*5.1. Effective Thermal Conductivity*

Thermal conductivity enhancement of heat transfer fluids has always been the main driving force that motivated researchers into developing nanofluids. This is because the solid particles added to the liquid have tremendously higher thermal conductivity compared to that of the base fluid, and thus cause the effective thermal conductivity of the mixture to improve significantly. At the early stages of their discovery, the claims on the enhancement caused by the dispersed particles on the hosting fluid were seen as a controversial topic because many published works across the literature reported divergence in the level of enhancement and measurement results were difficult to be replicated [194–197]. Nevertheless, a worldwide round-robin, including 33 research institutes, have demonstrated acceptable consistency in measuring the effective thermal conductivity of nanofluids, despite the fact that they unexplored any anomalous improvement in the effective thermal property [198]. Up to today, the effective thermal conductivity of the suspension remains a complicated topic, where it involves many vital elements such as the particles type and morphology, particles concentration, base fluid type and temperature, added surfactants (if any), and dispersion stability [13,199,200]. When constraining the first four parameters in fabricating a dispersion, the optimum effective thermal conductivity is usually reached when the particles are well distributed in the hosting fluid with minimum to no agglomerations/clustering between them. Since a stable state nanofluid reflects that its nanoparticles are homogeneously dispersed within the hosting base fluid, it should theoretically result in a superior overall suspension thermal conductivity to those of an unstable state. The potential influence of nanoparticles agglomeration on the thermal conduction emphasizes that colloid chemistry will play a significant role in enhancing the thermal conductivity of nanofluids. Scientists such as Yu et al. [201], Haghighi et al. [202], and Li et al. [203] have all proven, through their research work, that stabilized nanofluids have greater and steady effective thermal conductivity than their counterparts. Prasher et al. [204] and Wang et al. [205] explained this observation by analyzing the effect of nanoparticles aggregation on the thermal conductivity of nanofluids, where they assumed that solid liner and side chains get formed by particles clustering. Based on the researcher's conclusion, these chains are mainly responsible for enhancing the suspensions thermal conductivity. Still, as more nanoparticles get accumulated, the cluster becomes heavier, and therefore separates from the base fluid due to the gravitational force. The aforementioned causes the thermal conductivity of the colloidal to degrade, with respect to settling time, until it decreased to a minimum possible value when total separation is attained. The previous claim was also supported by the work of Hong et al. [206], where they examined the effective thermal conductivity of SWCNTs—water dispersion with magnetic-field-sensitive nanoparticles (Fe2O3) under various magnetic field strengths. In their experiment, the researchers successfully interconnected the dispersed CNTs using Fe2O<sup>3</sup> nanoparticles and

the employed magnetic field, and thus forming a well aligned chains of nanomaterials. This resulted in the effective thermal conductivity to increase by 50% over that of the base fluid. However, as the holding time under the magnetic field increased, the nanomaterials started to form larger clumps that caused the suspension effective thermal conductivity to degrade. Other studies have also proven the enhancement in nanofluids thermal conductivity through the chain concept, such as the work of Wright et al. [207], Wensel et al. [208], and Hong et al. [209]. All three groups of scholars relied on the magnetic field to form the dispersed particles connected networks in the host fluid. However, the first used a novel alignment approach via coating the SWCNTs with Ni, whereas the other two achieved the interconnection with the aid of metal oxide nanoparticles (e.g., Fe2O<sup>3</sup> and MgO). It is important to note that different types of base fluid and surfactants were used in the three previous studies. Younes et al. [210] have suggested an innovative nanoscale aggregation process that can be adopted to form nanosolids with an interconnect chain capability when dispersed in liquids. In their work, they coated the CNTs through their aggregation process with metal oxide nanoparticles and different types of surfactants. Afterwards, the scholars filtered and dried the aggregate to obtain their as-prepared CNTsbased nanosolids. These newly formed nanomaterial can interconnect when dispersed in a non-aqueous solution by applying a magnetic field. Figure 16 illustrates the effective thermal conductivity degradation theory, which describes the mechanism in which the particles separate from the base fluid due to the formation of both linear and side chains. Other aspects that have less influence on the effective thermal conductivity of nanofluids includes the liquid layering near the outer particles surface [211], Brownian motion of dispersed particles [212,213], thermophoresis [214,215], near-field radiation [216,217], and ballistic transport and nonlocal effects [218,219]. well aligned chains of nanomaterials. This resulted in the effective thermal conductivity to increase by 50% over that of the base fluid. However, as the holding time under the magnetic field increased, the nanomaterials started to form larger clumps that caused the suspension effective thermal conductivity to degrade. Other studies have also proven the enhancement in nanofluids thermal conductivity through the chain concept, such as the work of Wright et al. [207], Wensel et al. [208], and Hong et al. [209]. All three groups of scholars relied on the magnetic field to form the dispersed particles connected networks in the host fluid. However, the first used a novel alignment approach via coating the SWCNTs with Ni, whereas the other two achieved the interconnection with the aid of metal oxide nanoparticles (e.g., Fe2O<sup>3</sup> and MgO). It is important to note that different types of base fluid and surfactants were used in the three previous studies. Younes et al. [210] have suggested an innovative nanoscale aggregation process that can be adopted to form nanosolids with an interconnect chain capability when dispersed in liquids. In their work, they coated the CNTs through their aggregation process with metal oxide nanoparticles and different types of surfactants. Afterwards, the scholars filtered and dried the aggregate to obtain their as-prepared CNTs-based nanosolids. These newly formed nanomaterial can interconnect when dispersed in a non-aqueous solution by applying a magnetic field. Figure 16 illustrates the effective thermal conductivity degradation theory, which describes the mechanism in which the particles separate from the base fluid due to the formation of both linear and side chains. Other aspects that have less influence on the effective thermal conductivity of nanofluids includes the liquid layering near the outer particles surface [211], Brownian motion of dispersed particles [212,213], thermophoresis [214,215], near-field radiation [216,217], and ballistic transport and nonlocal effects [218,219].

with magnetic-field-sensitive nanoparticles (Fe2O3) under various magnetic field strengths. In their experiment, the researchers successfully interconnected the dispersed CNTs using Fe2O<sup>3</sup> nanoparticles and the employed magnetic field, and thus forming a

*Nanomaterials* **2021**, *11*, x FOR PEER REVIEW 26 of 79

**Figure 16.** Nanoparticles separation due to the formation of both linear and side chains in the base fluid. **Figure 16.** Nanoparticles separation due to the formation of both linear and side chains in the base fluid.

Many different techniques have been adopted for measuring the thermal conductivity of nanofluids, namely; 1—cylindrical cell method, 2—temperature oscillation approach, 3—steady state parallel-plate method, 4—3-ω method, 5—thermal constants analyzer approach, 6—thermal comparator method, 7—flash lamp method, 8—transient hotwire method, 9—laser flash method, and 10—transient plane source. More details on the usage, advantages, and disadvantages of these thermal conductivity measurement techniques can be found in Mashali et al. [17], Paul et al. [220], Qiu et al. [170], and Tawfik [221] published works. Among the previously mentioned techniques, the transient hotwire approach was mainly adopted across the literature for nanofluids effective thermal conductivity measurements, although it was the first measuring route for such property [17]. The reasons that attracted researchers into favoring the transient hot-wire method among other methods is due to its capability of eliminating measurements errors caused by the natural convection of the fluid, its minimal amount of time required to perform Many different techniques have been adopted for measuring the thermal conductivity of nanofluids, namely; 1—cylindrical cell method, 2—temperature oscillation approach, 3—steady state parallel-plate method, 4—3-ω method, 5—thermal constants analyzer approach, 6—thermal comparator method, 7—flash lamp method, 8—transient hot-wire method, 9—laser flash method, and 10—transient plane source. More details on the usage, advantages, and disadvantages of these thermal conductivity measurement techniques can be found in Mashali et al. [17], Paul et al. [220], Qiu et al. [170], and Tawfik [221] published works. Among the previously mentioned techniques, the transient hot-wire approach was mainly adopted across the literature for nanofluids effective thermal conductivity measurements, although it was the first measuring route for such property [17]. The reasons that attracted researchers into favoring the transient hot-wire method among other methods is due to its capability of eliminating measurements errors caused by the natural convection of the fluid, its minimal amount of time required to perform each measurement (i.e., within seconds), and its simple conceptual design compared to other available devices or apparatuses. One thing that needs to be emphasized here is that the high thermal conductivities of graphene, ND, and CNT found in the literature are based

on theoretical calculations for a single particle, and that when attempting to measure this thermal property for a powder sample, the results will show tremendously lower values due to the presence of air along with the limitation associated with the measuring tool itself [222,223].

Furthermore, researchers have published numerous amounts of literature on improving nanofluids effective thermal conductivity over their base fluids [224–228]. For example, Yu et al. [224] compared the thermal conductivity of their stable graphene—EG nanofluids to that of pure EG. The researchers have dispersed 2.0 and 5.0 vol. % of graphene, of 0.7–1.3 nm in size, in EG to fabricate their nanofluids at a set of temperatures from 10 to 60 ◦C, using the two-step approach. They have found that the as-prepared 5.0 vol. % suspension had 86% enhanced thermal conductivity over its base fluid at 60 ◦C. Yarmand et al. [225] synthesized water based nanofluids from 0.02 to 0.1 wt % of functionalized graphene nanoplatelets using the two-step method at 20–40 ◦C. The functionalization process was conducted through an acidic treatment to the graphene powder by dispersing the as-received graphene in a 1:3 mixture of HNO<sup>3</sup> and H2SO4, respectively. They found that the formation of sedimentation within their as-fabricated nanofluids was minimal throughout their 245 h test. The heat transfer coefficient improved by 19.68% compared to the base fluid when using the 0.1 wt % nanofluid. Furthermore, Yarmand et al. [225] concluded that the thermal property of the suspension is influenced by the temperature of fabrication and the dispersed solid concentration. Zhang et al. [226] compared the thermal conductivity of three ionic based nanofluids containing graphene sheets, graphite nanoparticles, and SWCNTs. All three types showed enhanced thermal conductivity with a partial increase in viscosity compared to their base fluids. Nevertheless, the nanofluid fabricated from graphene had a higher increase in thermal conductivity compared to the other two types of dispersions. Ghozatloo et al. [227] studied the effect of time, temperature, and concentration on the thermal conductivity of pure and functionalized CVD graphene–water nanofluids. The functionalizing process of graphene was conducted through an alkaline method, and the suspensions were fabricated using sonication (i.e., the two-step approach). Moreover, the concentration used in the production of the suspension was of 0.01–0.05 wt %, and the duration of the dispersion mechanism was 1 h. The authors found that the nanofluids samples containing pure graphene had promptly developed clusters between its solid content, whereas the functionalized suspensions were highly stable. Furthermore, the effective thermal conductivity was seen to reduce to a certain extent for all nanofluids after the time of production. In addition, the enhancement in the effective thermal conductivity using functionalized graphene showed to be 13.5% (0.05 wt %) and 17% (0.03 wt %) over 25 ◦C and 50 ◦C water, respectively. Askari et al. [46] experimentally investigated the thermal and rheological properties of 0.1–1.0 wt % CVD nanoporous graphene–water nanofluids along with heat transfer suspension effect on the thermal performance of a counter-flow arranged mechanical wet tower. The base fluid used in the two-step suspension fabrication was taken from one of the working cooling towers located in South Iran to reflect a real-life case scenario. Different types of surfactants were used to stabilize the dispersion of the as-prepared nanofluids, such as AG, Tween 80, CTAB, Triton X-100, and Acumer Terpolymer. The authors found through analyzing the physical stability of their nanofluids, utilizing the sedimentation capturing method and zeta potential measurements, that using Tween80 as a disperser resulted in a stabilized suspension that can last for up to two months. Furthermore, their 1.0 wt % nanofluid showed a 16% increase in the thermal conductivity at a dispersion temperature of 45 ◦C. At the same time, the low concentration suspensions would be appropriate for industrial applications because of their increasing effect on the effective density and viscosity. Moreover, the as-produced nanofluids enhanced the efficiency, cooling range, and tower characteristic compared to the conventional base fluid. For example, using a 0.1 wt % fabricated nanofluid had resulted in a 67% increase in the cooling range and a 19% decrease in the overall water consumption. Goodarzi et al. [229] studied the effective thermal conductivity, specific heat capacity, and viscosity of their as-prepared nitrogen-doped graphene–water nanofluids along with their

convective heat transfer behavior when employed in a double-pipe type heat exchanger. The authors used 0.025 wt % of Triton X-100, as their surfactant, along with 0.01–0.06 wt % of graphene to prepare the suspensions using the two-step method. Their results showed that the examined thermophysical properties where very sensitive to both temperature and concentration. As an example, the effective thermal conductivity of their suspension showed an increase from 0.774 to 0.942 W/m·K with the increase in temperature (from 20 to 60 ◦C). The maximum effective thermal conductivity achieved by the scholars was 37% higher than that of the base fluid. Furthermore, they found that increasing the concentration of their nanosheets in the base fluid had caused the heat transfer coefficient of their working fluid to improve but at the same time results in increasing the pressure drop in the system and the pumping power requirement. Liu et al. [230] examined the effective thermal conductivity and physical stability of their synthesized graphene oxide–water nanofluids. Moreover, the mass fraction and temperature of the investigated samples were 1.0–4.5 mg/mL and 25–50 ◦C, respectively. The researchers found that they can achieve a homogeneously stable nanofluid for about 3 months using their preparation process. They also found that the effective thermal conductivity of their as-prepared nanofluid was 25.27% higher than the base fluid, at 4.5 mg/mL mass fraction, and a temperature of 50 ◦C. Ghozatloo et al. [228] explored the possibility of improving the convection heat transfer behavior of a shell and tube heat exchanger, under laminar flow conditions, using CVD graphene nanofluid of water base. The researchers also investigated the effect of temperature and solid dispersed concentration of the mixture on the thermal conductivity and convective heat transfer coefficients. The dispersions were prepared using 0.05, 0.075, and 0.1 wt % of treated CVD graphene and 15 min sonication in water. According to the authors outcomes, using 0.05, 0.075, and 0.1 wt % suspensions, at 25 ◦C, enhanced the thermal conductivity over pure water by 15.0%, 29.2%, and 12.6%, respectively. Moreover, the convective heat transfer coefficients of the as-produced mixtures depended on the flow conditions in which the working fluid undergoes but were in all cases higher than the base fluid. From the previously mentioned studies, it can be concluded that carbonbased nanomaterials can form stabilized nanofluids, either by selecting the appropriate base fluid–nanoscaled material matrix or through external physical and/or chemical approaches. Moreover, these suspensions have enhanced thermal properties compared to their conventional base fluids, but the level of enhancement gets affected by parameters such as concentration, temperature, physical stability, etc. Thus, such factors should be carefully considered to obtain the optimum suspension thermophysical condition.

Besides the experimental studies, many researchers have developed theoretical correlations to predict the effective thermal conductivity of nanofluids. Still, most of these formulas have shown conceptual limitations towards their experimental origin. Table 4 demonstrates the developments in the effective thermal conductivity equations.


**Table 4.** Developments of nanofluids effective thermal conductivity formulas.


where ܥଵ is a proportional constant, ݀ is the diameter of the base fluid molecule, ܴ݁ௗ is the



