.9896 0.6330;0.5054;0.4882
incident radiation, electrical
fluid inlet efficiency
temperature
Ghaffarkhah CART; RF; SiO2, Al2O3, MgO, temperature, viscosity / /
et al. [50], SVM; RBF ZnO in engine oil volume fraction
2019
Esfe et al. [51], GA-RBF; LS- TiO2/SAE 50 temperature, dynamic 0.99998; 0.99991; 0.99752 /
2018 SVM; GEP volume fraction, viscosity
shear rate, base
fluid viscosity
Shahsavar et al. GMDH paraffin-Fe3O4 temperature, thermal 0.96; 0.96 /
[57], 2019 concentration, mass conductivity,
fraction dynamic
viscosity
Barati-Harooni RBF TiO2, Al2O3, SiO2, temperature, viscosity 0.99996 0.20
and Najafi- CuO in water, volume fraction,
Marghmaleki ethanol, propylene density, size
[58], 2016 glycol-water
mixture
Esfahani et al. ANFIS Ag, Cu, TiO2 in volume fraction, viscosity, 0.97722;0.99891;0.99806/ /
[59], 2017 mineral oil particles type thermal 0.98901;0.97865;0.98588
conductivity
Alrashed et al. ANFIS; ANN Diamond-COOH, temperature, thermal / 0.02744;0.162940; 0.01636;0.0842/
[60], 2018 MWCNT-COOH in volume, density, conductivity, 0.09998;0.00047;0.00096;0.0007/
water viscosity viscosity, 0.09894;0.09275;0.02877;0.04617
density
Shahsavar et al. LS-SVR; Graphene temperature, thermal / /
[61], 2019 RWLS-SVR oxide–silicon volume fraction conductivity
carbide/water
Ahmadi et al. LS-SVR; Al2O3/water temperature, thermal 0.88125;0.88393; 0.8999 /
[62], 2018 SOM; BP volume conductivity
concentration, size

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machine learning approach could match with experimental data better

than empirical correlations. Thus, machine learning would be very
useful and promising, though it is now scarcely used in the nanofluid
and renewable energy communities.
Table 3 briefly summarizes some important studies on machine
learning methods in nanofluid thermophysical property prediction and
heat transfer characterization. From the table it is seen that fluid tem­
perature, nanoparticle volume fraction, and nanoparticle size were
commonly taken as the input variables. The R2 value in most machine
learning predictions is above 0.99, though a low value of 0.876 is also
noticed in one study. The mean absolute percentage error (MAPE) varies
within the range from 0.008 to 9.53. The definition of coefficient of
determination varies in the open literature. It may include contributions
from three parts, i.e., training dataset, validation dataset, and testing
data. Here, all the R2 values are from the training data. In some cases, R2
is not sufficient to confirm the validity of the results obtained. Therefore,
other measures such as the MAPE and MSE may also be applied to
validate the predictions. In order to improve the prediction accuracy, the
neural network structure, weight coefficient, threshold coefficient,
numbers of hidden layers and neurons should be precisely designed
according to the specific requirements in a particular problem.
Certainly, the larger the size of training samples is, the more accurate the
machine learning prediction is. In general practice, however, samples
from experiments may not be sufficient for training and testing models.
In addition, ANN predictions using the toolbox of MATLAB were simple Fig. 7. Comparison between experimental data and predictions of machine
and popular, but might not be satisfactory. Instead, the present authors learning methods for viscosity of different nanofluids.
recommend machine learning integration with optimization algorithm.
To build confidence to use machine learning approaches, compari­ ethylene glycol mixture to prepare nanofluids for thermal conductivity
sons between machine learning predictions and actual values from some measurement and comparison with the dissimilar ANN predictions [44].
studies listed in Table 3 are presented in Figs. 6 and 7 for thermal 70% of the experimental data sets were used for training, 15% for test
conductivity and viscosity, respectively. Various nanofluids and and 15% for validation. It was concluded that the ANN predicted better
different machine learning methods are selected. The Al2O3, TiO2, and than the correlation formula. Both thermal conductivity and viscosity
CuO nanoparticles were dispersed into carboxymethyl cellulose aqueous were measured to understand the impacts of Fe3O4 nanoparticle volume
solution to prepare the respective nanofluids [41]. Thermal conductivity concentration and temperature in liquid paraffin based nanofluids [57].
with various nanoparticle loadings at different temperatures was Oleic acid was utilized as a surfactant for improving suspension dis­
measured. ANN models were employed to depict the thermal conduc­ persibility and stability. The GMDH type ANN was developed and its
tivity as a function of the temperature, nanoparticle concentration and predictions were compared with the experimental data. Cu, Ag, and
the thermal conductivity of the nanoparticles. MWCNT-TiO2 hybrid TiO2 nanoparticles were dispersed in mineral oil without use of surfac­
nanoparticles at a 50:50 vol ratio were dispersed into a water and tant to prepare nanofluids [59]. Their thermal conductivities and vis­
cosities were measured. The properties for MWCNT and diamond
nanofluids were also listed. The ANFIS model was utilized to predict the
thermophysical properties and to develop a comprehensive correlation.
Experiments were conducted to measure the thermal conductivity and
viscosity of diamond-COOH and MWCNT-COOH nanoparticles
dispersed in water without additives [60]. Both ANFIS and optimal ANN
models fed by 120 experimental data were applied to predict the
properties. 70% of the data were included for training and the rest 30%
were used for test. The ANN was found to provide the best fit for the
experimental data. Three machine learning approaches named as ge­
netic algorithm-radial basis function neural network (GA-RBF), gene
expression programming (GEP), and least square support vector ma­
chine (LS-SVM) were adopted to predict the viscosity of TiO2/SAE 50
nano-lubricant [51]. The non-Newtonian nanofluids have a power-law
behavior. The GA-RBF showed the best accuracy according to the
experimental data.
From Figs. 6 and 7, it is observed that the typical ANN and ANFIS
models developed by different researchers showed good prediction
performance for a wide variety of nanofluids. The maximum error be­
tween the predicted and actual values is less than 6% for the thermal
conductivity, and 5% for the viscosity. Therefore, the accuracies of
machine learning methods are acceptable for the prediction of nanofluid
physical properties. Moreover, machine learning methods are efficient
and cost-saving compared with experimental measurements. It is a
formidable task to seek universal correlations for nanofluid thermo­
Fig. 6. Comparison between experimental data and predictions by machine physical property and heat transfer assessment, although numerous
learning methods for thermal conductivity of different nanofluids.

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attempts have been made in the past. The previous studies established types of heat exchangers. To improve the heat transfer performance of
that empirical correlations are simple to use, but subjected to larger the PHEs, much attention was paid on the development of new heat
uncertainties. Through the comprehensive comparisons in Figs. 6 and 7, transfer surfaces, such as plain fin, louver fin, wavy fin, corrugated fin,
it is evident that machine learning has better accuracy than correlations perforated fin, and pin fin. Other heat transfer enhancement techniques
and is suitable for the prediction of the thermal properties of nanofluids. such as vortex generators and inserts were also considered. Nanofluids
as high-efficiency heat transfer media were evaluated and studied for the
3. Nanofluid heat transfer and machine learning in heat PHEs. In the recent five years, various nanoparticles like Al2O3 [74–76],
exchangers Ag [77–79], CuO [80], SiO [81,82], TiO2 [83], ZnO [84], and CNT [85,
86] have been demonstrated to be effective to augment the heat transfer
Heat exchanger is an indispensable device in energy systems. It im­ performance of PHEs. Attalla et al. [76] and Kumar et al. [84] investi­
proves thermal performance and augments energy efficiency. For gated the effects of heat exchanger structure and surface characteristics
example, electricity generated by wind power is much cheaper than that on nanofluid flow and heat transfer. Their results showed that, the
produced by coal and nuclear power plants [63]. Delvin et al. [64] chevron angles and surface roughness of the PHE had more significant
pointed out that wind energy was particularly important to increase the effects on the performance than the volume fraction of nanoparticles.
proportion of renewable energy in the binding European Union (EU) Kumar et al. [87] demonstrated that the geometrical parameters of
2020 targets. The performance of wind turbines has a significant effect protrusion transverse rib roughness were important to the Nusselt
on large-scale deployment of wind energy. It is necessary to obtain wind number and friction factor of nanofluid flow. In addition, the precipi­
power curves from actual wind turbines and wind farms [65]. However, tation and fouling of nanoparticles had adverse effects, which might
the wind turbines need to dissipate a large amount of heat during compensate the thermal property improvement and deteriorate the
operation. If the generated heat is not properly dissipated, it may cause a convective heat transfer performance, especially at high flow rates [81,
temperature rise in the electrical and mechanical components, leading 82]. Although the fouling resistance of MWCNT-based nanofluids was
to the reduction of overall energy efficiency. Therefore, the efficiency of found to be smaller than that of the metal oxide nanofluids, it could
the cooling system is critical for wind energy systems. Particularly reach between 0.1 and 0.3 after working for 600–700 h [85]. To ease
during the hot season, high temperature could damage the electric this concern, Sarafraz et al. [80] applied low-frequency vibration to
generator and mechanical parts of the turbine [66]. De Risi et al. [4] reduce the fouling of CuO nanoparticles in a PHE with chevron flat
proposed a cooling system to intensify heat transfer using Al2O3-water plates.
nanofluids, in which the wind turbine tower as a heat exchanger was Extensive work on the fluid flow and heat transfer performance of
used to dissipate waste heat in the environment. They found that use of nanofluids in double-pipe heat exchangers has been done both experi­
nanofluid could significantly reduce the maximum generator tempera­ mentally and numerically because the geometries of such heat ex­
ture. Alvarez-Regueiro et al. [67] claimed that the increasing size of changers are simple. In the recent five years, various nanofluids have
wind turbines up to 10 MW required sophisticated liquid cooling sys­ been explored for use in double-pipe heat exchangers, including MgO-oil
tems, and a 7% convective heat transfer coefficient enhancement was [88], Al-water [89], fly ash with metal oxides-water [90], Fe3O4-water
realized with nanoparticle loading of 0.25 wt.%. Rostamzadeh and [91,92], Ag-ethylene glycol/water [93,94], and Cu/CuO/CNT-water
Rostami [68] utilized waste heat extracted from the generator of a wind [95]. Ali et al. [88] investigated the heat transfer characteristics of
turbine to desalinate seawater and tested various nanofluids to harvest MgO-corn oil-based nanofluid in a miniature counter-flow double-pipe
more dissipated waste heat. It was found that Cu/water nanofluid could heat exchanger. Results showed that the nanofluid with 0.5 wt.% MgO at
produce more freshwater among the five nanofluids tested. 400 ml/min improved the overall heat transfer coefficient and heat
Another member in renewable and sustainable energy family is the transfer rate by 143% and 96%, respectively. Kumar et al. [92] used
geothermal energy, which is expected to develop rapidly in the near Fe3O4 nanoparticles to enhance Number of Transfer Units (NTU) and
future. It was estimated that the technical potentials for power genera­ effectiveness of water. In addition to the nanoparticle volume concen­
tion and heat production of combined heat and power production from tration, Reynolds number and friction factor were also important pa­
geothermal energy in Germany were 12.2 PWhel and 16.7 PWhth, rameters for the overall evaluation. The friction factor was found to
respectively [69]. In the Thirteenth Five-year Plan in China, the increase by 9.2% at Reynolds number of 28,970. Increasing the volume
geothermal power generation was specified as more than 500 MW. concentration and Reynolds number improved the heat transfer of
However, the development prospects are unpromising based on the Fe3O4-water nanofluid flow. Likewise, the structural characteristics of
present technologies [70]. One of the key challenges restricting the wide the tube heat exchanger were also inspected. Bahiraei et al. [93]
application of geothermal energy is the low energy conversion efficiency numerically studied Ag-EG/water nanofluid in a miniature counter-flow
[71]. The conversion efficiency could be significantly improved by double-tube heat exchanger. The inner and outer tube diameters were 1
enhancing the heat transfer between the heat carrier fluid and the mm and 2 mm, respectively. The average diameter of the Ag nano­
ground in the heat exchangers, so nanofluid could be an appropriate particles was 55 nm. The interesting fact of their result was that adding
choice as the heat carrier fluid [72]. Therefore, the heat transfer and the Ag nanoparticles reduced the pumping power while improved the
hydrodynamic performance of heat exchangers has significant effects on heat transfer.
the overall efficiency of the renewable and sustainable energy systems. Nanofluids have shown promising heat transfer enhancement in the
High-efficiency heat transfer enhancement technologies are always geothermal borehole heat exchangers [96–98]. The bore length could be
sought for in the development of heat exchangers. Utilizing a fluid with reduced by less than 1.3% using the Al2O3/water nanofluid [96]. In
better thermal properties is one of the most promising techniques for another study [97], the thermal resistance could be reduced by about
heat transfer enhancement in heat exchangers [73]. In recent years, 3.8% using the Copper-based nanofluid. Although the CuO-water
nanofluids have been examined in many kinds of heat exchangers such nanofluid had better heat transfer performance than the
as plate heat exchanger (PHE), double-pipe heat exchanger, and alumina-water nanofluid, it resulted in higher pressure loss and
shell-and-tube heat exchanger. Heat exchanger is an indispensable de­ consumed more pumping power.
vice in renewable and sustainable energy industries. Recent researches in shell-and-tube heat exchangers indicated that
nanofluids with various nanoparticles including TiO2 [99], Al2O3 [100],
3.1. Nanofluid heat transfer and pressure drop CuO [101], Ag [102], and graphene oxide [103] had better thermal
performance than their respective base fluid. For example, Ullah et al.
Since different heat exchangers have different structural character­ [99] conducted a numerical simulation to evaluate the heat transfer of
istics, it is necessary to compare the effects of nanofluid for different adding γ-Al2O3 and TiO2 nanoparticles into water under turbulent flow

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T. Ma et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx

conditions. The convective heat transfer coefficient was increased by

41.8% for the γ-Al2O3 nanofluid, and by 37% for the TiO2 nanofluid.
Said et al. [101] proposed a theoretical model and performed an
experiment to examine the performance of CuO-water nanofluid in a
shell-and-tube heat exchanger. Using the CuO-water nanofluid, the
overall heat transfer coefficient and the convective heat transfer coef­
ficient were enhanced by 7% and 11.39%, respectively. In the mean­
time, the heat transfer area was reduced by 6.81%. The above studies
showed that different nanoparticles exhibited different influences on the
performance of the three kinds of heat exchangers reviewed.
Fig. 8 compares the heat transfer coefficients of plate heat ex­
changers (PHEs) with nanofluids in different experiments with Re <
4000. Sun et al. [74] compared the performance of Cu-water, Fe2O3-­
water, and Al2O3-water nanofluids in a PHE. The average size of the
nanoparticles was 50 nm. Dispersants such as sodium dodecylbenzene
sulfonate were added to improve the stability of the nanofluids.
Increasing the nanoparticle concentration enhanced the heat transfer
coefficient. However, the resistance coefficient did not significantly in­
crease. Different nanoparticles led to different consequences. The
Cu-water nanofluid showed the highest heat transfer enhancement. Elias
et al. [75] also conducted Al2O3-water nanofluid experiments to inves­
tigate the heat transfer and pressure drop characteristics in a PHE. They
found that when the particle volume concentration or Reynolds number
Fig. 9. Nusselt numbers of double-pipe heat exchangers with nanofluids from
increased, the heat transfer coefficient and the overall heat transfer
different experiments.
coefficient as well as the heat transfer rate of the PHE increased
respectively. As shown in Fig. 8, however, the increasing pattern in Elias
number in the laminar flow regime. Their Nusselt numbers are much
et al. [75] is quite different from that in Sun et al. [74] with the same
smaller as compared with other cases in the figure. Water-based Cu,
nanofluid at the same concentration. Experiments with CuO-water
CuO, and CNT nanofluids at different volume concentrations were
nanofluid in a PHE with chevron flat plates [80] showed that fouling
evaluated mostly under laminar flow condition [95]. An increase in the
of nanoparticles could be mitigated via low-frequency vibration. The
volume concentration and Reynolds number augmented both heat
overall thermal performance of the system was also intensified when
transfer and pressure drop. For the CuO-water and Cu-water nanofluids,
vibration was continuously applied to the PHE. Fig. 8 shows that the
Nusselt number rose as the volume concentration increased; while for
CuO-water nanofluid heat transfer coefficients [80] are better than those
CNT-water, Nusselt number decreased as the volume concentration
of the Cu-water, Fe2O3-water, and Al2O3-water nanofluids [74].
increased. Anyhow, the difference of Nusselt numbers among the three
Fig. 9 compares the Nusselt numbers of double-pipe heat exchangers
different nanofluids was not big. A neural network was also applied to
with various nanofluids in a wide Reynolds number range. Both studies
predict Nusselt number and pressure gradient in terms of Reynolds
[89,92] indicated that the heat transfer enhancement and friction factor
number, volume concentration, and physical properties of particles in
of the nanofluids under turbulent flow conditions increased with the
the heat exchanger [95]. The neural network predicted the output var­
increase of volume concentration and Reynolds number. It is seen that
iables accurately.
the heat transfer enhancement magnitude for the Fe3O4-water nanofluid
From Figs. 8 and 9, it is evident that no general correlations exist for
is smaller than that for the Al2O3-water nanofluid. The base fluid for Ag
heat transfer characteristics of nanofluids in heat exchangers because
nanofluids was ethylene–glycol and water at 50:50 by volume [93]. The
the thermal performance (either heat transfer coefficient or Nusselt
three curves at different concentrations vary similarly with Reynolds
number) of the heat exchanger varies considerably, depending not only
on the thermal properties of the nanofluids (e.g., the nanoparticle pa­
rameters) but also on the flow conditions, and the geometrical and
structural parameters. It is extremely difficult and impractical to find
accurate relationships among different experimental setups and
different heat exchanger types. Comparability is lack among different
experimental works conducted by different groups even under similar
testing conditions. In such a tangled situation, machine learning could
shed a light on resolving the complexity of nanofluid flow and heat
transfer and providing practical thermal design guidance to improve the
efficiency for various types of heat exchangers.

3.2. Machine learning in heat exchangers

In the study of heat exchangers with traditional working fluid, ma­

chine learning has been widely employed. For instance, Wang et al.
[104] and Xie et al. [105,106] investigated heat transfer and friction
factor for shell-and-tube heat exchangers using the ANN. Zdaniuk et al.
[107] found that the ANN was well suited for helically finned tubes. The
ANN was compared with symbolic-regression-based correlations [108].
Wijayasekara et al. [109] selected optimal ANN architecture for per­
Fig. 8. Heat transfer coefficients of plate heat exchangers with nanofluids from formance prediction of compact heat exchangers with EBaLM-OTR
different experiments. techniques.

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Yet the thermal and hydrodynamic performance of a heat exchanger

with nanofluid is much more complicated. Machine learning would be
more beneficial in such an incomprehensible scenario, though it has not
been widely explored. Table 4 lists limited machine learning works in
the research and development of nanofluid heat exchangers. Different
nanoparticles including the Cu, CuO, CNT, iron oxide, Al2O3, and SiO2
are considered. The output variables include heat transfer coefficient,
Nusselt number, and pressure drop. The input variables include nano­
particle concentration and size, Reynolds number, Prandtl number,
thermal conductivity, viscosity, and some other important thermal
properties and geometrical parameters. Maddah et al. [114] used the
ANN model to predict the exergetic efficiency due to its ability to find
nonlinear functional patterns effectively without using extensive nu­
merical data or experimental data. The deviations between the experi­
mental data and the ANN predictions were within a reasonable range.
The ANN model was further used for the optimization process. Results
showed that the heat transfer coefficient and Nusselt number of the
nanofluids were improved, and the pressure drop was reduced as
compared with the use of base fluid. A maximum heat transfer and a
minimum pressure drop were simultaneously achieved using the ANN Fig. 10. Comparisons of heat transfer and pressure drop in nanofluid heat
model. Except for the ANN model, the GA was also considered for pre­ exchangers between experiments and predictions of various machine
learning methods.
dicting heat exchangers with nanofluids. Nasirzadehroshenin et al.
[115] utilized the trained networks with GA, in which the target func­
tion of exergy efficiency was considered when the optimization process enable broader applications of machine learning, it is paramount to
was started with the ANN model. The purpose was to maximize the establish large databases for training and learning and more rigorous
fitness value with a minimum MSE error. Results showed that there was comparisons among different machine learning methods are needed to
a strong correlation between the experimental data and the predictions find their best range of applicability.
of the ANN-GA. Safikhani et al. [110] performed multi-objective opti­
mization of Al2O3-water nanofluid parameters in flat tubes using CFD, 4. Radiative properties and machine learning in solar energy
ANN, and GA techniques. systems
Fig. 10 compares experiments and different machine learning
methods in the prediction of heat transfer and pressure drop in nanofluid As a type of developing renewable energy to resolve some current
heat exchangers. Data for heat transfer efficiency were extracted from energy and environmental issues facing human beings, solar energy has
Maddah and Ghasemi [111]. The ANN model prediction for the heat attracted increasing attention in recent years [116–118]. Conversion of
transfer efficiency has MSE of 0.002815 and R2 of 0.98537. Data of solar energy into thermal/electricity energy requires efficient heat ex­
exergetic efficiency and pressure drop from other machine learning change between the absorber and the working fluid. Compared with
works are also plotted in the figure for comparison. It is seen that the conventional working fluid, nanofluids have been utilized due to high
predictions by the ANN, ANN-GA, and ANN-LINMP agreed well with the thermal conductivity and heat capacity, better optical and radiative
experimental data in terms of heat transfer efficiency, exergetic effi­ properties, whereas avoiding sedimentation, clogging, and fouling [3].
ciency, and pressure drop, respectively. Though the machine learning Spectral tuning of nanofluids could serve dual-purpose: daylighting and
methods deviated each other, their relative deviations were in an en­ solar energy harvesting [39,119].
gineering acceptable range. The R2 value of the exergetic efficiency
predicted for CNT/CuO-water was 0.92 [115]. Hojjat et al. [113] 4.1. Optical enhancement with nanofluids
pointed out that the pressure drop value of TiO2/Al2O3-water nanofluid
predicted by the ANN-LINMP was about 12% below the experimental Solar collectors are the thermal devices that absorb solar irradiation
measurement. It should be mentioned that the machine learning results and convert it into internal thermal energy stored in and transported by
are only applicable in the respective experimental applicability. To the working fluid [120–122]. The efficiency of solar collectors is pri­
marily influenced by the absorbing process of the incident solar

Table 4
Machine learning works in heat exchangers with nanofluids.
Reference Method Nanofluid Input variable Output R2 MAPE
variable

Safikhani et al. [110], 2014 CFD/ANN/GA Al2O3-water flat tube internal height, volumetric flow rate, h, Δp 0.9741;0.9719 0.19;0.1967
wall shear stress, heat flux, axial coordinates in
tubes
Saeedan et al. [95], 2016 ANN Cu/CuO/CNT-water Re, Φ, NP properties Nu, Δp 0.9944; 0.0009;
0.9991 0.0002
Maddah et al. [111], 2017 ANN Iron oxide-water Φ,temperature, mass flow rate, twist ratio h 0.99181 0.001621
Bahiraei et al. [112], 2017 ANN/GA Cu- carboxymethy Φ, d, radius ratio h, Δp 0.999;0.999 /
cellulose-water
Hojjat et al. [113], 2020 ANN/ TiO2/Al2O3-water Re, Pr, Φ, knp Nu, Δp 0.9952;0.9992 /
LINMAP/
TOPSIS
Maddah et al. [114], 2017 ANN SiO2-water Re, Pr, Φ, twist ratio, geometrical progression exergetic 0.9779 /
ratio efficiency
Nasirzadehroshenin et al. ANN/GA CNT/CuO-water Re, Φ, twist ratios, cavity diameter ratio exergy 0.92 /
[115], 2019 efficiency

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T. Ma et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx

irradiation and the efficiency of heat transferred from the absorber to nanofluid volumetric-based collectors.
the working fluid. Nanofluids have the possibility to enhance the effi­ Hybrid PV/T devices convert sunlight into electrical and thermal
ciency of solar collectors by improving the solar irradiation absorption energy simultaneously which have a higher efficiency than a single
and heat transfer processes. In the recent two decades, utilization of photovoltaic module [142–147]. Usually, the working fluid of a PV/T
nanofluids in solar collectors as the working fluid has been widely system to absorb the heat is air or water [148]. Nowadays, nanofluid has
explored [123–129]. Tyagi et al. [130] theoretically studied the effi­ become a selectable working fluid choice for its usage of significantly
ciency of a low-temperature direct absorption solar collector (DASC) improving the overall performance of PV/T collectors without changing
using water/aluminum nanofluid and compared the performance with any structural design [149,150]. Sardarabadi et al. [151] explored the
that of a flat plate solar collector using pure water. Results showed feasibility of using SiO2-water nanofluid (1% and 3% by weight) in a
obvious augmentation of collector efficiency as the nanoparticle volume PV/T system, and found that, compared with the pure water system, the
fraction increased. Taylor et al. [131] compared a nanofluid-based thermal energy efficiency of the nanofluid system with 1 wt.% and 3 wt.
concentrating solar thermal system with a conventional one and a % was increased by 7.6% and 12.8%, respectively. Meanwhile, a PV/T
maximum of 10% efficiency promotion was reported by nanofluid system was also introduced to lower the solar electricity production cost
usage. Otanicar et al. [123] experimentally and numerically investi­ [152]. For instance, Xu et al. [153] proposed a novel dual concentration
gated the performance of a micro-scale DASC with different nanofluids PV/T system using a dilute nanofluid and declared an overall 70% ef­
containing CNT, graphite, and Ag nanoparticles, respectively. They ficiency increment through numerical modeling.
modified the Tyagi’s model by introducing the radiative transport Nanoparticles can be used as an optical filter to improve the radia­
equations coupled to the emission term in the energy equation. An tion properties of the working fluid in PV/T systems [154]. The
improvement up to 5% in the solar collector efficiency by utilizing nanofluid-based optical filter provided a better efficiency as compared
nanofluids was acquired. to a conventional optical filter, and the nanoparticles with 0.0011%
The efficiency improvement is mainly attributed to the radiation volume fraction was found to achieve optimal performance. Hjerrild
absorption enhancement effect, because the added nanoparticles are et al. [155] compared two types of nanofluid-based optical filters
capable of absorbing broad-band solar irradiation which increases the (MWCNTs and Ag-SiO2 nanodisks) for a hybrid PV/T system. It showed
solar energy harvesting. Tyagi et al. [130] proved that the absorption of that the overall efficiency increased about 30% for Ag-SiO2 nanofluid
incident solar energy could be increased by nine times using a small with 0.026% weight fraction as compared to that of the base fluid optical
amount of Al nanoparticles as compared with pure water. Taylor et al. filter. An et al. [156] experimentally investigated a concentrating PV/T
[124] investigated the optical properties of various nanofluids for usage collector with nanofluid-based optical filter. The Cu9S5 nanofluid was
in DASCs. They concluded that the nanoparticles with a reasonable applied as the optical filter to absorb the remaining heat at
volume fraction and thickness could absorb over 95% inlet sunlight. moderate-temperature levels and an overall 17.9% efficiency enhance­
Kameya and Hanamura [132] tested the radiation absorption properties ment had been obtained. Hassani et al. [157] analyzed the exergy and
of Ni nanoparticle suspension and found that the absorptivity of the environmental impact of using CNT− water nanofluid based optical filter
nanofluid increased drastically for the solar spectrum in the visible or in a PV/T hybrid system. Results showed that exergy increased
near-infrared wavelength ranges. Han et al. [133] and Saidur et al. [134] approximately 1.3 MWh/m2 per year and CO2 emissions of the PV/T
investigated the absorption coefficient of the carbon black-water and system reduced about 448 kg CO2 eq/(m2⋅yr). They also proposed a
Al-water nanofluids for solar collectors, respectively. Their results cascading nanofluid-based PV/T system with two separate channels
exhibited excellent potentiality of nanofluid usage in solar systems and [158], which enhanced electrical efficiency for the Si and GaAs PV cells
declared that the nanoparticle size should be under certain value in by 5.6% and 9%, and overall system efficiency by 4.5% and 5.8%,
order to benefit Rayleigh distribution (i.e., < 20 nm). Otanicar et al. respectively.
[123] and Said et al. [135] studied the photon thermal conversion It should be pointed out that the optical and radiative properties of a
process of the DASC utilizing different nanoparticles. They found that nanofluid are strongly affected by nanoparticles agglomeration and
nanoparticle type and size had significant influences on the optical sedimentation; and thus, the stability of nanofluids is critical. The issues
properties of the solar absorber, especially for the absorbance and on suspension stability, preparation, characterization, and their in­
transmissivity of the solar interception medium. Recently, Cai et al. [39] fluences on thermophysical properties, mainly thermal conductivity and
found that a dilute 0.00004 vol% Ni-water nanofluid in a glass louver viscosity, have been extensively reviewed previously [16,159,160].
could transmit 46.5% solar visible light for daylighting and harvest Nevertheless, studies on the optical effects of agglomeration and sedi­
65.7% of the total solar energy, which was a 25.9% increase as mentation are seldom.
compared to the use of pure water. According to Mie theory, the radiation absorption and scattering of
Researchers also found that better optical properties could be small particles are governed by three independent nondimensional pa­
attained in volumetric solar absorption structures [136]. Veeraragavan rameters, i.e., complex index of refraction, size parameter, and
et al. [137] promoted an analytical model for volumetric solar receivers. clearance-to-wavelength ratio. It is established that when the clearance
The thermal conversion efficiency was improved by decreasing the ratio is greater than 0.5, or the particle volume fraction is less than 0.6%,
temperature difference between the absorber and working medium. radiation scattering is independent, i.e., clearance is not important and
Lenert and Wang [138] examined the efficiency promotion effect of the the optical properties of the particles are dependent on the former two
nanofluid volumetric solar flow receivers using a 1-D transient heat parameters. Agglomeration and sedimentation will form large clusters
transfer model and experimentally investigated the influence of [32,34,159], i.e., increasing the size parameter and reducing the num­
different variations in the carbon-coated cobalt nanofluid volumetric ber of particles per unit volume. For low concentration nanofluids, the
receivers. Taylor et al. [139] investigated the possibility of volumetric optical properties variation due to the growth of size parameter and
absorption of three absorbing media (i.e., black dyes, black painted reduction of particle numbers resulted from agglomeration and sedi­
surfaces, and nanofluids) for direct steam collector employing laser light mentation should be understood for nanofluid solar and optical appli­
as the radiation source. Their experimental results indicated that cations. Recently, Al-Gebory and Mengüç [161] and Al-Gebory et al.
applying nanofluid enhanced the volumetric absorption and lower [162] showed important effects of pH on particle agglomeration and the
temperature was obtained for nanofluids although the vapor generation nanoparticle agglomerates on the optical properties and photo-thermal
was enhanced up to 50%. Kandasamy et al. [140,141] investigated the energy conversion. A recent review concerned about the particle
Hiemenz flow of Cu-nanofluid over a porous wedge plate which accrued agglomeration and sedimentation behaviors and the long-term stability
in the solar radiation absorption and transformation process and of nanoparticles, which may restrict their potential reliable applications
concluded that the thermal resistance was intensely decreased for [163].

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T. Ma et al. Renewable and Sustainable Energy Reviews xxx (xxxx) xxx

For nanoparticles whose size is much smaller than the incident solar
wavelength, the Rayleigh scattering theory can be used to predict the
optical absorption and scattering. Under general spherical particles
assumption, the Mie theory can be employed for the calculation of ra­
diation properties of particles and particle agglomerates as long as the
agglomerates are not much larger than the wavelength. The discrete
dipole approximation (DDA) is a useful method for computing light
scattering by particles of arbitrary shape and by periodic structures. It is
suitable for calculating the optical properties of arbitrary nanoparticle
agglomerates. Du and Tang [164] proposed a theoretical approach for
calculating the extinction coefficients of nanofluids with particle
agglomeration based on diffusion-limited cluster agglomeration simu­
lation and generalized multi-particle Mie solution method. Their results
showed that the particle agglomeration reduced the absorption peak in
the short-wavelength and enhanced the long-wavelength scattering in Fig. 11. Block diagram of proposed ANN and PSO hybrid technique used for a
the solar spectrum; and the agglomeration had led to a higher perfor­ photovoltaic thermal nanofluid based collector [49].
mance in solar energy harvest. Cai et al. [39] found that the absorption
efficiency of the Ni-water nanofluid increased with increasing particle system.
size, implying enhancement of solar energy absorption with the forming Al-Waeli et al. [177–180] conducted a series of research on the
of larger clusters. performance of PV/T systems using the MLP ANN. Fig. 12 presents the
experimentally measured and ANN output results of thermal efficiency
4.2. Machine learning in solar energy systems for three PV/T models under the same working conditions and envi­
ronment [179]. In the figure, WATER stands for a PV/T system supplied
The afore subsection establishes that addition of nanoparticles in with cooling tank filled with water and the cooling fluid is water; PCM
working fluid significantly improves the thermal-optical performance of represents a PV/T system supplied by a tank filled with paraffin wax (an
solar collectors or PV/T systems [3,24,165,166], though concerns organic PCM) and the cooling fluid is water; and NANO stands for a
remain with particle agglomeration and sedimentation, and suspension PV/T system supplied by a tank filled with PCM and nano-SiC and the
stability. Utilization of nanofluids usually leads to the increment of cooling fluid is SiC-water nanofluid. The comparison between the ex­
viscosity and pressure drop penalty. To enable system design, numerous periments and the ANN outputs proved that the NANO system had the
experimental and numerical studies have been performed to understand highest efficiency. Utilizing nanofluid and nano-PCM enhanced the
the effects of different operating parameters. Experimental studies are electrical efficiency from 8.07% to 13.32% and promoted the thermal
constrained by cost, time, and operation conditions. On the other hand, efficiency to 72%. The predictions of the ANN were consistent with the
analysis is a prediction with many simplified assumptions. Previous experimental results.
studies reported potential advantages of machine learning methods, The available machine learning works in solar energy systems with
such as high accuracy, generalization capabilities, and less nanofluids are listed in Table 5. In summary, machine learning methods
time-consuming. Machine learning also avoids tackling complicated have demonstrated superior ability for optimizing system design and
mathematical and physical models [167]. It has been employed for operation parameters in solar energy systems. They have good accuracy
modeling and optimizing nanofluid-based solar collectors [168–174]. in predicting the performance of different solar collectors and PV/T
The ANN and GA are the two most adopted methods. For instance, de systems.
Risi et al. [168] proposed a GA optimization method for an innovative
solar transparent parabolic through collector operated with a gas-phase 5. Conclusions and prospects
nanofluid. Results revealed the highest heat transfer efficiency of 62.5%
with nanoparticle volume fraction of 0.3% and outlet temperature at Various machine learning methods have been utilized for evaluating
650 ◦ C. Sadeghi et al. [174] investigated the energy and exergy effi­ thermophysical properties of nanofluids, thermal performance of
ciencies of an evacuated tube solar collector using Cu2O-water nano­ nanofluid heat exchangers, and thermal, optical, and radiative perfor­
fluid. The multi-layer perceptron (MLP) and radial basis function (RBF) mance of nanofluids in solar energy systems. This review focuses on
models of ANNs had been developed and compared. Results showed that literature overview to reveal recent trends of machine learning research
the MLP model was more accurate than the RBF model. in nanofluids and assessment of the features and applicability of
Though the ANN, GA, PSO, SA, fuzzy logic, and hybrid approaches different machine learning approaches for nanofluids in heat exchangers
have all been applied to analyze and design solar energy systems [175],
only a few studies have involved in nanofluids [176]. Kalani et al. [49]
presented an ANN and PSO hybrid approach to identify the relationship
of input/output parameters and to optimize the structure of a PV/T
nanofluid based collector at the system level. A block diagram of the
proposed technique in Kalani et al. [49] is displayed in Fig. 11. The PSO
was used to find the best reference value for the prediction process. The
MLP and RBF ANN and ANFIS sought for the best mapping function to
predict the targets based on the schematic provided by the PSO. The
optimized parameters were obtained separately for each approach. After
the neural network was optimized, evaluation using root mean square
error, variance and mean absolute percentage error was performed to
validate the trained model. The model was trained by 130 points from
experiments. Validation was conducted with 13 points of a different
experimental condition. The input variables included the ambient tem­
perature, incident radiation, and fluid inlet temperature. The output Fig. 12. Thermal efficiency of nanofluid and nano-PCM based PV/T systems
variables were fluid outlet temperature and electrical efficiency of the predicted using the ANN [179].

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Table 5
Machine learning works in solar energy systems with nanofluids.
Reference Method Application Nanofluid Input variable Output variable R2

Tomy et al. [172], ANN Solar Silver/Water Inlet temperature, heat flux, mass flow rate Outlet temperature, heat /
2016 Collector transfer coefficient,
efficiency
Ebrahimi-Moghadam ANN Solar Al2O3-EG/ T, Re, dp Optimal volume fraction 0.9992
et al. [116], 2018 Collector water
Delfani et al. [173], ANN Solar graphene Collector depth and length, working fluid Collector efficiency, Nu 0.99828, 0.99814
2019 Collector oxide/water flowrate and concentration, reduced
temperature difference
Kalani et al. [49], ANN PV/T system ZnO-water Ambient temperature, incident radiation, Outlet temperature, 0.9934;
2017 fluid inlet temperature electrical efficiency 0.9906
Al-Waeli et al. [178], MLP/ PV/T system SiC-water/ Solar radiation, PV/T_ cell temperature, Current, electrical 0.74308;
2018 SOFM/ paraffin wax efficiency 0.94753;
SVM 0.99662
Al-Waeli et al. [179], ANN PV/T system SiC-paraffin Solar irradiation, ambient temperature, Current, voltage, electrical
2019 wax efficiency, thermal 0.842;0.652;0.633;0.972
efficiency
Al-Waeli et al. [180], MLP/ PV/T system SiC-water/ Solar irradiance, ambient temperature Power 0.9562
2020 SOFM paraffin wax

and renewable energy systems. Many influential factors together with radiation scattering by agglomerates of arbitrary shape. Absorp­
their nonlinear effects complicate nanofluid research to a new altitude tion efficiency of the Ni-water nanofluid increases with
and restrict its practical potentials although thousands of archival pa­ increasing particle size in the solar spectrum, implying
pers publish yearly in this field. Noticeably, the powerful artificial in­ enhancement of solar energy absorption with forming of rela­
telligence has scarcely been applied to these complex problems. tively larger clusters. The spectral property of particles is useful
Nonetheless, machine learning could be very useful and cost-effective in for tuning and filtering of solar light.
nanofluid research to enable potential reliable practice in heat ex­ (4) Nanofluids are widely considered for use in solar collectors, and
changers, solar collectors, PV/T systems, etc. This review also notices PV/T systems, owing to their high thermal conductivity and
that traditional issues with nanoparticle agglomeration and sedimenta­ better optical characteristics. Machine learning methods, such as
tion have been extended to the optical and radiative aspects of nano­ the ANNs and ANN-based hybrid approaches, could give a more
fluids. Some concluding remarks can be drafted as follows: accurate prediction of the energy system performance, and
optimize the working conditions and structures.
(1) Many factors affect the thermophysical properties of nanofluids. (5) The ANN prediction using the toolbox of MATLAB is simple and
It is extremely difficult and impractical to measure the thermo­ popular, but may not be always satisfactory. The ANN integrated
physical properties for all kinds of nanofluids in wide parametric with other intelligence algorithms such as PSO, SA, and AC,
ranges and flow conditions. Theoretical analyses and empirical would improve the prediction accuracy. Carrying out the prob­
correlations are subjected to large uncertainties due to simplified ably approximately correct (PAC) learning can test the learn­
assumptions. Much work has demonstrated that machine ability of a certain machine learning algorithm when the number
learning methods including the ANN could give excellent pre­ of samples is limited. The PAC learning with empirical risk
diction of nanofluid properties. The input variables could include minimization justifies whether the sample size is sufficient.
temperature, pressure, nanoparticle type, size, shape and con­
centration, base fluid type, flow conditions, etc. The output var­ Although the machine learning methods have shown promising po­
iables, such as thermal conductivity, dynamic viscosity, specific tential and capability in nanofluid heat transfer research, thermal and
heat, and radiative absorption could be exported by using the hydrodynamic evaluation of heat exchangers, and assessment and
internal algorithms. optimization of energy systems, the following important issues and
(2) Nanofluids could improve the heat transfer of heat exchangers challenges remain to be resolved:
used in various energy systems, including renewable solar, wind,
and geothermal energy. Unlike pure fluids, the effects of structure (1) The predicted results obtained by the machine learning models
and surface characteristics of heat exchangers on the heat transfer are only applicable in their own experimental range. To enable
and pressure drop of a nanofluid are more significant. Different broader applications of machine learning models, it is necessary
nanoparticles exhibit different effects on the performance of the to establish large databases for the thermophysical properties of
PHEs, double-pipe heat exchangers, and shell-and-tube heat ex­ various nanofluids, for the thermal performance of various heat
changers. There is no general and universal correlation for the exchangers, and for the optical and radiative performance of
heat transfer of nanofluid in the heat exchangers. Machine nanofluids in the solar spectrum.
learning methods, such as the ANN, ANN-GA, and ANN-LINMP, (2) The ANN and ANN-based hybrid approaches could give an ac­
could provide good predictions for the heat transfer efficiency, curate prediction for the covered topics in this review. However,
exergy efficiency, and pressure drop of heat exchangers. The the relative errors of the machine learning methods are difficult
sedimentation, precipitation, and fouling of nanoparticles have to determine. It has been unknown yet which machine learning
adverse effects in heat exchangers. Applying low-frequency vi­ method is the best for a specific issue. Hence, more rigorous
bration to mitigate the fouling of nanoparticles in a PHE has comparisons of different machine learning methods are needed to
provided a potential solution. establish their best range of applicability.
(3) Nanoparticles agglomeration in a suspension will form large (3) Besides prediction accuracy, the data volume is also significant
clusters and thus increase the size parameter and reduce the in­ for machine learning methods. Unfortunately, little attention has
dividual particle number per unit volume. These will alter the been paid on the data volume issue yet.
optical and radiative properties of the nanofluids. The discrete (4) Machine learning methods for performance prediction and design
dipole approximation would be a useful tool for calculating optimization in the energy system levels are rare and needed.

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