Heat Transfer Enhancement of Nanofluids with Non-Spherical Nanoparticles: A Review

Abstract

This article reviews the heat transfer enhancement of nanofluids with non-spherical nanoparticles. We divided the non-spherical nanoparticles suspended in nanofluids into three categories based on the dimension of geometric particle structure. Based on the measured data in experimental studies, we then evaluated the shape effect of non-spherical nanoparticles on thermal conductivity and convective heat transfer enhancement of nanofluids. Recent studies explored the numerical predictions and related heat transfer mechanisms. Due to large aspect ratios, thermal conductivity is abnormally enhanced only for nanofluids with carbon nanotubes/nanofibers/nanowires. The approximate enhancement effect exerted by three types of non-spherical nanoparticles on thermal conductivity was 4.5:2.5:1. Thermal conductivity enhancement per concentration was larger for nanorods/ellipsoids with small aspect ratios. The convective heat transfer coefficient was increased by suspending non-spherical nanoparticles in the base fluid. Consequently, no significant thermohydraulic performance was discovered for convective heat transfer of non-spherical nanoparticle nanofluid flow, specifically for turbulent flows, due to increased pumping power. However, the temperature and particle concentration effect on convective heat transfer remains unclear. In addition, no perfect model for predicting the thermal conductivity and convective heat transfer of non-spherical nanoparticle nanofluids has been reported.

1. Introduction

Studies on heat transfer enhancement of nanofluids have largely matured over the past decade. Since Choi and Eastman [1] introduced the concept of “nanofluids,” which are fluids with suspended nanoparticles, scholars have reported significant heat transfer enhancement of nanofluids with low particle loadings. In addition, the suspension is stable and induces a small amount of pumping power compared to the base fluid [2]. Therefore, nanofluids are considered the next generation of a heat transfer medium that will be extensively applied in advanced heating or cooling technology.

Due to the complexity of the nanofluid flow transport, the mechanism underlying the excellent heat transfer performance of nanofluids is poorly understood. The bulk medium shows rheological behavior after the nanoparticles are dispersed in the base fluid [3,4]. Murshed and Estellé reviewed the viscosity of nanofluids with different types of nanoparticles or base fluids, particle concentration, shear rate, etc. [5]. However, they discovered scattered and inconsistent literature data from different researchers. Moreover, the conventional and proposed empirical models could not effectively predict the viscosity of nanofluids containing non-spherical nanoparticles. Similar scenarios have been reported in heat transfer characteristics of nanofluids. First, there is a substantial variance in the thermal conductivity of nanofluids measured in the literature [6,7].

On the other hand, the convective heat transfer coefficient or Nusselt number provided in literature for nanofluid flow is different and inconsistent [8,9]. The contributing factors for nanofluids’ heat transfer characteristics multiply, resulting in nonlinear correlations. Therefore, reviewing the results from previous studies is essential to identify research gaps.

Heat transfer enhancement of nanofluids is influenced by several factors, including particle material, size, shape, concentration, type of base fluid, the temperature of bulk fluid, etc. For convective heat transfer (CHT), the flow parameters and thermal boundary conditions promote nanofluids flow. Most of the previous studies focused on the importance of fluid type and particle concentration. Based on the effective medium theory, the enhancement of nanofluids heat transfer increases with the concentration and the thermal conductivity of the particle material. Nonetheless, the effect of particle shape and size distribution was partially reported and considered a constant in experiments or theoretical studies. The nanoparticles prepared for experiments in laboratories or applications in industries are polydisperse. The shape and size of particles vary around the nominal value given by nanomaterial producers.

Moreover, most studies on nanofluids’ heat transfer enhancement are based on bulk fluid with spherical nanoparticles. With nanotechnology, more nanoparticles with different shapes can be industrially developed. In recent years, several experimental, theoretical, and numerical studies reported that particle shape modulates the CHT characteristic of nanofluids [10,11]. Nanoparticles with shapes such as cylinders, bricks, blades, and platelets have been discussed (Figure 1). Furthermore, a theoretical and numerical investigation of heat transfer enhancement of nanofluids containing non-spherical nanoparticles (NSN nanofluids) has recently gained a premium [12,13]. Therefore, it is essential to review the existing research on the importance of the particle shape effect on the nanofluid application in heat transfer enhancement.

This article reviews research findings and the development of the heat transfer enhancement of NSN nanofluids. We collect and analyze thermal conductivity enhancement (TCE) measured in experiments based on NSN nanofluids. This work also summarizes the classical and recently proposed thermal conductivity models for NSN nanofluids and the related mechanisms. Further, we evaluate the experimental data in studies on CHT of NSN nanofluids. Finally, we present conclusions on the basic theory and numerical predictions for NSN nanofluids fluid with CHT.

2. Thermal Conductivity of NSN Nanofluids

Thermal energy transfer occurs through conduction, convection, or radiation [14]. Considering that radiative energy transport is quite distinct from the first two mechanisms because it does not require a material medium, we primarily focus on conduction and convection behaviors. This section deals with the thermal conductivity of NSN nanofluids, whereas heat transfer via convection will be discussed in the next sections.

2.1. Experimental Data Evaluation

Thermal conductivity is an essential physical property of nanofluid conduction. Several studies have been performed to enhance nanofluids’ thermal conductivity. For NSN nanofluids, Table 1 summarizes experimental studies on the thermal conductivity enhancement of NSN nanofluids. The experimental conditions vary in the nanofluid type, particle shape, size, volume fraction, and temperature. Distilled water (DW) was commonly used for aqueous nanofluids, and oil was used as the base fluid. Most of the experiments were performed by transient hotwire technology in the lab. The insulation treatment of the sensor and control of surfactant is significantly essential [15]. As shown in the table, all of the experimental results showed the thermal conductivities of nanofluids were enhanced after nanoparticles were suspended in the base fluid. Results showed that the thermal conductivity of nanofluids increases as the particle loading grows. However, not all data demonstrated the abnormal thermal conductivity capacity of nanofluids with non-spherical nanoparticles. Figure 2 presents the experimental data in Table 1 to compare the TCEs of different NSN nanofluids at room temperature. Considering the continuous variation in TCE with temperature, data were obtained by interpolation within the temperature range.

The shapes of non-spherical nanoparticles used in studies can be divided into three categories based on the dimensionality of particle geometry [13,16]. Carbon nanotubes (CNTs), nanofibers, and nanowires are approximated as one-dimensional elongated particles with a large aspect ratio (AR, ratio of length to diameter of particles). Their cross-section size is in the nanometer range. However, the length is several microns or even longer. In addition, their bending states differ due to different materials.

Nevertheless, these particles with large aspect ratios are easily intertwined, inducing a network effect [17]. Their rheological characteristics are significantly apparent. Rod-like and ellipsoidal particles are categorized as two-dimensional nanomaterials with a moderate aspect ratio of 1 to 10. If the length is much less than the cross-sectional diameter, the particle usually appears as a disk shaped like a platelet or a blade, as shown in Figure 1c. Additional types of particles with arbitrary shapes such as bricks, diamonds, and other polygonal shapes are three-dimensional classes. From the average slope of the three zones, the approximate enhancement effect by three types of non-spherical nanoparticles on thermal conductivity is 4.5:2.5:1. The thermal conductivity characteristics of three types of NSN nanofluids are discussed.

2.1.1. CNTs/Nanofibers/Nanowires

CNTs are the most popular suspension medium for nanofluids since they display an average thermal conductivity of 4000 W/(m·K), which is higher than that of other nanoparticles [18]. Many articles and reviews [19,20,21] focused on nanofluids with CNTs, and only representative work is listed in Table 1. The type of nanofluid with elongated nanoparticles shows excellent performance in TCE due to the large size and aspect ratio of CNTs, which are hundreds of nanometers in diameter and at least tens of microns in length [15,22]. Nevertheless, the addition of large-aspect-ratio particles into a base fluid could significantly increase viscosity compared to the continuous phase [23]. Moreover, CNTs, another nanofibrous polymer [15], and nanowires [24] entangle with each other, which could cause a complex particle morphology and heat transfer properties in different experiments. Ali et al. [21] recently reviewed the thermal conductivity of commonly used particles and base fluids for fabricating nanofluids and showed that carbon-based nanofluids hold superior thermal features to those prepared by metal oxides and metals.

Figure 2 displays a number of points showing the enhancement of heat conduction in varying ranges. Maheshwary et al. [25,26] reported doubled thermal conductivities after suspending 2.5 wt.% metal oxide nanoparticles. They compared three nanofluids with cubic, nanorod, and spherical nanoparticles; they concluded that cubic particles displayed the best performance. Their abnormal results are significantly more excellent than others represented in Figure 2a. Thus, they are not plotted in the figure. The TCE shows two distinct trends that the black dotted line can distinguish in the figure in a wide range of volume fractions. Several studies reported abnormal TCE within 1% particle loading. Xie et al. [27,28] prepared nanowires with high aspect ratios (25 for Ag and approximately 82 for CuO nanowires) and measured an intriguingly high thermal conductivity increment at low volume fractions.

In contrast, the TCE for nanofluid containing CuO nanospheres remains low. Therefore, thermal conductivities for NSN nanofluids can be much higher than those of nanofluids containing spherical nanoparticles. The study also showed that the TCE linearly increases with the volume fraction when the nanowire volume fraction is lower than 1%, and the authors discovered that their data effectively conforms to the Hamilton–Crosser (H-C) model. Intriguingly, Carbajal-Valdéz et al. [29] reported a TCE of 20.8% by suspending only 0.0174% Ag nanowires, which shows a performance approximately 20 times better than the results of Gu et al. [24]. Overall, nanofluids with CNTs/nanofibers/nanowires demonstrate the best performance in different types of nanofluids. Specifically, nanofluids prepared with Ag nanowires at low concentrations show abnormal TCE.

2.1.2. Nanorods/Ellipsoids

Nanofluids containing cylindrical nanoparticles are another type of suspension commonly used in research [2,10,30,31]. Notably, nanoparticles in cylindrical shape are referred to as nanorods with stiffness and finite length. These nanomaterials are synthesized from metals or semiconducting materials and cannot bend. The cross-section of particles is circular and nanosized, with a moderate aspect ratio range of around 5 [32]. Yang and Han [31] documented that nanofluids containing cylindrical nanoparticles with such an aspect ratio could show different behaviors.

In Figure 2, the findings reported by Murshed et al. [2] and Zhu et al. [33] are quite similar when particle loading ranges from 2% to 5%. The aspect ratios of used nanorods are approximately 4 and 6.25, and the materials include TiO₂ and CuO, respectively. Timofeeva et al. suspended aluminum oxide (Al₂O₃) nanoparticles of four different shapes [34] in DW and EG mixed 50/50 by volume to assess the particle shape effect on thermal conductivity of nanofluids. The nanoparticles supported by a company have the shapes of rods, bricks, platelets, and blades, with different sizes and aspect ratios. The data measured in experiments illustrated that nanofluids containing cylindrical nanoparticles exhibit the best heat conductivity performance. They found that particle shape and interfacial layer contribute to the particle volume fraction thermal conductivity of nanoparticle suspensions. The predictions of the classical H-C model are higher than the measured TCE for particles with blade and platelet shapes.

Other studies [10,31,35] measured similar values of TCE, which are approximately half of the TCE reported by Murshed et al. [2] and Zhu et al. [33]. Chen et al. [3] prepared aqueous nanofluids containing CNTs with an aspect ratio of 10, closer to rod-like. Nithiyanantham et al. [36] suspended rod-like Al₂O₃ nanoparticles into molten salt to prepare nanofluids and discovered approximately 10% TCE in the liquid state. The particle shapes discussed above have an aspect ratio larger than 1. As shown in Figure 1, the nanofluid TCE is positively related to the particle concentration. To eliminate the effect of particle concentration to examine the shape effect, we defined the enhancement per concentration as the ratio of TCE and particle volume fraction. Figure 3 shows the enhancement per concentration as a function of aspect ratio at room temperature. Only a handful of studies have provided particle aspect ratios. Ag nanowire/CNT-based nanofluids made by Gu et al. [24] and Carbajal-Valdéz et al. [29] were not plotted due to the out-of-range values.

Nanoparticles agglomerate and form aggregates with a small aspect ratio; this explains why many studies have found enhanced heat transfer except for the concentration increment. With increasing AR, the enhancement per concentration increases; this implies that a non-spherical shape helps TCE. The reported data are near the diagonal (enhancement per concentration/AR = 1). Interestingly, the increase induced by the aspect ratio appears to be more apparent in the small-aspect-ratio region (AR < 10), which represents rod-like particles. TCE per concentration no longer increased with increasing AR for a tubular/wire-shaped dispersed phase with a large aspect ratio. This means that the enhancement of the network effect on heat transfer is limited. Jiang et al. [37] discovered that the effect of particle AR on TCE was more apparent for small particles.

2.1.3. Platelets/Blades/Bricks/Diamonds/Polygons

Platelet/blade-shaped particles have a large section area. The data plotted in Figure 2 reveal a relatively small TCE of this nanofluid type. Singh et al. [38] measured a TCE of approximately 29.51% at a high volume fraction of SiC–water nanofluid of 7%. Timofeeva et al. [34] compared the effects of the particle shapes of platelets, blades, and cylinders on TCE by eliminating the material and agglomeration effect. They discovered that although the sphericities of blades and platelets are larger than those of cylinders, the measured TCE of blades and platelets is smaller than that of cylinders. The classical H-C model considers the sphericity of non-spherical particles and cannot estimate the shape effect on the TCE of nanofluids. Similar results were obtained by Kim et al. [39] in a comparison of platelet-, brick-, and blade-shaped particles.

Torii and Yang [40] and Xie et al. [41] investigated nanofluids with diamond-like particle shapes; however, these particles are treated as spheres. Their findings showed that TCE linearly increases with particle volume fraction. Ferrouillat et al. [42] tested nanofluids with polygonal nanoparticles and discovered a slight difference between nanofluids and base fluid. Notably, particle sizes differ among these studies, which could also influence the TCE. Enhancement per concentration as a function of particle size at room temperature is illustrated in Figure 4. Experimental data reported in Table 1 are plotted, except for those of Maheshwary et al. [25,26], whose findings were two orders of magnitude higher than other results. As shown in Figure 4, most of the enhancement per concentration is smaller than 10, indicating a relatively weak shape effect of these particles on TCE. From the data of diamond and platelet particles, the enhancement per concentration increases with increasing particle size.

Nonetheless, the materials of nanoparticles as additives dispersed in the nanofluids are different, and studies demonstrated a different behavior in particle size effect [43]. Tahmooressi et al. [44] recently argued that there is insufficient evidence that smaller nanoparticles increase ETC more than larger nanoparticles. Heat conductivities of nanofluids with blade- or brick-shaped nanoparticles measured by Kim et al. [39] and Timofeeva et al. [34] are close and lower than those of other shapes due to the sphericity of bricks being close to 1.

Table 1. Summary of experiments data for heat conductivity of NSN nanofluids.

Authors	Nanofluid Type	Particle Shape and Size (nm as Default)	Volume Fraction ϕ (Vol. as Default)	Temperature	Maximum TCE
Xie et al. [30]	SiC–water/EG	Cylindrical 600 (d)	<4.2%	4 °C	22.9%
Xie et al. [22]	CNTs–DE/EG/DW	Nanotube 15 (d) × 30 mm (l)	1%	-	19.6% in DE, 12.7% in EG, 7.0% in DW
Assael et al. [45]	CNTs–water	Nanotube, 30 to 250 (d), l > 70,000	0.6%	Room	38%
Murshed et al. [2]	TiO2–water	Nanorod 10 (d) × 40 (l)	<5%	Room	33%
Yang and Han [31]	Bi2Te3–perfluoro–n–hexane	Nanorod 20 (d) × 170 (l)	0.8%	3–50 °C	7.7% at 3 °C, 6.3% at 50 °C
Yang and Han [31]	Bi2Te3–hexadecane oil	Nanorod 20 (d) × 170 (l)	0.8%	20–50 °C	6.1% at 20 °C, 3.9% at 50 °C
Zhang et al. [15]	CNTs–water	Nanofiber 150 (d) × 10,000 (l)	0.1–0.89%	23 °C	40%
Zhu et al. [33]	CuO–water	Nanorod 30–50 (d) × 200–300 (l)	0.1–10%	Room	18% at ϕ = 1%, 28% at ϕ = 3%, 31% at ϕ = 5%
Chen et al. [3]	TiO2–water	Nanorod 10 (d) × 100 (l)	0.12, 0.24, and 0.60%	20–40 °C	5.38%
Singh et al. [38]	SiC–water	Platelet 170 (d)	<4%	Room	~29.51%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Platelet 16 (d) × 3 (l)	<7%	21 °C	18% at ϕ = 7%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Blade36 (d) × 6 (l)	<7%	21 °C	18% at ϕ = 7%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Cylinder 8 (d) × 64 (l)	<8.5%	21 °C	35% at ϕ = 8.5%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Brick 54 (l)	<7%	21 °C	25% at ϕ = 7%
Torii and Yang [40]	nanodiamonds–water	Diamond 10 (d)	<5%	-	16%
Xie et al. [41]	nanodiamonds–water/EG	Diamond 30–50 (d)	<2%	10–60 °C	18%
Yu et al. [10]	Al2O3–PAO	Nanorod 7 (d) ×85 (l)	<1.3%	25 °C	12% at ϕ = 1.3%
Nasiri et al. [46]	SWNT/SWNT/ FWNT/MWNT–water	-	0.25 wt.%	15–40 °C	13%, 16%, 21%
Gu et al. [24]	CNTs–water	Nanofiber 10–15 (d) × 10–20 µm (l)	0.2%	25 °C	3.7%
Gu et al. [24]	Ag–water	Nanowire 60 (d) × 20,000–30,000 (l)	0.2%	25 °C	12.1%
Gu et al. [24]	Cu–water	Nanowire 100–200 (d) × 800–6000 (l)	0.2%	25 °C	2.8%
Ferrouillat et al. [42]	SiO2–water	Banana-like	0.82%	20–70 °C	2% at 70 °C
Ferrouillat et al. [42]	ZnO–water	Nanorod	0.93%	20–70 °C	1% at 70 °C
Fang et al. [47]	Ag–EG	Nanowire 100 (d) × 50,000 (l)	0.1%	10–30 °C	15.6%
		Platelet, 300–400 (d) × 30–40 (l)			5.3%
Jeong et al. [48]	ZnO–water	Nanorod, 150–370 (d)	0.5–5%	Room	19.8%
Kim et al. [39]	Al2O3–water	Platelets,15 (d) × 5 (l)	0.3–7%	20–80 °C	23%
		Blades, 15 (l) × 8 (w) × 5 (h)			16%
		Bricks, 40 (d) × 40 (l) × 20 (l)			28%
Farbod et al. [49]	CuO–engine oil	Nanorod	<6 wt.%	25 °C	8.3%
8.3%	TiO2–water	Cubic, 87.21 (d) Nanorod, 8.27 (d) × 92.47 (l)	<2.5 wt.%	27–87 °C	169%
					96%
Zhang et al. [28]	Ag–EG	Nanowire 40 (d) × 1000 (l)	0.46%	25 °C	13.42%
Zhu et al. [27]	CuO–dimethicone	Nanowire 30–80 (d) × 3500–5500 (l)	0.15%	25 °C	13.42%
			0.3%		23.15%
			0.45%		36.98%
			0.6%		47.67%
			0.75%		60.78%
Shah et al. [50]	CuO–EG and DW (70/30)	Cube, 68.4 (l)	0.3%	30–80 °C	16.98%
		Brick, AR = 1.07			22.30%
		Polygonal, AR = 1.57			29.50%
		Nanorod, AR = 5.84			33.17%
Carbajal et al. [29]	Ag–water	Nanowire 96 (d) × 40,000 (l)	0.0174%	Room	20.8%
Maheshwary et al. [25]	CuO–water	Cubic,	2.5 wt.%	30 °C	72.49%
		Nanorod			48.81%
Maheshwary et al. [25]	MgO–water	Cubic,	2.5 wt.%	30 °C	110.96%
		Nanorod			72.57%
Maheshwary et al. [25]	TiO2–water	Cubic	2.5 wt.%	30 °C	148.46%
		Nanorod			115.55%
Maheshwary et al. [25]	ZrO2–water	Cubic,	2.5 wt.%	30 °C	164.01%
		Nanorod			135.36%
Maheshwary et al. [25]	Al2O3–water	Cubic,	2.5 wt.%	30 °C	209.70%
		Nanorod			173.31%
Nithiyanantham et al. [36]	Al2O3–molten salt	Nanorod, 3–7 (d) × 30–70 (l)	1 wt.%	50–200 °C	10.08%
Cui et al. [35]	TiO2–water	Ellipsoidal, 20 (d) × 30 (l)	0.5–4%	20–60 °C	20.58%
		Nanorod, 15 (d) × 35 (l)			20.63%
		Sheet, 5 (w) × 70 (l) × 70 (h)			23.43%
Ni et al. [51]	Cu2O–water	Nanowire, 2–3 (d)	-	30–80 °C	66.8%

Table 1. Summary of experiments data for heat conductivity of NSN nanofluids.

Authors	Nanofluid Type	Particle Shape and Size (nm as Default)	Volume Fraction ϕ (Vol. as Default)	Temperature	Maximum TCE
Xie et al. [30]	SiC–water/EG	Cylindrical 600 (d)	<4.2%	4 °C	22.9%
Xie et al. [22]	CNTs–DE/EG/DW	Nanotube 15 (d) × 30 mm (l)	1%	-	19.6% in DE, 12.7% in EG, 7.0% in DW
Assael et al. [45]	CNTs–water	Nanotube, 30 to 250 (d), l > 70,000	0.6%	Room	38%
Murshed et al. [2]	TiO2–water	Nanorod 10 (d) × 40 (l)	<5%	Room	33%
Yang and Han [31]	Bi2Te3–perfluoro–n–hexane	Nanorod 20 (d) × 170 (l)	0.8%	3–50 °C	7.7% at 3 °C, 6.3% at 50 °C
Yang and Han [31]	Bi2Te3–hexadecane oil	Nanorod 20 (d) × 170 (l)	0.8%	20–50 °C	6.1% at 20 °C, 3.9% at 50 °C
Zhang et al. [15]	CNTs–water	Nanofiber 150 (d) × 10,000 (l)	0.1–0.89%	23 °C	40%
Zhu et al. [33]	CuO–water	Nanorod 30–50 (d) × 200–300 (l)	0.1–10%	Room	18% at ϕ = 1%, 28% at ϕ = 3%, 31% at ϕ = 5%
Chen et al. [3]	TiO2–water	Nanorod 10 (d) × 100 (l)	0.12, 0.24, and 0.60%	20–40 °C	5.38%
Singh et al. [38]	SiC–water	Platelet 170 (d)	<4%	Room	~29.51%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Platelet 16 (d) × 3 (l)	<7%	21 °C	18% at ϕ = 7%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Blade36 (d) × 6 (l)	<7%	21 °C	18% at ϕ = 7%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Cylinder 8 (d) × 64 (l)	<8.5%	21 °C	35% at ϕ = 8.5%
Timofeeva et al. [34]	Al2O3–EG and water (50/50)	Brick 54 (l)	<7%	21 °C	25% at ϕ = 7%
Torii and Yang [40]	nanodiamonds–water	Diamond 10 (d)	<5%	-	16%
Xie et al. [41]	nanodiamonds–water/EG	Diamond 30–50 (d)	<2%	10–60 °C	18%
Yu et al. [10]	Al2O3–PAO	Nanorod 7 (d) ×85 (l)	<1.3%	25 °C	12% at ϕ = 1.3%
Nasiri et al. [46]	SWNT/SWNT/ FWNT/MWNT–water	-	0.25 wt.%	15–40 °C	13%, 16%, 21%
Gu et al. [24]	CNTs–water	Nanofiber 10–15 (d) × 10–20 µm (l)	0.2%	25 °C	3.7%
Gu et al. [24]	Ag–water	Nanowire 60 (d) × 20,000–30,000 (l)	0.2%	25 °C	12.1%
Gu et al. [24]	Cu–water	Nanowire 100–200 (d) × 800–6000 (l)	0.2%	25 °C	2.8%
Ferrouillat et al. [42]	SiO2–water	Banana-like	0.82%	20–70 °C	2% at 70 °C
Ferrouillat et al. [42]	ZnO–water	Nanorod	0.93%	20–70 °C	1% at 70 °C
Fang et al. [47]	Ag–EG	Nanowire 100 (d) × 50,000 (l)	0.1%	10–30 °C	15.6%
		Platelet, 300–400 (d) × 30–40 (l)			5.3%
Jeong et al. [48]	ZnO–water	Nanorod, 150–370 (d)	0.5–5%	Room	19.8%
Kim et al. [39]	Al2O3–water	Platelets,15 (d) × 5 (l)	0.3–7%	20–80 °C	23%
		Blades, 15 (l) × 8 (w) × 5 (h)			16%
		Bricks, 40 (d) × 40 (l) × 20 (l)			28%
Farbod et al. [49]	CuO–engine oil	Nanorod	<6 wt.%	25 °C	8.3%
8.3%	TiO2–water	Cubic, 87.21 (d) Nanorod, 8.27 (d) × 92.47 (l)	<2.5 wt.%	27–87 °C	169%
					96%
Zhang et al. [28]	Ag–EG	Nanowire 40 (d) × 1000 (l)	0.46%	25 °C	13.42%
Zhu et al. [27]	CuO–dimethicone	Nanowire 30–80 (d) × 3500–5500 (l)	0.15%	25 °C	13.42%
			0.3%		23.15%
			0.45%		36.98%
			0.6%		47.67%
			0.75%		60.78%
Shah et al. [50]	CuO–EG and DW (70/30)	Cube, 68.4 (l)	0.3%	30–80 °C	16.98%
		Brick, AR = 1.07			22.30%
		Polygonal, AR = 1.57			29.50%
		Nanorod, AR = 5.84			33.17%
Carbajal et al. [29]	Ag–water	Nanowire 96 (d) × 40,000 (l)	0.0174%	Room	20.8%
Maheshwary et al. [25]	CuO–water	Cubic,	2.5 wt.%	30 °C	72.49%
		Nanorod			48.81%
Maheshwary et al. [25]	MgO–water	Cubic,	2.5 wt.%	30 °C	110.96%
		Nanorod			72.57%
Maheshwary et al. [25]	TiO2–water	Cubic	2.5 wt.%	30 °C	148.46%
		Nanorod			115.55%
Maheshwary et al. [25]	ZrO2–water	Cubic,	2.5 wt.%	30 °C	164.01%
		Nanorod			135.36%
Maheshwary et al. [25]	Al2O3–water	Cubic,	2.5 wt.%	30 °C	209.70%
		Nanorod			173.31%
Nithiyanantham et al. [36]	Al2O3–molten salt	Nanorod, 3–7 (d) × 30–70 (l)	1 wt.%	50–200 °C	10.08%
Cui et al. [35]	TiO2–water	Ellipsoidal, 20 (d) × 30 (l)	0.5–4%	20–60 °C	20.58%
		Nanorod, 15 (d) × 35 (l)			20.63%
		Sheet, 5 (w) × 70 (l) × 70 (h)			23.43%
Ni et al. [51]	Cu2O–water	Nanowire, 2–3 (d)	-	30–80 °C	66.8%

Figure 2. Collection of experimental data for TCE of NSN nanofluids at room temperature (×: CNTs/nanofibers/nanowires; +: nanorods/cylinders/ellipsoids; : platelets; : blades; □: bricks; : diamonds). (a) Full range. (b) Enlarged low-volume-fraction region (volume fraction < 1.2%, TCE < 16%) [2,3,10,15,22,24,27,28,29,31,33,34,35,38,39,40,41,47,48,50].

Figure 2. Collection of experimental data for TCE of NSN nanofluids at room temperature (×: CNTs/nanofibers/nanowires; +: nanorods/cylinders/ellipsoids; : platelets; : blades; □: bricks; : diamonds). (a) Full range. (b) Enlarged low-volume-fraction region (volume fraction < 1.2%, TCE < 16%) [2,3,10,15,22,24,27,28,29,31,33,34,35,38,39,40,41,47,48,50].

Figure 3. Enhancement per concentration as a function of aspect ratio at room temperature [2,3,10,15,24,27,28,29,31,33,34,35,47,50].

Figure 3. Enhancement per concentration as a function of aspect ratio at room temperature [2,3,10,15,24,27,28,29,31,33,34,35,47,50].

Figure 4. Enhancement per concentration as a function of particle size at room temperature [34,35,38,39,40,41,47,50].

Figure 4. Enhancement per concentration as a function of particle size at room temperature [34,35,38,39,40,41,47,50].

2.2. Numerical Predictions and Mechanism Discussion

Effective heat conductivity (EHC) k is often used to describe the bulk ability of thermal conductivity. For suspensions with spherical particles, Maxwell [52] first presented the classical EHC model:

$$k_{nf}=k_f\left[\frac{(k_p+2k_f)+2\varphi (k_f-k_p)}{(k_p+2k_f)-\varphi (k_f-k_p)}\right]$$

(1)

The formula is derived from spherical particles, but recent studies have found that it is also effective for diluting Newtonian nanofluids [17]. Based on the Maxwell model, Hamilton and Crosser [53] presented the model for suspensions with non-spherical particles:

$$k_{nf}=k_f\left[\frac{k_p+\left(n-1\right)k_f-\left(n-1\right)(k_p-k_f)\varphi }{k_p+\left(n-1\right)k_f+(k_p-k_f)\varphi }\right]$$

(2)

where n is the shape factor, and n = 3/s_i. s_i is the sphericity, which equals 3 for spherical particles. The data listed in Table 1 indicate that the EHC for nanofluids is influenced by particle shape and materials, particle loading, and pH. Wang et al. [54] established a model for nanoparticle aggregates by combining the effective medium approximation and the fractal theory. Nonetheless, the fractal dimension or shape factor index could not provide particle shape characteristics and the interaction with base fluids. Therefore, there is no perfect model to predict the thermal conductivity of various nanofluids accurately. Table 2 lists several popular models and numerical studies for EHC of NSN nanofluids. Nanofluids with tube/wire/cylinder-shaped nanoparticles showed superior TCE. Thus, the models in the literature are primarily established to focus on this type of particle. Most of these models are based on the classical H-C model and modified based on the experimental data or by combining the characteristics of nanofluids.

2.2.1. Interfacial Layer Theory

Nanofluids are composites with particle additives [55]. The liquid atoms of the base fluid near a nanoparticle will be absorbed into the solid surface of the nanoparticle and form an absorption layer [56]. The interfacial layer between particles and base fluid has a remarkable effect on thermal conductivity. For non-spherical particles, the surface area of the interfacial layer is much larger than that of spherical particles, which can trigger a larger heat flux. Nan et al. [57] presented a model for CNT nanofluids considering the interfacial thermal barrier resistance and found a significant interface effect on TCE. Many models [58,59,60] were built by considering the interfacial layer effect. The benefit of this theory is that it considers the effect of particle morphology from the microscopic point of view. Chandrasekar et al. [61] proposed a model considering the interfacial layer thickness, particle shape, and Brownian motion. They attributed the anomalous TCE to the particle shape.

Timofeeva et al. [34] believed that TCE for NSN nanofluids depends on the competition between surface contact area (enhancement) and Kapitza resistance (weakening). The model predicted that TCE would be negative when sphericity is smaller than 0.6 for Al₂O₃–EG/water (50/50) nanofluids. Yang et al. [62,63,64] developed several EHC models based on the anisotropy analysis of cylindrical nanoparticles. They summed axial and radial direction heat transfer flux of cylindrical nanoparticles whose orientation distribution is uniform. These models are built exquisitely and are challenging to use. The shape of nanoparticles was first incorporated into an AI-based model for thermal conductivity by Cui et al. [35]. The results of the developed CFFNN model revealed that the cylindrical shape of nanoparticles with a large aspect ratio could trigger a rapid heat flow along longer thermally conducting pathways without the need to cross an interparticle boundary or junction point; this is beneficial to the thermal energy transfer in the nanofluids.

2.2.2. Nanoparticle Aggregation

The aggregation of nanoparticles significantly affects the thermal conductivity of nanofluid [65]. Studies based on nanofluid with spherical nanoparticles revealed that high TCE could be caused by particle aggregation [66]. Primary nanoparticles appear to aggregate to form aggregates or clusters which are non-spherical, particularly with increasing concentration. Wang et al. [67] evaluated the nanofluid thermal conductivity by molecular dynamics (MD) simulation and found that the aggregates can be divided into compact aggregation and loose aggregation. The atoms in the nanolayer are mobilized and dynamically balanced, which could be the mechanism for the TCE of the nanofluid. Due to the significant computational workload, only six nanoparticles were involved. Then, they proposed a hybrid method of multi-particle collision dynamics (MPCD) and MD to increase nanoparticles in calculations [68,69]. The simulations involving 32 nanoparticles showed that the EHC of nanofluid linearly increases with the decrease in the fractal dimension of the nanoparticle aggregates. Lee et al. [70] compared the classical density functional theory (DFT) to Poisson–Boltzmann theory and found a good agreement with experiments on heat transfer for nanofluids.

2.2.3. Network Effect

Sastry et al. [71] constructed a model based on the thermal resistance network by considering the random CNT orientation and CNT–CNT interaction. Their model effectively agreed with experimental data by assuming that a CNT contacts only two neighboring CNTs. Subsequently, Koo et al. [72] improved the model by considering the excluded volume of cylindrical particles. The revised model describes the effect of particle diameter and aspect ratio of CNTs and CNFs on TCE. The alignment of CNTs and CNFs due to the long-range repulsion force decreases the excluded volume, nonlinearly increasing the convexity and concavity and linearly increasing the thermal conductivity with particle concentration. Tahmooressi et al. [44] recently simulated the TCE of nanofluid using the lattice Boltzmann method and discovered that the network effect promotes the enhancement of heat transfer. Their algorithm prevents nanoparticles from forming aggregations by defining a minimum proximity distance.

2.2.4. Rotational Diffusion and Micro Convection

Xue [73] presented the equivalent field factor for CNTs distributed randomly in the base fluid and constructed a model for CNT nanofluids based on the Maxwell theory. They took the CNT as a rotational elliptical particle with a large aspect ratio. Ebrahimi et al. [74,75] built a model by neglecting the micro convection at the surface of cylindrical particles because the Brownian motion is slow. In addition, the collision model for non-spherical particles is difficult to construct. Models with the Brownian effect are based on spherical particles [76,77]. Cui et al. [78] found that cylindrical nanoparticles have a larger surface area and more energetic atoms than spherical nanoparticles, resulting in a larger TCE. Moreover, the high-speed rotation of cylindrical nanoparticles accelerates micro convection in the base fluid due to the stirring effect.

Table 2. Typical models for TCE of NSN nanofluids.

Authors	Particle Shape	Models (knf/kf as Default)	Remarks
Hamilton and Crosser [53]	Arbitrary	$\frac{k_p+\left(n-1\right)k_f-\left(n-1\right)(k_p-k_f)\varphi }{k_p+\left(n-1\right)k_f+(k_p-k_f)\varphi }$	Reduce to Maxwell model when n = 3
Yamada and Ota [79]	Cylinder	$\frac{k_p/k_f+K-K\varphi (1-k_p/k_f)}{k_p/k_f+K+\varphi (1-k_p/k_f)}$	Unit-cell model Consider the shape factor K = 2ϕ0.2 (2 l/d) for cylindrical particles
Wang et al. [54]	Aggregates	${{\displaystyle k}}_{eff}=(1-\mathsf{\Phi })+3\mathsf{\Phi }{{\displaystyle \int }}_0^{\infty }\frac{\frac{{{\displaystyle k}}_{cl}(r)n(r)}{{{\displaystyle k}}_{cl}(r)+2{{\displaystyle k}}_f}dr}{(1-\mathsf{\Phi })+3\mathsf{\Phi }{{\displaystyle \int }}_0^{\infty }\frac{{{\displaystyle k}}_{f}n(r)}{{{\displaystyle k}}_{cl}(r)+2{{\displaystyle k}}_f}dr}$	Combine the effective medium approximation and the fractal theory
Nan et al. [57]	CNTs	$\frac{3+(\frac{2({{\displaystyle k}}_{11}^c-{{\displaystyle k}}_f)}{{{\displaystyle k}}_{11}^c+{{\displaystyle k}}_f}+\frac{{{\displaystyle k}}_{33}^c}{{{\displaystyle k}}_f}-1)\mathsf{\Phi }}{3-\frac{2({{\displaystyle k}}_{11}^c-{{\displaystyle k}}_f)}{{{\displaystyle k}}_{11}^c+{{\displaystyle k}}_f}\mathsf{\Phi }}$	Incorporating the interface thermal resistance
Xue [73]	CNTs	$\frac{1-\mathsf{\Phi }+2\mathsf{\Phi }\frac{{{\displaystyle k}}_p}{{{\displaystyle k}}_p-{{\displaystyle k}}_f}\ln \frac{{{\displaystyle k}}_p+{{\displaystyle k}}_f}{2{{\displaystyle k}}_f}}{1-\mathsf{\Phi }+2\mathsf{\Phi }\frac{{{\displaystyle k}}_f}{{{\displaystyle k}}_p-{{\displaystyle k}}_f}\ln \frac{{{\displaystyle k}}_p+{{\displaystyle k}}_f}{2{{\displaystyle k}}_f}}$	Based on Maxwell theory and considering the random CNT orientation distribution
Zhou and Gao [58]	Ellipsoid	Complicated	Differential effective medium theory
Ebrahimi et al. [74,75]	Cylinders/CNTs	$\begin{array}{l}1-\varphi \left(1+M^{\prime }\right)+\varphi k_f\left(k_p+k_{layer}{M}^{\prime }\right)+\varphi \left(1+M^{\prime }\right)\\ \frac{a_f}{{\mathrm{Pr}}_f\left(2a_p+\delta \right)}\left(0.35+0.56{\mathrm{Re}}_f^{0.52}\right){\mathrm{Pr}}_f^{0.3}\end{array}$	Interfacial layer theory Brownian motion is neglected
Sastry et al. [71]	CNTs	${{\displaystyle k}}_{eff}=\frac{X}{A}{({\displaystyle \sum _{i=1}^N\frac{1}{\frac{k_{Fluid}A}{d{x}_i}+\frac{M}{\frac{L_i}{\pi k_{CNT}{d}^2}+\frac{2}{G{d}^2}}}})}^{-1}$	Assuming CNT contacts only two neighboring CNTs
Koo et al. [72]	CNTs/CNFs	Based on model proposed by [71]	Excluded volume concept Monte Carlo simulation
Murshed et al. [59]	Cylinder	$\begin{array}{l}{{\displaystyle k}}_{eff}=(({{\displaystyle k}}_p-{{\displaystyle k}}_{lr}){{\displaystyle \mathsf{\Phi }}}_p{{\displaystyle k}}_{lr}[2{{\displaystyle \gamma }}_1^3-{\gamma }^3+1]\\ +(k_{\mathrm{p}}+2k_{\mathrm{lr}})\times {\gamma }_1^3\left[{\mathsf{\Phi }}_{\mathrm{p}}{\gamma }^3\right({{\displaystyle k}}_{\mathrm{lr}}-{{\displaystyle k}}_{\mathrm{f}})\\ +{{\displaystyle k}}_{\mathrm{f}}\left]\right)({{\displaystyle \gamma }}_1^3({{\displaystyle k}}_{\mathrm{p}}+2{{\displaystyle k}}_{\mathrm{lr}})-\\ ({{\displaystyle k}}_{\mathrm{p}}-{{\displaystyle k}}_{\mathrm{lr}}){{\displaystyle \mathsf{\Phi }}}_p[{\gamma }_1^3+{{\displaystyle \gamma }}^3-1]{)}^{-1}\end{array}$	Deduced in cylindrical coordinates
Timofeeva et al. [34]	Rods/bricks/ platelets/blades	$1+(C_k^{shape}+C_k^{surface})\mathsf{\Phi }$	Consider particle shape and interfacial contributions
Chandrasekar et al. [61]	Arbitrary	$\frac{k_s+(n-1)k+(n-1){(1+\beta )}^3\mathsf{\Phi }(k_s-k)}{k_s+(n-1)k-{(1+\beta )}^3\mathsf{\Phi }({{\displaystyle k}}_s-k)}+c\frac{\mathsf{\Phi }(T-T_0)}{\mu k{a}^4}$	Consider interfacial layer, particle shape, and Brownian motion
Cui et al. [78]	Cylinder	$k=\frac{1}{3V{k}_B{T}^2}{\int }_0^{\infty }〈J(0)J\left(\mathrm{t}\right)〉dt$	14.8% enhancement MD simulation based on the Green–Kubo formula
Jiang et al. [60]	CNTs	$\frac{k_{p}R(1+t/R-k_f/k_p)\ln (1+t/R)}{t{k}_f\ln \left[(1+t/R)k_p/k_f)\right]}{\beta }_1=1+t/R$	Interfacial layer theory
Yang et al. [64]	Cylinder	$k_{eff}=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\pi }{\int }}(k_z^2},{\sin }^2\phi +k_x^2,{\cos }^2\phi {)}^{1/2}d\phi$ $k_{eff}=k_{eff2}\frac{2\pi rH}{2\pi r^2+2\pi rH}+k_{eff2}\frac{R_x}{R_z}\frac{2\pi r^2}{2\pi r^2+2\pi rH}$ $k_{eff2}=\frac{(k_p-k_{lr})\varphi k_{lr}({\beta }_1^2-{\beta }^2+1)+({{\displaystyle k}}_p+k_{lr}){\beta }_1^2\left[\varphi {\beta }^2(k_{lr}-k_f)+k_f\right]}{{\beta }_1^2(k_p+k_{lr})-(k_p-k_{lr}){\varphi }_p({\beta }_1^2+{\beta }^2-1)}$	Interfacial layer theory Consider end effect of cylinder
Yang et al. [62]	Cylinder	$k_{eff}=\frac{(H+2t)k_{eff\_x}+(R+t)k_{eff\_z}}{H+R+3t}$	Interfacial layer theory Anisotropy analysis
Yang and Xu [63]	Cylinder	$\frac{\overline{k_{pe}}+k_{bf}(n-1)+(n+1)(\overline{k_{pe}}-k_{bf})(1+C)\varphi }{\overline{k_{pe}}+k_{bf}(n-1)-(\overline{k_{pe}}-k_{bf})(1+C)\varphi }$	Based on Hamilton–Crosser model Interfacial layer theory Anisotropy analysis
Wang et al. [67]	Aggregates (2–6 spheres)	Increases linearly with decrease in fractal dimension of aggregations	MD simulation Interfacial layer effect
Du et al. [69]	Aggregates (6–32 spheres)	Increases linearly with decrease in fractal dimension of aggregations	MPCD-MD simulation Interfacial layer effect
Tahmooressi et al. [44]	Cylinder	$k_{eff}=\frac{L{\displaystyle \int qdA}}{\Delta T{\displaystyle \int dA}}$	Lattice Boltzmann method
Cui et al. [35]	Arbitrary	-	CFFNN model Artificial intelligence estimation

Table 2. Typical models for TCE of NSN nanofluids.

Authors	Particle Shape	Models (knf/kf as Default)	Remarks
Hamilton and Crosser [53]	Arbitrary	$\frac{k_p+\left(n-1\right)k_f-\left(n-1\right)(k_p-k_f)\varphi }{k_p+\left(n-1\right)k_f+(k_p-k_f)\varphi }$	Reduce to Maxwell model when n = 3
Yamada and Ota [79]	Cylinder	$\frac{k_p/k_f+K-K\varphi (1-k_p/k_f)}{k_p/k_f+K+\varphi (1-k_p/k_f)}$	Unit-cell model Consider the shape factor K = 2ϕ0.2 (2 l/d) for cylindrical particles
Wang et al. [54]	Aggregates	${{\displaystyle k}}_{eff}=(1-\mathsf{\Phi })+3\mathsf{\Phi }{{\displaystyle \int }}_0^{\infty }\frac{\frac{{{\displaystyle k}}_{cl}(r)n(r)}{{{\displaystyle k}}_{cl}(r)+2{{\displaystyle k}}_f}dr}{(1-\mathsf{\Phi })+3\mathsf{\Phi }{{\displaystyle \int }}_0^{\infty }\frac{{{\displaystyle k}}_{f}n(r)}{{{\displaystyle k}}_{cl}(r)+2{{\displaystyle k}}_f}dr}$	Combine the effective medium approximation and the fractal theory
Nan et al. [57]	CNTs	$\frac{3+(\frac{2({{\displaystyle k}}_{11}^c-{{\displaystyle k}}_f)}{{{\displaystyle k}}_{11}^c+{{\displaystyle k}}_f}+\frac{{{\displaystyle k}}_{33}^c}{{{\displaystyle k}}_f}-1)\mathsf{\Phi }}{3-\frac{2({{\displaystyle k}}_{11}^c-{{\displaystyle k}}_f)}{{{\displaystyle k}}_{11}^c+{{\displaystyle k}}_f}\mathsf{\Phi }}$	Incorporating the interface thermal resistance
Xue [73]	CNTs	$\frac{1-\mathsf{\Phi }+2\mathsf{\Phi }\frac{{{\displaystyle k}}_p}{{{\displaystyle k}}_p-{{\displaystyle k}}_f}\ln \frac{{{\displaystyle k}}_p+{{\displaystyle k}}_f}{2{{\displaystyle k}}_f}}{1-\mathsf{\Phi }+2\mathsf{\Phi }\frac{{{\displaystyle k}}_f}{{{\displaystyle k}}_p-{{\displaystyle k}}_f}\ln \frac{{{\displaystyle k}}_p+{{\displaystyle k}}_f}{2{{\displaystyle k}}_f}}$	Based on Maxwell theory and considering the random CNT orientation distribution
Zhou and Gao [58]	Ellipsoid	Complicated	Differential effective medium theory
Ebrahimi et al. [74,75]	Cylinders/CNTs	$\begin{array}{l}1-\varphi \left(1+M^{\prime }\right)+\varphi k_f\left(k_p+k_{layer}{M}^{\prime }\right)+\varphi \left(1+M^{\prime }\right)\\ \frac{a_f}{{\mathrm{Pr}}_f\left(2a_p+\delta \right)}\left(0.35+0.56{\mathrm{Re}}_f^{0.52}\right){\mathrm{Pr}}_f^{0.3}\end{array}$	Interfacial layer theory Brownian motion is neglected
Sastry et al. [71]	CNTs	${{\displaystyle k}}_{eff}=\frac{X}{A}{({\displaystyle \sum _{i=1}^N\frac{1}{\frac{k_{Fluid}A}{d{x}_i}+\frac{M}{\frac{L_i}{\pi k_{CNT}{d}^2}+\frac{2}{G{d}^2}}}})}^{-1}$	Assuming CNT contacts only two neighboring CNTs
Koo et al. [72]	CNTs/CNFs	Based on model proposed by [71]	Excluded volume concept Monte Carlo simulation
Murshed et al. [59]	Cylinder	$\begin{array}{l}{{\displaystyle k}}_{eff}=(({{\displaystyle k}}_p-{{\displaystyle k}}_{lr}){{\displaystyle \mathsf{\Phi }}}_p{{\displaystyle k}}_{lr}[2{{\displaystyle \gamma }}_1^3-{\gamma }^3+1]\\ +(k_{\mathrm{p}}+2k_{\mathrm{lr}})\times {\gamma }_1^3\left[{\mathsf{\Phi }}_{\mathrm{p}}{\gamma }^3\right({{\displaystyle k}}_{\mathrm{lr}}-{{\displaystyle k}}_{\mathrm{f}})\\ +{{\displaystyle k}}_{\mathrm{f}}\left]\right)({{\displaystyle \gamma }}_1^3({{\displaystyle k}}_{\mathrm{p}}+2{{\displaystyle k}}_{\mathrm{lr}})-\\ ({{\displaystyle k}}_{\mathrm{p}}-{{\displaystyle k}}_{\mathrm{lr}}){{\displaystyle \mathsf{\Phi }}}_p[{\gamma }_1^3+{{\displaystyle \gamma }}^3-1]{)}^{-1}\end{array}$	Deduced in cylindrical coordinates
Timofeeva et al. [34]	Rods/bricks/ platelets/blades	$1+(C_k^{shape}+C_k^{surface})\mathsf{\Phi }$	Consider particle shape and interfacial contributions
Chandrasekar et al. [61]	Arbitrary	$\frac{k_s+(n-1)k+(n-1){(1+\beta )}^3\mathsf{\Phi }(k_s-k)}{k_s+(n-1)k-{(1+\beta )}^3\mathsf{\Phi }({{\displaystyle k}}_s-k)}+c\frac{\mathsf{\Phi }(T-T_0)}{\mu k{a}^4}$	Consider interfacial layer, particle shape, and Brownian motion
Cui et al. [78]	Cylinder	$k=\frac{1}{3V{k}_B{T}^2}{\int }_0^{\infty }〈J(0)J\left(\mathrm{t}\right)〉dt$	14.8% enhancement MD simulation based on the Green–Kubo formula
Jiang et al. [60]	CNTs	$\frac{k_{p}R(1+t/R-k_f/k_p)\ln (1+t/R)}{t{k}_f\ln \left[(1+t/R)k_p/k_f)\right]}{\beta }_1=1+t/R$	Interfacial layer theory
Yang et al. [64]	Cylinder	$k_{eff}=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\pi }{\int }}(k_z^2},{\sin }^2\phi +k_x^2,{\cos }^2\phi {)}^{1/2}d\phi$ $k_{eff}=k_{eff2}\frac{2\pi rH}{2\pi r^2+2\pi rH}+k_{eff2}\frac{R_x}{R_z}\frac{2\pi r^2}{2\pi r^2+2\pi rH}$ $k_{eff2}=\frac{(k_p-k_{lr})\varphi k_{lr}({\beta }_1^2-{\beta }^2+1)+({{\displaystyle k}}_p+k_{lr}){\beta }_1^2\left[\varphi {\beta }^2(k_{lr}-k_f)+k_f\right]}{{\beta }_1^2(k_p+k_{lr})-(k_p-k_{lr}){\varphi }_p({\beta }_1^2+{\beta }^2-1)}$	Interfacial layer theory Consider end effect of cylinder
Yang et al. [62]	Cylinder	$k_{eff}=\frac{(H+2t)k_{eff\_x}+(R+t)k_{eff\_z}}{H+R+3t}$	Interfacial layer theory Anisotropy analysis
Yang and Xu [63]	Cylinder	$\frac{\overline{k_{pe}}+k_{bf}(n-1)+(n+1)(\overline{k_{pe}}-k_{bf})(1+C)\varphi }{\overline{k_{pe}}+k_{bf}(n-1)-(\overline{k_{pe}}-k_{bf})(1+C)\varphi }$	Based on Hamilton–Crosser model Interfacial layer theory Anisotropy analysis
Wang et al. [67]	Aggregates (2–6 spheres)	Increases linearly with decrease in fractal dimension of aggregations	MD simulation Interfacial layer effect
Du et al. [69]	Aggregates (6–32 spheres)	Increases linearly with decrease in fractal dimension of aggregations	MPCD-MD simulation Interfacial layer effect
Tahmooressi et al. [44]	Cylinder	$k_{eff}=\frac{L{\displaystyle \int qdA}}{\Delta T{\displaystyle \int dA}}$	Lattice Boltzmann method
Cui et al. [35]	Arbitrary	-	CFFNN model Artificial intelligence estimation

3. Convective Heat Transfer of NSN Nanofluids

Convective heat transport occurs when the bulk motion of nanofluids transports energy. The migration of suspended nanoparticles is induced by fluid hydrodynamics and thermodynamics. Furthermore, the relative motion between particles and a fluid affects the hydrodynamics and thermodynamics of the fluid. The complex interaction between discrete and continuous phases shows differences under different particle morphologies and surface treatments, flow structures, and heat transfer conditions. In this section, the experimental and numerical studies of NSN nanofluids are reviewed. The pool boiling heat transfer studies are not discussed since they have been exhaustively covered in the literature [8,80,81,82]. In addition, CHT based on hybrid nanofluids is not included; the related studies have been reviewed by Vallejo et al. [83]. Several recent studies have shown that hybrid nanofluids have significant potential as a coolant in solar cells [84,85].

3.1. Experimental Data Evaluation

The Nusselt number is used to evaluate the ratio of CHT across the boundary. A more significant Nusselt number corresponds to more active convection. The dimensionless local Nusselt number in the channel is defined as:

$$\mathrm{Nu}=\frac{h_{nf}D}{k_{nf}}$$

(3)

where the CHT coefficient is:

$$h_{nf}=\frac{q}{T_w-T_b}$$

(4)

where T_w is the wall temperature, T_b is the bulk temperature, and q is the heat flux. Flow loop experiments measure the parameters in Equation (4). A test section is set in a fully developed region with a straight or curved pipe/microchannel and a square or circular cross-section. In addition, it includes boundary layer flow, cavity flow [86,87], impinging jets, peristaltic flow, and flow in heat exchangers [12]. It can be divided into forced convection heat transfer or natural convection heat transfer. Based on the Reynolds number (Re = u₀ L/ν_nf), the flow state is laminar, turbulent, or transitional flow [88]. Ghasemiasl et al. [89] analyzed the studies on the forced convection of nanofluids in circular and non-circular channels in terms of geometry, particles, methodology, and regime. Researchers evaluated the CHT features of nanofluids affected by different types of parameters and flow conditions. Table 3 presents the experimental and numerical studies for CHT of NSN nanofluids. The nanofluid type, particle shape and size, particle loading, and flow state are listed with CHT characteristics. Notably, all of the variations of the CHT coefficient or Nusselt number are typically nonlinear.

3.1.1. Different Analysis Parameters and Values

Research findings on nanofluid CHT document controversial arguments. The first is whether the CHT, not just the factor of TCE, is enhanced by suspending nanoparticles in the base fluid. The second is whether the thermohydraulic performance of nanofluids is better than that of the base fluid, relating to the efficacy of nanofluids for practical cooling applications. The different views could be caused by different analysis parameters. Studies perform the standard dimensionless analysis of CHT based on the Nusselt number and Reynolds number.

Nonetheless, researchers believe that the constant Reynolds number basis can be misleading since the net result for the constant Reynolds number comparison combines the nanofluid property effect and the flow velocity effect [90]. In the interpretation of nanofluid CHT, Buschmann et al. [17] argued that no anomalous phenomena are involved in the forced convection heat transfer of nanofluids. Their results show that heat transfer enhancement provided by nanofluids equals the increase in thermal conductivity of nanofluids compared to the base fluid. The CHT coefficient rather than the Nusselt number is more suitable to evaluate the intensity of the CHT of nanofluids. A notable exception was the experiments performed with non-spherical particles showing CHT enhancement of NSN nanofluids. Therefore, it is necessary to discuss the CHT of NSN nanofluids.

The magnitude of parameters selected for study is another point of view in nanofluid research. For experimental studies, the values are practical. However, for some numerical studies, the range of parameters could be beyond the scope of practical applications. Buongiorno [91] first evaluated different mechanisms in the convective transport in nanofluids. Myers et al. [92] claimed that the use of parameter values should represent an actual physical situation. Therefore, the experimental and numerical studies are discussed separately in the next section.

3.1.2. Thermohydraulic Performance Evaluation

Thermohydraulic performance is evaluated via a different criterion. As a heat transfer medium, a nanofluid should meet the appropriate guidelines before it can be applied. Yu et al. [93] evaluated their experimental data by different forms of figures of merit (FOMs) as follows:

• The ratio of CHT coefficient, $\mathrm{F}\mathrm{O}{\mathrm{M}}_h=h_{nf}/h_b$;
• The ratio of the maximum overall temperature difference, $\mathrm{F}\mathrm{O}{\mathrm{M}}_T={\left(T_{w,o}-T_{in}\right)}_{nf}/{\left(T_{w,o}-T_{in}\right)}_b$;
• Cooling with minimum pumping power, $\mathrm{F}\mathrm{O}{\mathrm{M}}_P={\left(c_{p}h/P\right)}_{nf}/{\left(c_{p}h/P\right)}_b$;
• The relative ratio of heat transfer rate and pumping power, $\mathrm{F}\mathrm{O}{\mathrm{M}}_Q={\left(q/P\right)}_{nf}/{\left(q/P\right)}_b$.

The following criteria should be met: $\mathrm{F}\mathrm{O}{\mathrm{M}}_h>1$, $\mathrm{F}\mathrm{O}{\mathrm{M}}_T<1$, $\mathrm{F}\mathrm{O}{\mathrm{M}}_P>1$, and $\mathrm{F}\mathrm{O}{\mathrm{M}}_Q>1$. Research [94,95] has shown that the criteria for nanofluids with spherical particles are hardly met in tests. We sampled the CHT data of NSN nanofluids reported in the literature (Table 3). Ji et al. [96] used the relative thermal resistance to estimate the CHT performance of the nanofluid in an oscillating heat pipe; hence, the data are not shown. Nelson et al. [97] reported about 110 times viscosity of nanofluid with EG of 0.6% by weight in PAO, leading to a quite small FOM_P compared to others, which was excluded. The pumping power for other studies can be estimated based on Mansour et al. [98] for laminar and turbulent flows.

Most of the studies found an enhancement of the CHT coefficient if the FOM_h or FOM_T were used to evaluate the CHT varying with the Reynolds number. Nevertheless, suppose other performance evaluation criteria (PEC) are used. In that case, it can be found from the experimental data in Figure 5 that CHT was not far beyond the base fluid, with the majority of thermohydraulic FOM values being between 0.8 and 1.2. This is because the FOM_P and FOM_Q criteria were employed in most research, which combines heat transfer enhancement with an increase in pumping power. The heat capacity of nanofluids with low particle loading is close to that of the base fluid. The FOM_P for CNT nanofluids at Re = 1200 was a maximum of 1.536, which possibly meant that the data collection location was not fully developed. Ali et al. [99,100] tested the hydrodynamic performance of graphene nanoplatelet (GNP) nanofluids and discovered that the pumping power of nanofluids (caused by increased viscosity) was over twice that of the base fluid. Consequently, their results had the lowest FOM_P and FOM_Q values. Yu et al. [93] also found that different FOMs presented similar PEC for the same nanofluid.

Mikkola et al. [101] investigated the particle properties of CHT of nanofluids in the turbulent regime. Their experimental results based on oval-shaped Al₂O₃ nanoparticles demonstrated an increase of less than 5% in Nusselt number. Additionally, the CHT coefficient of nanofluids was roughly equal to that of base fluid when the volume concentration was lower than 1%. They used near-spherical particles. Furthermore, Ferrouillat et al. [42] and Wu et al. [102] investigated the CHT performance of nanofluids in turbulent regimes, and the PEC values were smaller than 1. Although the increased pumping power in turbulent flow is less than that of laminar flow, the thermohydraulic performance for NSN nanofluid in turbulent regimes is uneconomical. This also confirms why most recent studies are based on the laminar flow [89].

Yang et al. [23] and Contreras et al. [103] measured CHT coefficients of several types of nanofluids containing GNPs at different temperatures. The effect of operating temperature on CHT was unclear. In contrast, nanoparticle additives have a more significant impact on PEC. Table 3 shows that most tests are performed based on CNT or GNP nanofluids. These materials are easily accessible and commercially used in flow loop experiments. They have more significant thermal conductivity and specific surface area than those spherical particles. Bai et al. [104] also prepared GNP nanofluids with different particle loadings. The reported results revealed an increase in PEC with particle volume fraction.

Nonetheless, no similar findings were reported in other studies [93,101,102]. Similarly, no significant effect of shape factors on CHT was found, as shown in Figure 5. Additional data should be collected to confirm the CHT pattern of nanofluids under multiple factors.

Table 3. Experimental studies for CHT of NSN nanofluids.

Authors	Nanofluid	Particle Shape and Size (nm)	Particle Loading	Flow State	CHT Enhancement
Yang et al. [23]	Graphite–ATF graphite–oils	Plate-like, 1–2 µm (d) × 20–40 (l)	2, 2.5 wt.%	Laminar, 5 < Re < 110	Re↑, h↑ ϕ↑, h↑ T↑, h↓
Ding et al. [105]	CNTs–water	-	<1 wt.%	Laminar, 800 < Re < 1200	ϕ↑, h↑ (significantly) x/D↑, h↓, Δh/h pH↑, h↓
Chen et al. [3]	Titanate NTs–water	Nanotube 10 (d) × 100 (l)	0.5, 1.0 and 2.5 wt.%	Laminar, 1100 < Re < 2300	ϕ↑, h↑ x/D↑, h↓ Re↑, h↑
Nelson et al. [97]	Graphite–PAO	Plate-like, 20 µm (d) × 100 (l)	0.3 and 0.6 wt.%	Laminar, 72 < Re < 365	ϕ↑, h↑
Ji et al. [96]	Al2O3–EG and water (50/50)	Platelet, 9 (l) Blade, 60 (l) Cylinder, 80 (l)Brick, 40 (l)	0.3, 1, 3, and 5 vol.%	Oscillating heat pipe with input power 25–250 W	Heat transfer was enhanced significantly, nanofluids with cylindrical nanoparticles achieve the best performance
Yu et al. [10]	Al2O3–PAO	Nanorod 7 (d) × 85 (l)	0.65, 1.3 vol.%	Laminar, 150 < Re < 450	Re↑, h↑ ϕ↑, h↑ x/D↑, h↓
Ferrouillat et al. [42]	SiO2–water	Banana-like (nanorod)	2.28 vol.%	200 < Re < 15,000	Larger Nu for particles in banana shape than sphere in turbulent regime
Ferrouillat et al. [42]	ZnO–water	Polygonal/nanorod	0.82, 0.9 vol.%	200 < Re < 15,000	8% and 3% increase in Nu, respectively
Paul et al. [95]	Al2O3–NEILs	Whisker	0.18, 0.36, 0.9 vol.%	-	Degradation of natural convection
Wu et al. [102]	CNTs–water	Nanotube 9.5 (d) × 1500 (l)	<1 wt.%	-	Has no CHT enhancement
Arshad and Ali [100]	Graphene–water	Platelet, 5000–10,000 (d)	10 vol.%	300 < Re < 1000	Re↑, h↑ Pumping power increases as well
Mikkola et al. [101]	Al2O3–water	Ellipsoid, 10 (d)	0.5, 1 vol.%	1000 < Re < 11,000	Re↑, h↑, Nu↑ Φ/k↑, h = enhancement < 5%
Contreras et al. [103]	Graphene–EG and water (50/50)	Platelet	0.01, 0.05, 1 vol.%		Thermohydraulic performance coefficient ≈ 1
Bai et al. [104]	Graphene oxide–DI	Platelet, 0.8–1.2 (h) × 500–5000 (d)	0.02, 0.05, 0.075, 0.1 vol.%	150–800	ϕ↑, Nu ratio↑ Re↑, Nu ratio↑

Table 3. Experimental studies for CHT of NSN nanofluids.

Authors	Nanofluid	Particle Shape and Size (nm)	Particle Loading	Flow State	CHT Enhancement
Yang et al. [23]	Graphite–ATF graphite–oils	Plate-like, 1–2 µm (d) × 20–40 (l)	2, 2.5 wt.%	Laminar, 5 < Re < 110	Re↑, h↑ ϕ↑, h↑ T↑, h↓
Ding et al. [105]	CNTs–water	-	<1 wt.%	Laminar, 800 < Re < 1200	ϕ↑, h↑ (significantly) x/D↑, h↓, Δh/h pH↑, h↓
Chen et al. [3]	Titanate NTs–water	Nanotube 10 (d) × 100 (l)	0.5, 1.0 and 2.5 wt.%	Laminar, 1100 < Re < 2300	ϕ↑, h↑ x/D↑, h↓ Re↑, h↑
Nelson et al. [97]	Graphite–PAO	Plate-like, 20 µm (d) × 100 (l)	0.3 and 0.6 wt.%	Laminar, 72 < Re < 365	ϕ↑, h↑
Ji et al. [96]	Al2O3–EG and water (50/50)	Platelet, 9 (l) Blade, 60 (l) Cylinder, 80 (l)Brick, 40 (l)	0.3, 1, 3, and 5 vol.%	Oscillating heat pipe with input power 25–250 W	Heat transfer was enhanced significantly, nanofluids with cylindrical nanoparticles achieve the best performance
Yu et al. [10]	Al2O3–PAO	Nanorod 7 (d) × 85 (l)	0.65, 1.3 vol.%	Laminar, 150 < Re < 450	Re↑, h↑ ϕ↑, h↑ x/D↑, h↓
Ferrouillat et al. [42]	SiO2–water	Banana-like (nanorod)	2.28 vol.%	200 < Re < 15,000	Larger Nu for particles in banana shape than sphere in turbulent regime
Ferrouillat et al. [42]	ZnO–water	Polygonal/nanorod	0.82, 0.9 vol.%	200 < Re < 15,000	8% and 3% increase in Nu, respectively
Paul et al. [95]	Al2O3–NEILs	Whisker	0.18, 0.36, 0.9 vol.%	-	Degradation of natural convection
Wu et al. [102]	CNTs–water	Nanotube 9.5 (d) × 1500 (l)	<1 wt.%	-	Has no CHT enhancement
Arshad and Ali [100]	Graphene–water	Platelet, 5000–10,000 (d)	10 vol.%	300 < Re < 1000	Re↑, h↑ Pumping power increases as well
Mikkola et al. [101]	Al2O3–water	Ellipsoid, 10 (d)	0.5, 1 vol.%	1000 < Re < 11,000	Re↑, h↑, Nu↑ Φ/k↑, h = enhancement < 5%
Contreras et al. [103]	Graphene–EG and water (50/50)	Platelet	0.01, 0.05, 1 vol.%		Thermohydraulic performance coefficient ≈ 1
Bai et al. [104]	Graphene oxide–DI	Platelet, 0.8–1.2 (h) × 500–5000 (d)	0.02, 0.05, 0.075, 0.1 vol.%	150–800	ϕ↑, Nu ratio↑ Re↑, Nu ratio↑

Figure 5. Thermohydraulic performance evaluation in the literature [3,10,23,42,100,101,103,104,105].

Figure 5. Thermohydraulic performance evaluation in the literature [3,10,23,42,100,101,103,104,105].

3.2. Numerical Predictions and Mechanism Discussion

Zahmatkesh et al. [12] recently reviewed nanoparticle shape effects in different flow regimes. They listed approximately 60 relevant publications and found no uniform conclusion on the effect of nanoparticle shape on CHT. The platelet-shaped nanoparticles caused the best CHT performance in the natural and forced convection regimes. Nonetheless, most of the works reported the optimum CHT for the blade-shaped nanoparticles in the mixed convection regime. More attention has been channeled to numerical predictions [89], and only one of these studies is based on experiments [95]. Some typical numerical studies for CHT of NSN nanofluids are listed chronologically in Table 4. Minea et al. [106] recently performed a benchmark study on nanofluid simulations. The main difference between thermal conductivity and CHT is the state of particle additives. Driven by the hydrodynamics and the inhomogeneous temperature field, the movement and distribution of particles will be inhomogeneous.

3.2.1. Particle Concentration Distribution and Interaction

Sonication promotes the uniform dispersion of nanoparticles in the base fluid during preparation. Nonetheless, there is no uniform standard for optimal ultrasonication duration for different types of nanofluids [13]. In addition, the uniform distribution of nanoparticles is overlooked by researchers. Lin et al. [107] simulated the particle number concentration in a straight pipe using the method of moments. The results revealed the non-uniformity of the cylindrical nanoparticle volume concentration across the section. Yuan et al. [108] modeled the Poiseuille flow and CHT of nanofluids in a circular minichannel and found that the nanorod volume fraction distribution is non-uniform near the boundary.

In contrast, the particles are more uniform when their aspect ratio is larger. The thermal resistance and temperature gradient are largest near the wall and are sensitive to particle concentration. Lin et al. [109,110,111] investigated the distribution and deposition of cylindrical nanoparticles in turbulent straight and curved pipes. The coupled model considered the effect of turbulent diffusivity on particle concentration distribution and interaction. The results revealed that the distribution of the particle concentration in the cross-section becomes non-uniform along the flow direction. In the curved duct, the extent of non-uniformity of the distribution of the particle number concentration increases with increasing Stokes number, Dean number, Reynolds number, and particle AR. They showed that particle transport and deposition in curved tubes are important; however, limited studies have considered the effect. Their numerical results demonstrated that the penetration efficiency increases as the Dean number, Reynolds number, and particle aspect ratio decrease. The penetration efficiency is highest when the Stokes number is approximately 0.02.

3.2.2. Particle Rotational Diffusion and Orientation Distribution

The morphology and orientation of the dispersed solids are complex in particle suspensions. Yu et al. [10] suggested four possible particle configurations in nanofluids, including the parallel series, Hashin–Shtrikman (or H-S), and EMT configurations. Researchers assume the H-S configuration when the TCE is estimated [64,72]. Nevertheless, the alignment of non-spherical nanoparticles is apparent in internal flows, specifically near the wall. Researchers give less consideration to the orientation distribution of nanoparticles. Elias et al. [112,113] found the highest overall heat transfer coefficient when nanofluids with cylindrical shapes were used for nanofluid flow in a shell and tube heat exchanger.

Moreover, non-spherical nanoparticles rotate, which delays and disturbs the thermal boundary layer [102]. The rotational diffusion coefficient of nanoparticles has recently attracted research attention. Lin et al. [109,110,111] and Yuan et al. [108] analyzed the turbulent and laminar NSN nanofluid flows in straight or turbulent pipes by considering the Brownian rotational diffusion and orientation distribution. They found that the orientation distribution of cylindrical nanoparticles was less concentrated as the Reynolds number increased in the turbulent regime. Particle orientation components at the cross-section are nearly 1/3, implying that the nanorod orientation is nearly random in space at the channel center. The nanorod is more likely to align with the flow direction with the increasing shear near the wall. A nanorod with a higher aspect ratio is likely to be rotating towards the flow direction.

Table 4. Typical numerical studies for CHT of NSN nanofluids.

Authors	Nanofluid	Particle Shape and Size (nm)	Particle Loading	Flow State	CHT Enhancement
Elias et al. [112,113]	γ-AlOOH–EG and water (50/50)	Cylinder, AR = 1:8 Brick, AR = 1:1:1 Blade, AR = 1:6:1/12 Platelet, AR = 1:1/8	<1 vol.%	In shell and tube heat exchanger	Cylinder >brick > blade > platelet > sphere, for h, entropy generation, and heat transfer rate of nanofluid
Amin et al. [114]	Al2O3–water/Ethylene glycol	Platelets, AR = 0.125 Blades, 1:6:1.12 Cylinders, AR = 8 Bricks, 1:1:1	1 vol.%	Flat-plate solar collector tube 12,000 < Re < 25,000	Brick-shape particles have the highest Nusselt number
Ooi and Popov [115]	Cu–water	Oblate spheroid, Prolate spheroid	<20 vol.%	Natural convection in a square cavity	Increases the CHT as well as flow resistance
Lin et al. [116]	Cu–water	Cube, rod, lamina, tetrahedron	<6 vol.%	Marangoni boundary layer flow	Sphere nanoparticles have the best CHT enhancement
Lin et al. [107]	Al2O3–PAO	Cylinder AR = 6, 12, 18	0.65, 1.3, 2.5 vol.%	Laminar, 100 < Re < 2000	Nusselt number increases with ϕ, derived Nu formula based on the numerical data
Yuan et al. [117]	ZnO–water	Cylinder AR = 8, 12, 16	0.4, 0.93, 1.3 vol.%	Turbulent, 2500 < Re < 15,000	Nunf/Nuf increases when Reynolds number, AR and ϕ grow
Trodi and Benhamza [118]	Al2O3–water	Oblate spheroid, dp = 1 Prolate spheroid, dp = 2, 5, 7.5 and 10	5, 10 vol.%	Flow in differentially heated square enclosures, 103 < Ra < 106	Heat transfer increases with Ra and ϕ, oblate spheroid has the best performance
Liu et al. [119]	Al2O3–water	Platelet, 78.6 (d) × 9.8 (l) Blade, 85 (l) × 14.15 (w) ×1.18 (h) Cylinder, 19.6 (d) × 157 (l) Brick, 36.6 (l)	0.5, 1, 1.5, 2 vol.%	Curved square duct laminar flow	Eulerian–Lagrangian two-phase approach
Sheikhzadeh and Aghaei [120]	Al2O3/SiO2–water	Platelets, AR = 0.125 Blades, 1:6:1.12 Cylinders, AR = 8 Bricks, 1:1:1	2–4 vol.%	Square cavity flow, 105 < Ra < 107	Platelets and cylindrical nanoparticles are more effective
Lin et al. [121]	ZnO–water	Cylinder AR = 2, 6, 10, 14	<5 vol.%	Curved pipe flow, 5000 ≤ Re ≤ 30,000	Nanofluid PEC is higher than base fluid PEC

Table 4. Typical numerical studies for CHT of NSN nanofluids.

Authors	Nanofluid	Particle Shape and Size (nm)	Particle Loading	Flow State	CHT Enhancement
Elias et al. [112,113]	γ-AlOOH–EG and water (50/50)	Cylinder, AR = 1:8 Brick, AR = 1:1:1 Blade, AR = 1:6:1/12 Platelet, AR = 1:1/8	<1 vol.%	In shell and tube heat exchanger	Cylinder >brick > blade > platelet > sphere, for h, entropy generation, and heat transfer rate of nanofluid
Amin et al. [114]	Al2O3–water/Ethylene glycol	Platelets, AR = 0.125 Blades, 1:6:1.12 Cylinders, AR = 8 Bricks, 1:1:1	1 vol.%	Flat-plate solar collector tube 12,000 < Re < 25,000	Brick-shape particles have the highest Nusselt number
Ooi and Popov [115]	Cu–water	Oblate spheroid, Prolate spheroid	<20 vol.%	Natural convection in a square cavity	Increases the CHT as well as flow resistance
Lin et al. [116]	Cu–water	Cube, rod, lamina, tetrahedron	<6 vol.%	Marangoni boundary layer flow	Sphere nanoparticles have the best CHT enhancement
Lin et al. [107]	Al2O3–PAO	Cylinder AR = 6, 12, 18	0.65, 1.3, 2.5 vol.%	Laminar, 100 < Re < 2000	Nusselt number increases with ϕ, derived Nu formula based on the numerical data
Yuan et al. [117]	ZnO–water	Cylinder AR = 8, 12, 16	0.4, 0.93, 1.3 vol.%	Turbulent, 2500 < Re < 15,000	Nunf/Nuf increases when Reynolds number, AR and ϕ grow
Trodi and Benhamza [118]	Al2O3–water	Oblate spheroid, dp = 1 Prolate spheroid, dp = 2, 5, 7.5 and 10	5, 10 vol.%	Flow in differentially heated square enclosures, 103 < Ra < 106	Heat transfer increases with Ra and ϕ, oblate spheroid has the best performance
Liu et al. [119]	Al2O3–water	Platelet, 78.6 (d) × 9.8 (l) Blade, 85 (l) × 14.15 (w) ×1.18 (h) Cylinder, 19.6 (d) × 157 (l) Brick, 36.6 (l)	0.5, 1, 1.5, 2 vol.%	Curved square duct laminar flow	Eulerian–Lagrangian two-phase approach
Sheikhzadeh and Aghaei [120]	Al2O3/SiO2–water	Platelets, AR = 0.125 Blades, 1:6:1.12 Cylinders, AR = 8 Bricks, 1:1:1	2–4 vol.%	Square cavity flow, 105 < Ra < 107	Platelets and cylindrical nanoparticles are more effective
Lin et al. [121]	ZnO–water	Cylinder AR = 2, 6, 10, 14	<5 vol.%	Curved pipe flow, 5000 ≤ Re ≤ 30,000	Nanofluid PEC is higher than base fluid PEC

4. Conclusions

Research on heat transfer enhancement of nanofluids is a long-term global initiative, and the unified understanding of this issue continues. Herein, we reviewed the heat transfer enhancement of nanofluids containing non-spherical nanoparticles. Non-spherical nanoparticles suspended in nanofluids were divided into three categories based on the dimension of the geometric particle structure. We collected and analyzed data on thermal conductivity and convective heat transfer enhancement of nanofluids measured in experiments. Recent studies investigated the numerical predictions and related heat transfer mechanisms. The main conclusions for NSN nanofluids are as follows:

Due to large aspect ratios, thermal conductivity is enhanced abnormally only for nanofluids containing carbon nanotubes/nanofibers/nanowires. On the other hand, thermal conductivity enhancement per concentration is larger for nanorods/ellipsoids with small aspect ratios. The enhancement of the network effect on heat transfer is limited. Polygonal particles enhanced the thermal conductivity least due to the sphericity being close to 1. The approximate enhancement effect by three types of non-spherical nanoparticles on thermal conductivity is 4.5:2.5:1. However, the particle size effect on nanofluids’ thermal conductivity is unclear.

The convective heat transfer coefficient is increased by suspending non-spherical nanoparticles in the base fluid. Due to the increase in pumping power, no significant thermohydraulic performance was found for convective heat transfer of NSN nanofluid flow. NSN nanofluid is uneconomical for turbulent flows, and the temperature and particle concentration effect on convective heat transfer remains unclear. In addition, there is no perfect model to precisely predict the thermal conductivity and convective heat transfer of NSN nanofluids.