3.2. Viscosity of nanofluid

Besides the thermal conductivity of the nanofluid, another important thermophysical property is viscosity. Viscosity describes the internal resistance of a fluid to flow, and it is an essential property for all thermal applications involving fluids [10]. In laminar flow, the pressure drop is directly proportional to viscosity. Furthermore, convective heat transfer coefficient is influenced by viscosity. Hence, viscosity is as essential as thermal conductivity in engineering systems involving fluid flow. There has been a lot of research done about nanofluids but mostly related to heat transfer [16]. The increase in viscosity doubled, and energy is required to move the fluid to fourfold so that fluid viscosity plays a significant role in the use of energy in the cooling system.

Most of the viscosity enhancement studies obtained with the dispersion of nanoparticles in the base fluid correlated with the effect of volume fraction, size, and temperature were available in the literature. The rheological behavior of nanofluid categorized into four groups [17, 18], nanofluids with volume concentration less than 0.1 vol.% whose viscosity fits with the Einstein equation, semi-dilute nanofluids with 0.1–5 vol.% with aggregation of nanoparticles, semi-concentrated nanofluids with 5–10 vol.% with aggregation of nanoparticles, and concentrated nanofluid with 10 vol.% concentration, is out of the usual nanofluids [19–21].

Theoretical investigations.

of 70 CMC surfactant is also shown. The effective medium theory (EMT) fits on the experimental data indicated by the solid line, which shows a perfect agreement with empirical data. It can be seen that the value of knf/kb with pure surfactant was negative, while it was positive at all other concentrations of nanoparticles [15]. In general the higher the particle volume

Figure 3. Variation of knf =kb as a function of alumina nanoparticle volume fraction with and without CTAB and its best fit

Besides the thermal conductivity of the nanofluid, another important thermophysical property is viscosity. Viscosity describes the internal resistance of a fluid to flow, and it is an essential property for all thermal applications involving fluids [10]. In laminar flow, the pressure drop is directly proportional to viscosity. Furthermore, convective heat transfer coefficient is influenced by viscosity. Hence, viscosity is as essential as thermal conductivity in engineering systems involving fluid flow. There has been a lot of research done about nanofluids but mostly related to heat transfer [16]. The increase in viscosity doubled, and energy is required to move the fluid to fourfold so that fluid viscosity plays a significant role in the use of energy in the cooling

Most of the viscosity enhancement studies obtained with the dispersion of nanoparticles in the base fluid correlated with the effect of volume fraction, size, and temperature were available in the literature. The rheological behavior of nanofluid categorized into four groups [17, 18], nanofluids with volume concentration less than 0.1 vol.% whose viscosity fits with the Einstein equation, semi-dilute nanofluids with 0.1–5 vol.% with aggregation of nanoparticles,

fraction, the higher the nanofluid thermal conductivity of nanofluids.

3.2. Viscosity of nanofluid

with an interfacial resistance.

282 Microfluidics and Nanofluidics

system.

There are some existing theoretical formulas to estimate the viscosity of nanofluid. Among them, equation suggested by Einstein [22] is a pioneer in determining the viscosity equation. The assumptions based on the linear viscous fluid containing spherical particles and low particle volume fractions (φ < 0.02). The suggested formula is as follows:

$$
\mu\_{nf} = \mu\_b (1 + 2.5\varphi) \tag{4}
$$

where μnf is the viscosity of nanofluid, μ<sup>b</sup> is the viscosity of the base fluid, and φ is the volume fraction. It is a linear increase of the viscosity with increasing volume concentration. This formula has a limitation that is very small particle concentration. Later on, many researchers contributed to correct this formula [16].

In 1952, Brinkman [23] extended Einstein's formula to be used with moderate particle concentrations, and this correlation has more acceptance among the researchers. For particle concentrations less than 4%, the expression is as follows:

$$
\mu\_{nf} = \mu\_b (1 - \varphi)^{2.5} \tag{5}
$$

Considering the effect due to the Brownian motion of particles on the bulk stress of an approximately isotropic suspension of rigid and spherical particles, Batchelor [24] proposed the following formula in 1977:

$$
\mu\_{nf} = \mu\_b \left( 1 + 2.5\varphi + 6.5\varphi^2 \right) \tag{6}
$$

It is clear from the above two relations that, if the second or higher order of φ is ignored, then these formulas will be the same as Einstein's equation has been validated for a particle volume fraction up to φ < 0:1 [16].

Nguyen et al. [17] showed that both the Brinkman [23] and Batchelor [24] equations severely underestimate nanofluid viscosities, except at very low particle volume fractions (lower than 1%). They have proposed two correlations for nanofluids consisting 47 and 36 nm of Al2O<sup>3</sup> nanoparticles with water, respectively, as follows:

$$
\mu\_{\rm nf} = \mu\_b \times 0.904e^{0.1842\rho} \tag{7}
$$

$$
\mu\_{\eta f} = \mu\_b \left( 1 + 0.025\rho + 0.015\rho^2 \right) \tag{8}
$$

Both of these models determine the viscosity by only considering base fluid viscosity and the particle volume fraction. Furthermore, they proposed a correlation for computing CuO water viscosity as shown in Eq. (9) [16]:

$$
\mu\_{\eta^{\circ}} = \mu\_{b} \left( 1.475 - 0.319\varphi + 0.051\varphi^{2} + 0.009\varphi^{3} \right) \tag{9}
$$

conservation and environmental protection. The increase in heat transfer statement is usually expressed by increasing the heat transfer coefficient of a system. The purposes of improving the heat transfer rate are to reduce the size and simultaneously increase the capacity of the

The thermal system is expressed by thermal performance, which is the increase of heat transfer coefficient (h) and hydraulic performance, that is, the amount of energy required to circulate fluid within the system. The thermohydraulic performance is used as the performance indicator of heat exchange tool. The heat exchanger performance test means comparing the characteristics of the heat transfer coefficient and pressure loss (pressure drop) on a device of the

Heat transfer enhancement is the process of increasing the effectiveness of heat exchanger. It can be achieved when the heat transfer power of a given device increased or when the pressure

The main advantage of the nanofluid is it has a high thermal conductivity, which is used for improving the efficiency of the thermal system. Adding small particles to the base fluid liquid increases the viscosity of nanofluid [31], which also increases the pressure drop on the systems. Due to the increased pressure drop, the operational costs of a system will be high due to the increase in pumping power. Hence, the viscosity of nanofluid is a significant parameter for determining the feasibility of nanofluid for heat transfer applications, depending on the significant increase in both thermophysical-properties of thermal conductivity and increased viscos-

As heat transfer and pressure drop are the most critical factors, they can be compared to several approaches. It is defined as the ratio of heat transferred to the required pumping power in the test section. To evaluate the benefits provided by the enhanced properties of the nanofluids studied, an energetic performance evaluation criterion (PEC) is defined as heat transfer and hydrodynamics are the most critical factors. They can be compared to a global energy approach using the PEC defined as the ratio of heat flow rate transferred to the

PEC <sup>¼</sup> mCpð Þ Ti � To

Additionally, the heat transfer rate of nanofluids increased due to increased thermal conductivity, and the pressure drop also increased due to the increase in the nanofluid viscosity.

The pressure drop (Δp ¼ p<sup>1</sup> � p2) is directly related to the pumping power to maintain flow;

<sup>v</sup>Δ<sup>P</sup> (13)

Performance Evaluation Criterion of Nanofluid http://dx.doi.org/10.5772/intechopen.74610 285

thermal system.

same dimension.

ity [19].

5.1. Pressure drop

losses generated by the device are reduced.

required pumping power in the system [32]:

for laminar flow the pressure drop is shown in Eq. (14):

5. Performance evaluation criteria (PEC)

Most of the equations have been developed to express viscosity as a function of volume fraction of nanoparticles. However, the temperature is an important factor in nanofluid viscosity, and, consequently, several equations have been created to investigate the temperature effect on viscosity. Some literature is available about the temperature effect over nanofluid viscosity [16]. Yang et al. [25] experimentally measured temperature effect of viscosity with four temperatures (35, 43, 50, and 70�C) for four nanofluid solutions taking graphite as nanoparticles. They experimentally showed that kinematic nanofluid viscosity decreases with the increase of temperature. Anoop et al. [26] studied the viscosity of CuO-ethylene glycol, Al2O3-ethylene glycol, and Al2O3-water for the temperature range of 20–50�C with a volume concentration of 0.5, 1, 2, 4, and 6 vol.%. They found that viscosity reduces with an increase in temperature. Investigation studies by Duangthongsuk and Wongwises [27] with TiO2 and water for a temperature range of 15–50�C have found that viscosity of nanofluids decreases with the rise in temperatures.

A correlation between viscosity and temperature for pure fluids was presented by Reid et al. [28]:

$$
\mu\_{\text{vf}} = A \exp\left(\frac{B}{T}\right) \tag{10}
$$

where A and B are the functions of concentrations and T is temperature that is written by Yaws [29] as

$$\log\left(\imath f\right) = A + BT^{-1} + CT + DT^2\tag{11}$$

where A, B, C, and D are the fitting parameters.

Some correlations have also been suggested taking into account both temperature and volume fraction effects on viscosity [16]. In 2006, Kulkarni et al. [30] proposed correlations that relate viscosity of copper oxide nanoparticles suspended in water with a temperature range of 5–50�C:

$$A \ln \mu\_{nf} = A \left(\frac{1}{T}\right) - B \tag{12}$$

here, A and B are functions of volume fraction φ. This correlation is mainly for aqueous solution and is not applicable to nanofluids in the subzero temperature range.

The application for nanofluid with low viscosity (high temperature) and high thermal conductivity (small volume fraction) is promising for the future.

#### 4. Heat transfer enhancement

Enhancement of heat transfer is a favorite and an important topic that is highly relevant to current and future energy systems and renewable energy systems as well as for energy conservation and environmental protection. The increase in heat transfer statement is usually expressed by increasing the heat transfer coefficient of a system. The purposes of improving the heat transfer rate are to reduce the size and simultaneously increase the capacity of the thermal system.

The thermal system is expressed by thermal performance, which is the increase of heat transfer coefficient (h) and hydraulic performance, that is, the amount of energy required to circulate fluid within the system. The thermohydraulic performance is used as the performance indicator of heat exchange tool. The heat exchanger performance test means comparing the characteristics of the heat transfer coefficient and pressure loss (pressure drop) on a device of the same dimension.

Heat transfer enhancement is the process of increasing the effectiveness of heat exchanger. It can be achieved when the heat transfer power of a given device increased or when the pressure losses generated by the device are reduced.
