Thermophysical Properties of Hybrid Nanofluids and the Proposed Models: An Updated Comprehensive Study

Thermal performance of energy conversion systems is one of the most important goals to improve the system’s efficiency. Such thermal performance is strongly dependent on the thermophysical features of the applied fluids used in energy conversion systems. Thermal conductivity, specific heat in addition to dynamic viscosity are the properties that dramatically affect heat transfer characteristics. These features of hybrid nanofluids, as promising heat transfer fluids, are influenced by different constituents, including volume fraction, size of solid parts and temperature. In this article, the mentioned features of the nanofluids with hybrid nanostructures and the proposed models for these properties are reviewed. It is concluded that the increase in the volume fraction of solids causes improvement in thermal conductivity and dynamic viscosity, while the trend of variations in the specific heat depends on the base fluid. In addition, the increase in temperature increases the thermal conductivity while it decreases the dynamic viscosity. Moreover, as stated by the reviewed works, different approaches have applicability for modeling these properties with high accuracy, while intelligent algorithms, including artificial neural networks, are able to reach a higher precision compared with the correlations. In addition to the used method, some other factors, such as the model architecture, influence the reliability and exactness of the proposed models.


Introduction
The heat transfer capacity of single-phase fluids, including water, oil and ethylene glycol, is relatively poor due to their low thermal conductivity. Since the intensification of heat transfer in industries and power plants is very important from both technical and economic points of view, a new generation of fluids with solid nanostructures has been recently applied. These fluids, known as nanofluids, are made of a base fluid and suspended solid particles, sheets or tubes in nano dimensions [1]. There are different approaches for the preparation of nanofluids. Physical methods, such as ball milling and ultrasonication, in addition to chemical processes, such as functionalization, are among the main approaches used for the preparation of nanofluids [2]. Metal oxide particles, such as CuO, Al 2 O 3 , TiO 2 in addition to the carbonic materials, including Carbon Nano Tubes (CNTs), graphene and graphite, are among the most commonly used nanostructures in the nanofluids that are applied as heat transfer fluids [3,4]. By applying functionalization, it would be possible to modify some properties of CNTs, such as solubility, that makes them more dispersible in the base fluid [2]. The dispersion of solid materials with nanometer • Which factors affect the thermophysical properties of the hybrid nanofluids? • How do the influential factors affect the properties of hybrid nanofluids? • How can we model and forecast the thermophysical properties of hybrid nanofluids? • Which factors influence the accuracy of the models used for the properties of the hybrid nanofluids? • How can we improve the exactness of the proposed models?

Thermal Conductivity
Thermal conductivity (TC) of the fluids plays a crucial role in their heat transfer ability; in this regard, it is desirable to utilize fluids with higher thermal conductivity. The dispersion of hybrid solids in nanometer dimensions can notably improve the TC owing to the Brownian motion, intermolecular interaction of the nanostructures, higher TC of solids compared with the liquids and clustering of the nanostructures [24][25][26][27][28]. The enhancement rate of hybrid nanofluid TC depends on some factors, such as the temperature and volume fraction (VF) [29][30][31][32][33][34]. For instance, Esfe et al. [35] measured the TC of a hybrid nanofluid composed of SiO 2 -MWCNT and ethylene glycol (EG) at different temperatures and VFs of the solid phase. They found that the increase in the temperature and solid VF caused an increase in the thermal conductivity ratio (TCR). They found that in the considered Nanomaterials 2021, 11, 3084 4 of 25 ranges of VF (0.05-1.95%) and temperature  • C), the highest value of the increase in TCR was 22.2%, as shown in Figure 1. The increase in the TC with temperature is mainly attributed to the Brownian motions of the nanostructures, while increases in the TC with VF are mainly due to higher TC of the solid materials compared with the base fluids. In another work [36], the influences of temperature and VF on the TC of WO 3 -MWCNT/engine oil were investigated. The ranges of VF and temperature were 0.05-0.6% and 20-60 • C, respectively. It was found that despite the increase in the TC by increasing VF and temperature, the effect of VF was more notable. The highest enhancement in the TC of the investigated hybrid nanofluid was 19.85% compared with the base fluid that was obtained at the highest temperature and VF. Higher enhancement in the TC of hybrid nanofluids has been observed by using other nanostructures. Utilizing hybrid material containing carbonic-based materials, such as graphene, graphite and CNTs, can lead to significant enhancement in the TC. As an example, Kazemi et al. [37] measured the TC of graphene-SiO 2 /water in various conditions. As shown in Figure 2, it was observed that around 36% enhancement in TC was reachable at 50 • C and VF of 1%. Esfe et al. [38] measured TC of SiO 2 -DWCNT/EG in various temperature and VF ranges of 30-50 • C and 0.03-1.71%, respectively. The highest improvement in the TC of nanofluid compared with EG as the base fluid was 38%. In another study, Pourrajab et al. [39] found that the existence of 0.04% vol and 0.16% vol MWCNT in water could improve the TC by up to 47.3% compared with water as the base fluid. Trinh et al. [40] measured the TC of Gr-CNT/EG nanofluid at different temperatures and observed that it was enhanced by 50% at 50 • C in solid VF of 0.07%. Nanomaterials 2021, 11, x FOR PEER REVIEW 4 of 26 and volume fraction (VF) [29][30][31][32][33][34]. For instance, Esfe et al. [35] measured the TC of a hybrid nanofluid composed of SiO2-MWCNT and ethylene glycol (EG) at different temperatures and VFs of the solid phase. They found that the increase in the temperature and solid VF caused an increase in the thermal conductivity ratio (TCR). They found that in the considered ranges of VF (0.05-1.95%) and temperature (30-50 °C ), the highest value of the increase in TCR was 22.2%, as shown in Figure 1. The increase in the TC with temperature is mainly attributed to the Brownian motions of the nanostructures, while increases in the TC with VF are mainly due to higher TC of the solid materials compared with the base fluids. In another work [36], the influences of temperature and VF on the TC of WO3-MWCNT/engine oil were investigated. The ranges of VF and temperature were 0.05-0.6% and 20-60 °C, respectively. It was found that despite the increase in the TC by increasing VF and temperature, the effect of VF was more notable. The highest enhancement in the TC of the investigated hybrid nanofluid was 19.85% compared with the base fluid that was obtained at the highest temperature and VF. Higher enhancement in the TC of hybrid nanofluids has been observed by using other nanostructures. Utilizing hybrid material containing carbonic-based materials, such as graphene, graphite and CNTs, can lead to significant enhancement in the TC. As an example, Kazemi et al. [37] measured the TC of graphene-SiO2/water in various conditions. As shown in Figure 2, it was observed that around 36% enhancement in TC was reachable at 50 °C and VF of 1%. Esfe et al. [38] measured TC of SiO2-DWCNT/EG in various temperature and VF ranges of 30-50 °C and 0.03-1.71%, respectively. The highest improvement in the TC of nanofluid compared with EG as the base fluid was 38%. In another study, Pourrajab et al. [39] found that the existence of 0.04% vol and 0.16% vol MWCNT in water could improve the TC by up to 47.3% compared with water as the base fluid. Trinh et al. [40] measured the TC of Gr-CNT/EG nanofluid at different temperatures and observed that it was enhanced by 50% at 50 °C in solid VF of 0.07%. Aside from the temperature and VF of solid parts, other factors are involved in the TC enhancement of hybrid nanofluids. As an example, Dalkılıç et al. [41] measured the TC of CNT-SiO 2 /water nanofluid under different conditions. In addition to the temperature and VF of nanostructures, the mass ratio of solid structures was varied to investigate its effect on TC. It was noticed that the highest enhancement of TC obtained for VF of 1%, and mass ratio of 0.8 CNT and 0.2 SiO 2 and was equal to 26.29%, while the minimum enhancement was noticed for 0.1% VF and 0.2 CNT and 0.8 SiO 2 that was equal to 0.78%. In another work, impacts of other variables, such as sonication duration and surfactant on the TC of a hybrid CeO 2 -MWCNT/water nanofluid, were investigated by Tiwari et al. [42]. They found that there was an optimal sonication time to reach the maximum TCR. Furthermore, they noticed that the surfactant could influence the TC, as shown in Figure 3. The mixture ratio, indicating the ratio of the nanomaterials in the hybrid nanofluids, can remarkably influence the thermophysical properties. Different mixture ratios, depending on the properties of each nanomaterial, can affect the TC of hybrid nanofluids. For instance, Osho et al. [43] considered mixture ratios in addition to VF and temperature in measuring the TC of a hybrid nanofluid. The mixture ratios of the nanostructure composed of both Al 2 O 3 and ZnO were 1:2, 1:1 and 2:1. The maximum improvement in the TC was observed for a mixture ratio of 2:1 (Al 2 O 3 :ZnO), which was equal to 40% for a VF of 1.67%. Aside from the temperature and VF of solid parts, other factors are involved in the TC enhancement of hybrid nanofluids. As an example, Dalkılıç et al. [41] measured the TC of CNT-SiO2/water nanofluid under different conditions. In addition to the temperature and VF of nanostructures, the mass ratio of solid structures was varied to investigate its effect on TC. It was noticed that the highest enhancement of TC obtained for VF of 1%, and mass ratio of 0.8 CNT and 0.2 SiO2 and was equal to 26.29%, while the minimum enhancement was noticed for 0.1% VF and 0.2 CNT and 0.8 SiO2 that was equal to 0.78%. In another work, impacts of other variables, such as sonication duration and surfactant on the TC of a hybrid CeO2-MWCNT/water nanofluid, were investigated by Tiwari et al. [42]. They found that there was an optimal sonication time to reach the maximum TCR. Furthermore, they noticed that the surfactant could influence the TC, as shown in Figure 3. The mixture ratio, indicating the ratio of the nanomaterials in the hybrid nanofluids, can remarkably influence the thermophysical properties. Different mixture ratios, depending on the properties of each nanomaterial, can affect the TC of hybrid nanofluids. For instance, Osho et al. [43] considered mixture ratios in addition to VF and temperature in measuring the TC of a hybrid nanofluid. The mixture ratios of the nanostructure composed of both Al2O3 and ZnO were 1:2, 1:1 and 2:1. The maximum improvement in the TC was observed for a mixture ratio of 2:1 (Al2O3:ZnO), which was equal to 40% for a VF of 1.67%.   Aside from the single base fluid, a solution of two or more fluids could be applied as the base fluid of hybrid nanofluids [44][45][46][47]. The dispersion of hybrid nanostructures in these types of fluids leads to TC enhancement [48]. Esfe et al. [49] assessed the influences of both concentration and temperature on the TC of a hybrid nanofluid composed of Single-Walled Carbon Nanotube (SWCNT)-ZnO and EG-water as the base fluid. Similar to the hybrid nanofluids with a single base fluid, they found that TCR increased by increases of the temperature and VF of solid structures, as shown in Figure 4. In addition, according to the sensitivity analysis, it was deduced that the sensitivity of TC enhancement was more remarkable to VF compared with the temperature. In another work [50], the TC of a Aside from the single base fluid, a solution of two or more fluids could be applied as the base fluid of hybrid nanofluids [44][45][46][47]. The dispersion of hybrid nanostructures in these types of fluids leads to TC enhancement [48]. Esfe et al. [49] assessed the influences of both concentration and temperature on the TC of a hybrid nanofluid composed of Single-Walled Carbon Nanotube (SWCNT)-ZnO and EG-water as the base fluid. Similar to the hybrid nanofluids with a single base fluid, they found that TCR increased by increases of the temperature and VF of solid structures, as shown in Figure 4. In addition, according to the sensitivity analysis, it was deduced that the sensitivity of TC enhancement was more remarkable to VF compared with the temperature. In another work [50], the TC of a nanofluid composed of SiO 2 -TiO 2 nanostructures in water-EG was investigated. It was noticed that TCR had higher values in cases of increasing both temperature and solid fraction, and its value could exceed 1.2 at the highest VF and temperature, as shown in Figure 5. In another work [51], the TC of antifreeze-based nanofluid (Go-CuO/EGwater) was measured under different conditions by varying the temperature and VF of solids. Similar to the previously mentioned works, they found that TCR increased by increasing the VF and temperature. In the maximum considered temperature and VF, 50 • C and 1.6%, respectively, the TCR exceeded 1.4. In another research carried out by Esfe et al. [52], the TC of MWCNT-MgO/water-EG nanofluid was investigated in the temperature and concentration ranges of 30-50 • C and 0.015-0.96%, respectively. Despite the low concentrations of the nanostructures, around a 22% improvement in the TC was observed at the maximum temperature and concentration. This noticeable enhancement in the TC by adding the hybrid nanostructures is mainly due to the higher TC of the solid phase compared with the binary base fluid.     Hybrid nanofluids are not restricted to the ones containing two dissimilar materials. Cakmak et al. [53] prepared a hybrid nanofluid composed of three materials as nanostructures, including reduced graphene oxide (rGO), Fe 3 O 4 and TiO 2 and EG as the base fluid. The ranges of concentrations and temperatures considered in their study were 0.01-0.25% mass and 25-60 • C, respectively. An improvement of 13.3% in the TC at temperature and concentration of 60 • C and 0.25% wt was observed compared with EG. In another work [54], the TC of a ternary hybrid nanofluid, MWCNT-TiO 2 -ZnO/water-EG, was measured in temperature and VF ranges of 25-50 • C and 0.1-0.4%, respectively. At the maximum temperature and VF, the TC enhancement was around 10%. In Table 1, the works on the hybrid nanofluids' TC are summarized.  Hybrid nanofluids are not restricted to the ones containing two dissimilar materials. Cakmak et al. [53] prepared a hybrid nanofluid composed of three materials as nanostructures, including reduced graphene oxide (rGO), Fe3O4 and TiO2 and EG as the base fluid. The ranges of concentrations and temperatures considered in their study were 0.01-0.25% mass and 25-60 °C, respectively. An improvement of 13.3% in the TC at temperature and concentration of 60 °C and 0.25% wt was observed compared with EG. In another work [54], the TC of a ternary hybrid nanofluid, MWCNT-TiO2-ZnO/water-EG, was measured in temperature and VF ranges of 25-50 °C and 0.1-0.4%, respectively. At the maximum temperature and VF, the TC enhancement was around 10%. In Table 1, the works on the hybrid nanofluids' TC are summarized.

Proposed Models for Thermal Conductivity
Different techniques are employable to estimate the characteristics of hybrid nanofluids. In several studies, mathematical correlations have been used to estimate hybrid nanofluids' TC with relatively high precision and reliability. Taherialekouhi et al. [29] proposed a correlation based on the VF of hybrid structures and temperature to model the TCR of a hybrid nanofluid composed of GO-Al 2 O 3 and water. The ranges of concentration and temperature were 0.1-1% and 25-50 • C, respectively. The highest deviation of the model was 1.598%, showing remarkable accuracy. In another work, the TCR of CNT-SiO 2 /water nanofluid in different temperatures, concentrations and mass fractions of solid materials were modeled by considering all of these variables. The maximum deviation of their model, based on the correlation, was 8.3%. In another research, Esfe et al. [34] applied a correlation for the TCR of EG-based nanofluid containing SWCNT-MgO nanostructures with an R-squared value of around 0.993.
Despite the advantage of correlation in terms of simplicity to use, the exactness of these models is relatively lower compared with the models based on intelligent techniques, including artificial neural networks (ANNs). By using artificial intelligent methods, models with improved exactness can be developed due to the more complex structure of these networks. These models are generally developed on the basis of simulating the processes of human intelligence by machines. Models based on artificial intelligence are applicable for different purposes related to nanofluids. By these methods, it is possible to model the heat transfer of nanofluidic flows, the performance of the systems utilizing nanofluids and the properties of the fluids containing nanomaterials. In modeling with intelligent methods, it is crucial to consider some factors, including the architecture of the model, input and functions, to reach the outputs with the highest possible accuracy.
Esfe et al. [35] evaluated the performance of a correlation and ANN in modeling the TCR of SiO 2 -MWCNT/EG and observed that the R-squared of the indicated models were equal to 0.9864 and 0.9981, respectively. In another work [49], correlation and ANN were compared in modeling the TCR of SWCNT-ZnO/EG-water. The obtained values of R-squared for the mentioned models were 0.9918 and 0.9972, respectively. Efficiency of the ANNs in modeling is dependent on different elements, such as applied function and the network architecture. In this regard, to propose an ANN-based model with the highest accuracy in predicting the TC of hybrid nanofluids, testing different architectures and functions would be useful. In a work performed by Vafaei et al. [57], 6, 8, 10 and 12 neurons were tested in the hidden layer (HL) of the applied network proposed for TC modeling of MgO-MWCNT/EG nanofluid. They found that using 12 neurons led to a minimum error, and the predicted data were nearer to the corresponding experimental quantities in comparison with the networks with other numbers of neurons. Aside from the number of neurons, applied functions and the number of HL influence the exactness and performance of ANN-based models. Safaei et al. [58] tested different architectures to find the best network for modeling the TC of ZnO-TiO 2 /EG nanofluid. They found that the most accurate model was obtained using 2 HLs with six and five neurons in the first and second layers, respectively, where the transfer functions in these layers were tan-sig and log-sig, respectively. In addition to the architecture, applied optimization methods in the ANN-based models affect the exactness of the models. Alarifi et al. [59] applied two optimization approaches, GA and PSO, in the models based on ANFIS used for TC of Al 2 O 3 -MWCNT/oil. They found that employing the ANFIS-PSO model led to a lower value of the mean square error compared with ANFIS-GA, which means that by using the PSO algorithm as the optimization approach, the hyperparameters of the models, which significantly affect the error of the predicted values, could be obtained more properly.
Similar to the hybrid nanofluids with a single base fluid, several models have been proposed for the hybrid ones with base fluids composed of two or more fluids. As an example, Nabil et al. [50] proposed a correlation to model TCR of SiO 2 -TiO 2 /EG-water. The highest value of deviation between the obtained data by correlation and experimental measurement was around 4.6%, showing acceptable exactness of the correlation. In another work, Kakavandi et al. [44] proposed a correlation for the TC modeling of MWCNT-SiC/water EG with a maximum deviation of 1.58%. Rostami et al. [51] applied both correlation and ANN to model the TCR of a hybrid nanofluid composed of binary base fluid (Go-CuO/EG-water). They found that applying ANN led to closer prediction to the experimental values, as was expected, due to its more complex structure and estimation procedures compared with the correlation. In a work done by Akhgar et al. [24], correlation and ANN with different numbers of neurons in HL in range the of 6-31 were tested for modeling the TC of MWCNT-TiO 2 /water-EG nanofluid by considering temperature and VF in the inputs. They found that utilizing eight neurons in the HL led to the network with the highest accuracy, with the maximum error of 2.1%, while the highest error in the case of applying the correlation was 2.72%. In another research [48], the TC of Cu-TiO 2 /water-EG nanofluid was modeled by applying different architectures of ANN. One and two HLs were tested with the 1 to 10 neurons in each layer. They observed that using two layers with five neurons in each one resulted in the highest exactness, with an MSE of 2.62 × 10 −5 .
Since the utilization of more hidden layers enables the network to model the complex systems with higher accuracy, this finding was expected; however, in the case of using more hidden layers, the possibility of overfitting is increased.
There are some models that are applicable for more than one nanofluid. In these cases, it is necessary to consider more inputs compared with the models used for a single case of hybrid nanofluids. In a study by Pourrajab et al. [60], different methods were used to propose models for the TC of hybrid nanofluids with water, EG and the mixture of water and EG as the base fluids. In their work, Locally Weighted Linear Regression (LWLR), Linear Genetic Programming (LGP), Gene Expression Programming (GEP) and some empirical correlations were used for comparison. Aside from temperature and VF, which are commonly used in other studies, the density of materials, their mean size and TC and mixture ratio of water and EG were used as inputs. Root Mean Squared Error (RMSE) of training datasets for the proposed models by LWLR, LGP and GEP were 0.011, 0.0279 and 0.044, respectively. These RMSE values demonstrated higher exactness of the model based on LWLR compared with the others. Considering the effect of the mixture ratio on the TC of hybrid nanofluids, it must be used as one of the inputs in the cases where a model is developed for various mixture ratios. For instance, in [43] different approaches were used to propose a model for TC of Al 2 O 3 -ZnO/water nanofluid in different temperatures, VFs and mixture ratios of the nanostructures. They used ANN, ANFIS and correlation for this purpose and found that applying ANFIS resulted in the highest accuracy. In a work performed by Jamei et al. [61], three methods, including genetic programming (GP), multilinear regression (MLR) and model tree (MT), were used to predict the TC of EG-based hybrid nanofluids. In their models, besides temperature and VF, the sizes of particles in addition to their densities were utilized as inputs. Among the used methods, GP led to the best performance that was followed by MT and MLR, respectively. Table 2 demonstrates the models provided for the TC of hybrid nanofluids.

Specific Heat
Another thermophysical property of the fluids affecting their heat transfer is specific heat capacity. Similar to the TC, specific heat (SH) is influenced by several factors. In a study conducted by Çolak et al. [62], the SH of Cu-Al 2 O 3 /water nanofluid was investigated at different temperatures and VFs of solids in ranges of 20-65 • C and 0.01255-0.2%, respectively. As illustrated in Figure 6, the SH gradually increased by increasing the temperature, while the increase in the solid VF reduced the SH. In another work [63], the effects of these parameters on the SH were investigated for a MgO-TiO 2 /distilled water hybrid nanofluid. As shown in Figure 7, the increase in temperature reduces the SH to their minimum values, while a further increase in temperature causes an increase in the SH. Similar to the previously mentioned nanofluid, the increase in solid VF results in lower SH in all temperatures. The trend of variations in the SH of the nanofluids in different concentrations was similar to the base fluid since it is the main component of the nanofluid. Gao et al. [64] experimentally investigated the SH of GO-Al 2 O 3 /water nanofluid and observed that a higher solid fraction caused more reduction in the SH. The highest reduction ratio in the SH was observed at the lowest temperature (20 • C) and the highest mass fraction of solids (0.15% wt), which was equal to 7%. More reduction at a higher concentration can be attributed to the lower SH of solid materials in comparison with the liquids used as the base fluid.

Specific Heat
Another thermophysical property of the fluids affecting their heat transfer is specific heat capacity. Similar to the TC, specific heat (SH) is influenced by several factors. In a study conducted by Ç olak et al. [62], the SH of Cu-Al 2 O 3 /water nanofluid was investigated at different temperatures and VFs of solids in ranges of 20-65 °C and 0.01255-0.2%, respectively. As illustrated in Figure 6, the SH gradually increased by increasing the temperature, while the increase in the solid VF reduced the SH. In another work [63], the effects of these parameters on the SH were investigated for a MgO-TiO2/distilled water hybrid nanofluid. As shown in Figure 7, the increase in temperature reduces the SH to their minimum values, while a further increase in temperature causes an increase in the SH. Similar to the previously mentioned nanofluid, the increase in solid VF results in lower SH in all temperatures. The trend of variations in the SH of the nanofluids in different concentrations was similar to the base fluid since it is the main component of the nanofluid. Gao et al. [64] experimentally investigated the SH of GO-Al2O3/water nanofluid and observed that a higher solid fraction caused more reduction in the SH. The highest reduction ratio in the SH was observed at the lowest temperature (20 °C ) and the highest mass fraction of solids (0.15% wt), which was equal to 7%. More reduction at a higher concentration can be attributed to the lower SH of solid materials in comparison with the liquids used as the base fluid. Aside from temperature and solid fraction, other factors, such as the size of particles and their types, influence the reduction in SH. For instance, Tiwari et al. [65] measured the SH of different hybrid nanofluids, including CuO-MWCNT/water, MgO-MWCNT/water and SnO 2 -MWCNT/water, in different solid fractions, temperature and sizes of metal oxide particles (20 to 50 nm). They observed that in cases of the lower size of particles, a higher decrease in the SH occurred, which was attributed to the reduction in the density of the nanofluids due to the increase in particles size. The highest reduction in the SH of the nanofluids was 15.09% at a temperature of 25 • C and a mean size of 20 nm.
In addition to the nanofluids with two dissimilar nanomaterials, the SH of ternary hybrid nanofluids with three nanomaterials has been investigated. In a study conducted by Mousavi et al. [66], the SH of a ternary hybrid nanofluid with various mass ratios of the particles CuO-MgO-TiO 2 was measured. The mass ratios of the particles were (A: 33.4%:33.3%:33.3%, B: 50%:25%:25%, C: 60%:30%:10%, D: 25%:50%:25% and E: 25%:25%:50%). The considered VF and temperature were 0.1-0.5% and 15-60 • C, respectively. The measured values of the SH revealed that it had a reducing trend up to 35 • C, afterward it had an increasing trend by increasing the temperature. The maximum decrease in the SH of the nanofluids was noticed for the C type. Consequently, it was concluded that the material specifications of the nanostructures influenced the SH of the hybrid nanofluid. The influence of the materials on the SH of the hybrid nanofluids has been observed in other studies [67]. Table 3 summarizes the works on the SH of hybrid nanofluids. Aside from temperature and solid fraction, other factors, such as the size of particles and their types, influence the reduction in SH. For instance, Tiwari et al. [65] measured the SH of different hybrid nanofluids, including CuO-MWCNT/water, MgO-MWCNT/water and SnO2-MWCNT/water, in different solid fractions, temperature and sizes of metal oxide particles (20 to 50 nm). They observed that in cases of the lower size of particles, a higher decrease in the SH occurred, which was attributed to the reduction in the density of the nanofluids due to the increase in particles size. The highest reduction in the SH of the nanofluids was 15.09% at a temperature of 25 °C and a mean size of 20 nm.
In addition to the nanofluids with two dissimilar nanomaterials, the SH of ternary hybrid nanofluids with three nanomaterials has been investigated. In a study conducted by Mousavi et al. [66], the SH of a ternary hybrid nanofluid with various mass ratios of the particles CuO-MgO-TiO2 was measured. The mass ratios of the particles were (A: 33.4%:33.3%:33.3%, B: 50%:25%:25%, C: 60%:30%:10%, D: 25%:50%:25% and E: 25%:25%:50%). The considered VF and temperature were 0.1-0.5% and 15-60 °C, respectively. The measured values of the SH revealed that it had a reducing trend up to 35 °C , afterward it had an increasing trend by increasing the temperature. The maximum decrease in the SH of the nanofluids was noticed for the C type. Consequently, it was concluded that the material specifications of the nanostructures influenced the SH of the hybrid nanofluid. The influence of the materials on the SH of the hybrid nanofluids has been observed in other studies [67]. Table 3 summarizes the works on the SH of hybrid nanofluids.

Proposed Models for Specific Heat
Compared with the TC and dynamic viscosity, there are few works on the modeling of SH. This property of the hybrid nanofluids has been modeled and predicted by different techniques, such as correlation, support vector machines and ANN [68][69][70]. For instance, Mousavi et al. [63] proposed a correlation for SH of MgO-TiO 2 /water and found the model reliable since its R-squared was 0.993. Çolak et al. [62] used both correlation and ANN to model the SH of Cu-Al 2 O 3 /water by using temperature and solid fraction. They found that using ANN provided a model with a much lower relative error. Similar to TC, lower errors of the model based on ANN for predicting the SH are mainly due to its more complex structure and determination procedures.
There are some models with improved comprehensiveness that are applicable for more than one nanofluid. For instance, Tiwari et al. [65] proposed a correlation by considering the density, size and SH of nanoparticles besides temperature and VF for SH modeling of three different nanofluids, including CuO-MWCNT/water, MgO-MWCNT/water and SnO 2 -MWCNT/water. The maximum error of their model was 2.93%, while the average absolute relative error was 0.903%, demonstrating the high exactness of the model. In another work [67], a correlation was proposed to model the SH of water-based hybrid nanofluids containing Al 2 O 3 -TiO 2 and Al 2 O 3 -Si 2 O 3 for different temperatures and VFs. In their correlation, densities of water and nanostructure in addition to size and concentration were used for regression; however, the model was not very accurate, and the average deviation was 11%, and they concluded that to reach an accurate prediction, it would be preferred not to use the unified model. In Table 4, the results of the works on SH estimation of hybrid nanofluids are provided.

Dynamic Viscosity
Dynamic viscosity (DV) is an important property of heat transfer fluid that affects the fluid heat transfer characteristics. Generally, nanoparticles suspension in the liquid increases the fluid DV, which is a function of different factors [71][72][73][74][75]. In a study done by Motahari et al. [76], the impacts of the solid fraction and temperature on the DV of MWCNT-SiO 2 /20W50 oil were assessed. The considered solid fraction and temperature ranges in their work were 0.05-1% and 40-100 • C, respectively. They found that at the highest temperature and solid fraction, DV increased up to 171% compared with the base fluid. In another work [77], the DV of graphene-NiO/coconut oil was investigated in different solid fractions and temperatures. Similar to the previous study [76], it was observed that DV increased by increasing the solid fraction while it decreased by increasing the temperature. The enhancement in the DV of the nanofluid at a temperature of 120 • C and solid weight fraction of 0.5% was 28.49%. In addition to the abovementioned factors, the material of the nanostructures can affect the DV of the hybrid nanofluids. As an example, Ghaffarkhah et al. [78] investigated the DV of oil-based hybrid nanofluids with various materials, including MWCNT-SiO 2 , MWCNT-Al 2 O 3 and MWCNT-TiO 2 . It was found that the impact of the material was very low, and the maximum improvements in the DV of the hybrid nanofluids with the mentioned materials were 13.015%, 13.618% and 12.559%, respectively. However, in a work by Dalkılıç et al. [79] on the DV of SiO 2 -graphite/water, it was found that SiO 2 particles had more effect on the DV compared with graphite. The maximum increase in the DV was 36.12%, which was obtained for a solid fraction of 2%.
The surfactant of the hybrid nanofluids and their concentration influence the DV. Ma et al. [80] investigated the impacts of surfactant on the DV of Al 2 O 3 -TiO 2 /water and Al 2 O 3 -CuO/water nanofluids and found that the increase in the PVP, used as a surfactant, led to the enhancement in the DV of the nanofluid. In addition, it was noticed that an increase in the concentration of the surfactant to more than 0.02% wt caused a significant increase in the DV.
The DV of hybrid nanofluids with the base fluids composed of two liquids has been considered in some works. For instance, Urmi et al. [81] carried out a study on the DV of TiO 2 -Al 2 O 3 /water-EG nanofluids considering the impacts of solid fraction and temperature. As shown in Figure 8, similar to single base fluid hybrid nanofluids, the DV increased by increasing the VF and decreased by increasing the temperature. The highest value of relative DV was observed at a temperature of 80 • C and a VF of 0.1%, which was equal to 161.8%. In another work [82], the DV of Al 2 O 3 -CuO/EG-water and Al 2 O 3 -CuO/propylene glycol (PG) was measured in the temperature range of 50-70 • C and solid VF of 0-1.5%. Moreover, the mixture ratio of the base fluid was varied to investigate its effect. It was observed that the increase in the fraction of nanostructures, EG and PG, led to higher DV of the hybrid nanofluids; however, at a temperature of 70 • C, the increase in the fraction of EG from 50% to 55% led to lower dynamic viscosity. Aside from the hybrid nanofluids with two dissimilar materials, the DV of the ones with three dissimilar materials has been investigated by some researchers. For instance, Sahoo [83] performed a study on the DV of a ternary hybrid nanofluid. This nanofluid was composed of water as the base fluid and Al2O3, TiO2and SiC nanoparticles. Similar to the conventional hybrid nanofluids, it was observed that the increase in the temperature caused a reduction in the DV while an increase in solid fraction led to higher DV values. In another work [84], the DV of Al2O3-CuO-TiO2/water was measured for temperature and solid fraction ranges of 35-50 °C and 0.01-0.1%, respectively. It was noticed that by increasing the temperature from 35 to 50 °C , the DV decreased by up to 23.64%. In addition, a comparison between the ternary hybrid nanofluid and Al2O3-CuO/water and Al2O3-TiO2/water revealed a higher DV of the ternary nanofluid.
Due to the non-Newtonian behavior of some of the nanofluids [85,86], it is crucial to consider the shear rate in measuring and reporting the DV. Contrary to the Newtonian fluids, shear rate affects the DV of non-Newtonian fluids. In Newtonian fluids, the DV is influenced by the stress and the behavior of the fluid under the force can change to more solid or more liquid. In order to find the impacts of stress on the DV of these types of fluids, different shear rates can be applied in the measurement procedure. Esfe [87] measured the DV of MgO-MWCNT/5W50 oil in various solid fractions (0.05-1%), temperatures (5-55 °C and shear rates (665.5 s −1 -11997 s −1 ). According to their observations, at low temperatures, the DV had relatively high dependency on the shear rate and its value de- Aside from the hybrid nanofluids with two dissimilar materials, the DV of the ones with three dissimilar materials has been investigated by some researchers. For instance, Sahoo [83] performed a study on the DV of a ternary hybrid nanofluid. This nanofluid was composed of water as the base fluid and Al 2 O 3 , TiO 2 and SiC nanoparticles. Similar to the conventional hybrid nanofluids, it was observed that the increase in the temperature caused a reduction in the DV while an increase in solid fraction led to higher DV values. In another work [84], the DV of Al 2 O 3 -CuO-TiO 2 /water was measured for temperature and solid fraction ranges of 35-50 • C and 0.01-0.1%, respectively. It was noticed that by increasing the temperature from 35 to 50 • C, the DV decreased by up to 23.64%. In addition, a comparison between the ternary hybrid nanofluid and Al 2 O 3 -CuO/water and Al 2 O 3 -TiO 2 /water revealed a higher DV of the ternary nanofluid.
Due to the non-Newtonian behavior of some of the nanofluids [85,86], it is crucial to consider the shear rate in measuring and reporting the DV. Contrary to the Newtonian fluids, shear rate affects the DV of non-Newtonian fluids. In Newtonian fluids, the DV is influenced by the stress and the behavior of the fluid under the force can change to more solid or more liquid. In order to find the impacts of stress on the DV of these types of fluids, different shear rates can be applied in the measurement procedure. Esfe [87] measured the DV of MgO-MWCNT/5W50 oil in various solid fractions (0.05-1%), temperatures (5-55 • C and shear rates (665.5-11997 s −1 ). According to their observations, at low temperatures, the DV had relatively high dependency on the shear rate and its value decreased by shear rate; however, at higher temperatures, this dependency diminished. In addition, it was observed that the increase in the VF caused an increase in the DV, while the effect of temperature was the reverse. In another work, the effects of temperature, shear rate and solid fraction on the DV of SiO 2 -MWCNT/10W40 oil were investigated by Nadooshan et al. [88]. It was observed that the nanofluid had non-Newtonian behavior at all temperatures, but the base fluid had non-Newtonian behavior just at high temperatures. Alirezaie et al. [89] investigated the DV of MWCNT (COOH-Functionalized)-MgO/engine oil in a temperature range of 25-50 • C and a shear rate of 670-8700 s −1 . They found that the nanofluid showed relatively non-Newtonian behavior; however, at high temperatures, it became Newtonian. Similar to previous nanofluids, the DV increases with the increase in the solid fraction. Kazemi et al. [90] investigated the DV of graphene-SiO 2 /water at different shear rates and found that the nanofluid was non-Newtonian. As shown in Figure 9, the DV of the nanofluid increased by increasing the solid fraction and reducing the shear rate. Hybrid nanofluids with binary base fluids may show non-Newtonian behavior. As an example, Bahrami et al. [91] investigated the DV of Fe-CuO/water-EG in different mixture ratios of the base fluid, temperatures, shear rates and solid fractions. They found that the nanofluid showed Newtonian behavior at low solid fractions while it became non-Newtonian at high concentrations.  In Table 5, the main findings of the works on the DV of hybrid nanofluids are provided. Table 5. Findings of the works on the DV of hybrid nanofluids.

Nanostructures Base Fluid Important Findings
Asadi et al. [72] MWCNT-MgO SAE50 oil Up to 65% increase in DV at temperature of 40 °C and solid fraction of 2%.
Alarifi et al. [73] TiO2−MWCNT 5W50 oil Up to 42% increase in DV at temperature of 50 °C and solid fraction of 2%. Asadi et al. [75] CuO-TiO2 Water Increase in the DV by increase in the solid fraction. Goodarzi et al. [74] ZnO-MWCNT SAE 10W40 Up to around 100% increase in the DV was observed.
Esfe [87] MgO-MWCNT 5W50 oil Dependency of viscosity on shear rate decreased at higher temperatures. In Table 5, the main findings of the works on the DV of hybrid nanofluids are provided.

Proposed Models for Dynamic Viscosity
Similar to TC and SH, there are several models for the DV of hybrid nanofluids by using correlations, ANNs, etc. For instance, in a study by Motahari et al. [76] regarding the temperature of solid volume, a correlation was provided for the DV ratio of MWCNT-SiO 2 /20W50 oil with an average deviation of 1.75%. Asadi et al. [72] proposed a simple model for DV considering temperature and solid fraction of MWCNT-MgO-SAE50. In the suggested correlation, the maximum error was around 8%. Urmin et al. [81] proposed a correlation in terms of solid fraction and temperature for the DV of TiO 2 -Al 2 O 3 /water-EG and found that the maximum deviation of the model was 12.7%. In another study [72], a correlation was suggested for the DV ratio of ZnO-Ag/water nanofluid regarding the VF of solid particles. In the proposed correlation, a polynomial of the third degree was used, and the deviation margin of the obtained model was 1.8%. Models based on correlations are employable for ternary hybrid nanofluids. As an example, Sahoo et al. [84] used a correlation in terms of solid fraction and temperature to suggest a model for the DV of Al 2 O 3 -CuO-TiO 2 /water. The maximum deviation of their correlation for estimating the DV of the nanofluid was 1.5%. The models based on the correlation can be improved in terms of comprehensiveness by using more variables as inputs. Since the mixture ratio of the nanomaterials can affect the DV of hybrid nanofluids, similar to the TC, considering it as one of the variables would lead to improvement in the comprehensiveness of the models. For instance, Dalkılıç et al. [79] used the ratio of graphite weight to silica weight in addition to the temperature and solid fraction to provide a model for the DV of SiO 2 -graphite/water for different mixture ratios of the solid materials. The average deviation of the model by using the mentioned variables as input was 6.75%.  Aghaei et al. [97] CuO-MWCNT SAE5W50 Up to 35.52% increase in the DV by increasing the solid fraction from 0.05% to 1%.
Since the nanofluids may have non-Newtonian behavior, other factors in addition to solid fraction and temperature must be used in the models to have more accurate outputs. For instance, Esfe [87] proposed a correlation for the DV of MgO-MWCNT/5W50 oil nanofluid by considering temperature, solid fraction and shear rate. The proposed model had adequate exactness with a maximum error of 8%. Toghraie et al. [86] suggested two models based on correlation and ANN for the DV of a non-Newtonian hybrid nanofluid composed of WO 3 and MWCNT. In their work, various numbers of neurons were tested to find the optimum structure, and it was found that using 39 neurons in the HL led to the best performance. In addition, they found that ANN leads to higher exactness in comparison with the correlation. In another work [89], the DV of MWCNT (COOH-Functionalized)-MgO/engine oil was modeled by considering the shear rate as one of the inputs and employing correlation and ANN. They found that the R-squared of the models by using the ANN was 0.9973 while it was 0.98 in the case of applying correlation.
In addition to correlations, other approaches would be useful for proposing more precise models [77]. For instance, Jamei et al. [98] applied advanced Genetic Programming (GP), which was called Multigene Genetic Programming (MGGP), in addition to Multivariate Linear Regression (MLR) and Gene Expression Programming (GEP) to predict the relative DV of various hybrid nanofluids with Newtonian behavior. The inputs in their models were density and size of the particles, temperature, the DV of the base fluid and the VF of solids. It was noticed that MGGP had the highest exactness with a root mean squared error (RMSE) of 0.05, followed by GEP and MLR with the values of 0.083 and 0.153, respectively. Furthermore, according to the sensitivity analysis, they concluded that the solid fraction, temperature and size of particles were the most influential elements in the relative DV of the investigated hybrid nanofluids. In another work conducted by Ghaffarkhah et al. [78], various approaches, including the Group Method of Data Handling (GMDH), Support Vector Machine (SVM), Radial Basis Function (RBF) and Multi-layer Perceptron (MLP), coupled with different optimization algorithms were used to model the DV of hybrid nanofluids. Comparing the exactness of the proposed models demonstrates that GMDH outperforms other approaches. Table 6 summarizes the works on the estimation of hybrid nanofluids' DV.

Conclusions
The main challenge in improving the thermal performance of a fluid is to improve the working fluid thermophysical properties. In the present work, the thermophysical properties of the hybrid nanofluids, including thermal conductivity, specific heat and dynamic viscosity, as well as their proposed models, are reviewed. The main findings of the study, regarding the questions provided in the methodology section, can be summarized as follows: • Temperature and solid fraction significantly influence the characteristics of hybrid nanofluids.

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In addition to the abovementioned factors, nanostructure material, mixture ratio and base fluid affect the features of hybrid nanofluids. • Dispersion of the hybrid nanostructures can notably improve the TC of hybrid nanofluids, which is more remarkable at higher temperatures.

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The DV of hybrid nanofluids increases with an increase in the solid fraction. • Some of the hybrid nanofluids show Newtonian behavior, while some others are non-Newtonian. At higher solid fractions, there is more tendency toward non-Newtonian behavior.

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Both simple correlations and intelligent methods are applicable for modeling the properties of hybrid nanofluids.

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The exactness of the models proposed for thermophysical properties of a nanofluid is mainly under the influences of method and input variables.

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Intelligent methods, such as ANNs, are preferred in terms of accuracy compared with the correlation for modeling the properties of hybrid nanofluids.

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The accuracy of the intelligent methods can be modified by applying more proper functions and optimization algorithms.

Future Recommendations
In this review paper, important thermophysical features of the hybrid nanofluids, including the TC, specific heat and DV, and the proposed models were reviewed. Despite the numerous studies in the relevant fields, some suggestions are provided for upcoming studies to reach more desirable outcomes. First of all, the effects of other factors, such as the shape of nanostructures and type of surfactants, can be considered in future work regarding their influence on the thermal performance of the nanofluidic devices [100]. Furthermore, it would be attractive to propose models with higher comprehensiveness by applying more variables as inputs. The features of the nanostructure are among the variables that can develop the models' applicability. In addition, despite the key role of the mixture ratio of nanomaterials on the thermophysical properties of the hybrid nanofluids, only a few studies have considered this factor for the TC and DV. Future works should consider the mixture ratio with wider ranges for different hybrid nanofluids. In addition, the effect of mixture ratio on the SH of hybrid nanofluids should be considered in future works.
Furthermore, different data-driven methods, such as SVM, can be used more widely. In addition, novel and efficient optimization algorithms should be used and coupled with data driven approaches to reach the minim deviation in modeling the properties of the hybrid nanofluids.