Thermophysical Property Assessment of Metal Oxide-Based Nanofluids: Comparison
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Energy consumption in the industrial sector can be significantly reduced by improving heat transfer rates in heat exchanger circuits, pool boiling, metal cutting industries, etc. Numerous energy-related issues can be overcome to a large extent by improving heat flow properties by utilizing nanofluids. As to the improvement in thermophysical properties of metal oxide-based nanofluids, key parameters affecting the thermophysical properties of nanofluids, such as particle volume fraction, temperature, particle size and various stabilizers, were involved. The importance of DLVO theory and zeta potential to control the electrostatic repulsion and pH values of nanofluids for stable nanofluid formulations were highlighted. It has been observed that classical theories of thermal conductivity and viscosity cannot predict exact values for a wide range of variables. Therefore, various extensive correlations have been introduced to predict the thermophysical properties of nanofluids.

  • thermal conductivity
  • zetapotential
  • viscosity
  • specific heat
  • wettability
  • pool boiling
  • energy efficiency

1. Introduction

Out of the total energy harnessed directly and indirectly, 70% is produced by heat generation
[1]
. Therefore, heat exchange systems must be better engineered for more efficient energy consumption. The improvement of conductive and convective heat transfer is one of the most significant scientific challenges in almost every industrial sector. This can be achieved by changing flow geometry, boundary conditions, or by enhancing thermophysical properties of the fluid. It has been proven over the years that thermal fluids are responsible for minimizing energy loss in heat transfer systems
[2][3]
. Due to the exhaustion of natural resources and the increase in the demand for energy, it is very important to increase the energy efficiency of heat transfer devices. After many years of investigation, researchers have proved that nanofluids have the potential for improving the efficiency of heating and devices
[4][5]
. Traditionally, heat dissipation is augmented by increasing the surface area of the system, but this leads to an undesirable size of the thermal management system. Therefore, the innovative concept of nanofluids has attracted great attention to maintain miniaturized systems with improved efficiency. The emergence of nanofluids has improved the heat transfer in the thermal systems like solar heat collectors, high power engines, microelectronic devices, and nuclear reactors
[6]
. Nanofluids are homogeneous suspensions of nanoparticles in different base fluids such as water, ethylene glycol, lubricating oils, etc.
[7][8]
. These nanoparticles upgrade the thermophysical properties such as viscosity, thermal conductivity, specific heat capacity (SHC), diffusivity, and density of the base fluids to a great extent. These suspended nanoparticles can be metallic, nonmetallic, metal oxides, and other compounds. Out of these, the suspensions of metal oxide nanoparticles are widely used due to their chemical stability, economy, and ease of production. Widely used metal oxide nano particles include Al2O3, SiO2, TiO2 and CuO
[9][10][11][12]
.
Maxwell originally proposed the theoretical model for improving the thermal conductivity of suspensions containing solid particles compared to the base liquid
[13]
. When the density of coarse particles is high or the average particle size is large, the suspensions lead to a lack of stability, and it finally settles down. This leads to additional flow resistance and possible erosion in the components of the system. Fluids with suspended nanometer-scaled particles (less than 100 nm) are termed as nanofluids, a term proposed by Choi in 1995
[14]
. These fluids are considered as next generation heat transfer fluids. The large surface area of nano particles enhances both the stability and heat transfer within the system. It also improves the abrasion-related properties as compared to the conventional solid–liquid mixtures.
Nano particles are classified as metallic and nonmetallic according to the material type. Depending on the constituent material type, stabilizing methods of the nano particles are varied. Among various nanofluids, metal-oxide based nanofluids are most widely applicable due to their long shelf life and chemical and thermal stability
[15]
.

2. Effect of Metal-Oxide Based Nanofluids on Thermophysical Properties

2.1. Specific Heat

Specific heat capacity (SHC) of a nanofluid is defined as the capability of the nanofluid to absorb heat energy without any phase change. It quantifies various essential thermal behaviors such as the rate of heat transfer, the efficiency of the heat exchanger and the average Nusselt number. Specific heat capacity is critical to the accurate design and assembly of heat transfer applications through cooling and lubrication systems, such as solar collectors, refrigeration and air conditioning, machining, etc.

2.1. Specific Heat

Specific heat capacity (SHC) of a nanofluid is defined as the capability of the nanofluid to absorb heat energy without any phase change. It quantifies various essential thermal behaviors such as the rate of heat transfer, the efficiency of the heat exchanger and the average Nusselt number. Specific heat capacity is critical to the accurate design and assembly of heat transfer applications through cooling and lubrication systems, such as solar collectors, refrigeration and air conditioning, machining, etc.
[16][17][18]
. The governing equations below show the effect of specific heat capacity on thermal transport properties such as thermal diffusivity, thermal conductivity, density, and the efficiency of the heat exchanger, etc.
(1)
where k, ρ, Cp and α denote thermal conductivity, density, specific heat capacity and thermal diffusivity, respectively. Rate of heat transfer, ,is given by the following equation.
 (2)
where m
. and ΔT represent mass flow rate and temperature difference, respectively [17]. For example, the effectiveness of the heat exchanger system, ε, is given by the following equation.
(3)
(4)
where NTU, Cmin, Cmax, U and A are the number of transfer units, minimum heat capacity rate, maximum heat capacity rate, overall heat transfer coefficient and heat transfer area, respectively. The experimentally developed local heat transfer coefficients are generally validated by the Dittus–Boelter correlation, which is given below [18].
(5)
（6）
where Nu, Re and Pr are Nusselt, Reynolds and Prandtl numbers, respectively.
and ΔT represent mass flow rate and temperature difference, respectively [27]. For example, the effectiveness of the heat exchanger system, ε, is given by the following equation.
(3)
(4)
where NTU, Cmin, Cmax, U and A are the number of transfer units, minimum heat capacity rate, maximum heat capacity rate, overall heat transfer coefficient and heat transfer area, respectively. The experimentally developed local heat transfer coefficients are generally validated by the Dittus–Boelter correlation, which is given below [28].
(5)
（6）
where Nu, Re and Pr are Nusselt, Reynolds and Prandtl numbers, respectively.
Table 1
lists a few models and correlations for the calculation of SHC of nanofluids available from various literature with respect to intensive experimentation. Pak and Cho
[19]
developed a mixing model for the turbulent friction and heat transfer behavior of metal oxide-based nanofluids. Vajjiha and Das
[20]
reported the specific heat measurement of three nanofluids containing ZnO, Al2O3, and SiO2 nanoparticles in the aqueous solution of 40 wt.% ethylene glycol. The experimental data were not in close agreement with the existing correlations; hence a new correlation for specific heat as a function of temperature, volume fraction of particles, and specific heat of the base fluid was developed and predicted with an average error of 2.7%. Zhou et al.
[21]
investigated the specific heat capacity of CuO nanoparticles with ethylene glycol as the base fluid. As the difference in density between the base fluid and nanoparticles is large, a new correlation has been developed taking into account both the density of the base fluid and nanoparticles. After reviewing more than 80 experimental data on water-based Al2O3 nanoparticles, Sekhar and Sharma
[22]
developed a novel correlation by regression involving the effect of temperature and nanoparticle diameter. The below mentioned are the major theoretical models for calculating the specific heat of metal oxide-based nanofluids with good accuracy.
Table 1.
Specific heat capacity estimation of metal oxide-based nanofluids (model and correlations).
Maxwell
[13]
Burggeman
[3325]
Timoofeva
[3429]
Sujith et al.
[3527]

for cylindrical particles,

for spherical particles

You and Choi
[3628]
Hamilton-crosser
[3724]

Koo and Kleinstreuer
[3830]
Sadik et al.
[3931]
Liu and Lin
[4032]
Models/CorrelationsAuthor

2.3. Viscosity

The study of a fluid’s response to the applied shear stress is called rheology

2.3. Viscosity

The study of a fluid’s response to the applied shear stress is called rheology [54]. Shear stress versus shear rate gives the rheological behavior of a particular fluid. The ratio of shear stress and strain rate is termed as viscosity, and this determines the rheological properties of a fluid. In general, fluids are categorized into Newtonian and non-Newtonian types. Newtonian fluids exhibit a linear relation between the shear rate and shear stress. While non-Newtonian fluids show a nonlinear relationship, and the fluid flow curve does not intersect the center of the axes of the coordinate system
[4133]. Shear stress versus shear rate gives the rheological behavior of a particular fluid. The ratio of shear stress and strain rate is termed as viscosity, and this determines the rheological properties of a fluid. In general, fluids are categorized into Newtonian and non-Newtonian types. Newtonian fluids exhibit a linear relation between the shear rate and shear stress. While non-Newtonian fluids show a nonlinear relationship, and the fluid flow curve does not intersect the center of the axes of the coordinate system [23].
.
Figure 1
shows the difference in the fluid flow curves of Newtonian and non-Newtonian fluids. Viscosity is one of the most critical factors determining the stability of a fluid especially in high temperature applications. It also determines the interfacial friction between the fluid layers. To analyze the pumping power requirement in various thermal applications, the rheological behavior of fluid flow must be considered. Many experimental reports showed that the increase in the nanoparticle concentration improved the viscosity of metal oxide-based nanofluids
. This is because the internal friction between the fluid layers increases with the increase in the viscosity.
Table 3
presents the relative viscosity of metal oxide-based nanofluids at several different temperatures. Metals 12 00165 g006
Figure 1.
Various rheological behaviors of different fluids.
Table 3.
Relative viscosity of various metal oxide based nanofluids at several different temperatures.
Author Nanoparticles Base Fluid Temperature-Range (°C) Relative Viscosity (Maximum)
Xichen et al. [2636] Al2O3 Engine oil (SN 5W−40 Ambient 1.12
Mostafizur et al. [2737] TiO2 Methanol 1–20 1.65
Chiam et al. [4238] Al2O3 60:40 (W:EG) 30–70 1.67
Fedele et al. [4339] TiO2 Bidistilled water 10–70 2.8
Sujith et al. [9] Al2O3 Coconut oil 30–140 2.5
Georgiana et al. [4440] Al2O3/SiO2 Distilled water Ambient 2.7
Suhaib et al. [4541] ZnO Paraffin oil 25–55 1.62
Yan et al. [4642] TiO2/MWCNT Ethylene glycol 25–55 1.94
Kole et al. [4743] CuO Gearoil 10–80 2.8
Andac et al. [4844] ZrO2 Water 10–70 1.8
Sonawane [
Pak and Cho
[2319]

A, B and C are correlation coefficients

Vajjha and Das
[2420]
Zhou et al.
[2521]
Shekar and Sharma
[2622]
Donghyun and Debjyoti
[2723]

2.2. Thermal Conductivity

Over the years, several studies have been conducted on the thermal conductivity of nanofluids, and various theoretical and numerical models have been proposed. Classical models based on mixture and compound theory include those of Maxwell
[13]
, Hamilton crosser
[2824]
, Bruggemen
[2925]
, Yamada, and Ota
[3026]
. For example, Sujith et al.
[3127]
experimentally investigated the thermal conductivity of pure coconut oil-based Al2O3 nanofluids, and the results obtained from Maxwell’s and Yamada’s models differed from experimental data by 22 and 28%, respectively. This is because these models considered only the conventional factors such as particle type, volume fraction, and base fluid type. Researchers also found many other simultaneous factors affecting the thermal conductivity of the nanosuspensions. Therefore, new mathematical models and empirical correlations were proposed by considering Brownian motion of the nanoparticles, nano-layering of the base fluid at liquid/nanoparticle interface, temperature of the base fluid, diameter of the nanoparticles and nanoparticle clustering
[3228]
.
Table 2
shows the selected models and correlations widely used for thermal conductivity evaluation of metal oxide-based nanofluids.
Table 2.
Thermal conductivity estimation of metal oxide-based nanofluids (model and correlations).
Models/CorrelationsAuthor
49
45
]
Fe3O4
Ethylene glycol
20–80
2.18

3. Conclusions

Herein concluded the preparation and application of metal oxide-based nanofluids, especially on heat transfer application. Due to their chemical inertness and ability to enhance the thermophysical properties of heat transfer fluids, metal oxide-based nanofluids have attracted considerable attention in a variety of heat transfer applications. For the wide application of nanofluids by commercialization, several key challenges such as stability and production cost must be analyzed. For example, the main heat transfer mechanisms in heat pipes are convective evaporation and convective condensation during boiling. A variety of industrial heat pipes include capillary pump loop (CPL) heat pipes, flat shaped axial heat pipes, and ordinary cylindrical heat pipes
[5046][3747][3348]
. The addition of nanoparticles to the base fluid improved the heat transfer performance to a greater extent. The increase in wettability due to the addition of nanoparticles also increased the capillary force of the CPL pipe, but it increased the viscosity and density to increase the flow resistance as well. Therefore, it is necessary to determine the optimal concentration of nanoparticles to balance drag and capillary forces. In the case of the pool boiling process, the boiling characteristics are governed by the nanoparticles, the stabilizers and the affinity of base fluid and heater. A thin layer of porous sediment can form on the heater surface, reducing the number of active nucleation sites
[5149]
. In addition, sedimentation of nanoparticles can reduce the half cone angle of the roughness cavity and reduce the number of active nucleation sites. The reduction in the number of active nucleation sites weakens heat transfer. Various nanofluid formulations exist to improve heat transfer and lubrication performance in machining processes
[3550][3651]. The efficiency and reliability of machine tools are greatly improved by nanofluids. The direction of future nanofluid studies should mainly be to find the optimal nanoparticle group, nanoparticle size, stabilizer and various operating parameters such as temperature, concentration and ambient temperature. These will enable practical applications of nanofluids for improved heat transfer in a variety of engineering applications.
. The efficiency and reliability of machine tools are greatly improved by nanofluids. The direction of future nanofluid studies should mainly be to find the optimal nanoparticle group, nanoparticle size, stabilizer and various operating parameters such as temperature, concentration and ambient temperature. These will enable practical applications of nanofluids for improved heat transfer in a variety of engineering applications.

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