5.1. Pressure drop

<sup>μ</sup>nf <sup>¼</sup> <sup>μ</sup><sup>b</sup> <sup>1</sup>:<sup>475</sup> � <sup>0</sup>:319<sup>φ</sup> <sup>þ</sup> <sup>0</sup>:051φ<sup>2</sup> <sup>þ</sup> <sup>0</sup>:009φ<sup>3</sup> (9)

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

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

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

μ

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:

here, A and B are functions of volume fraction φ. This correlation is mainly for aqueous

The application for nanofluid with low viscosity (high temperature) and high thermal conduc-

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

T 

ln <sup>μ</sup>nf <sup>¼</sup> <sup>A</sup> <sup>1</sup>

solution and is not applicable to nanofluids in the subzero temperature range.

B T 

log ð Þ¼ nf <sup>A</sup> <sup>þ</sup> BT�<sup>1</sup> <sup>þ</sup> CT <sup>þ</sup> DT<sup>2</sup> (11)

� B (12)

(10)

μnf ¼ Aexp

with the rise in temperatures.

284 Microfluidics and Nanofluidics

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

tivity (small volume fraction) is promising for the future.

4. Heat transfer enhancement

[29] as

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

$$
\Delta p = \frac{32\mu LV\_{avg}}{D^2} \tag{14}
$$

The pressure drop for a channel with length L as follows:

The above equation can be written to d as follows:

For laminar flow, f ¼ 64=ℜ

and

ΔP ¼ f

N � �L

<sup>d</sup> <sup>¼</sup> <sup>128</sup>μVL πWΔP � �<sup>1</sup>=<sup>3</sup>

Therefore, at a fixed volume flow rate, fixed pumping power, and a given channel length, the following correlation can be obtained for laminar flow with constant a Nusselt number:

If the nanofluid is more efficient than their base fluids, the difference between the wall and

μnf <sup>μ</sup>bf !<sup>1</sup>=<sup>3</sup>

Eq. (24) shows that nanofluids are effective as long as the thermal conductivity enhancement is more than the one-third power of the viscosity enhancement for laminar flow regime. The boundary line for the performance of nanofluids in laminar flow regime is shown in Figure 5a. The thermal conductivity and viscosity ratios of Al2O<sup>3</sup> and multiwalled carbon nanotube (MWCNT) nanofluids are measured in the work of Wu et al. [34] plotted in Figure 5. Alumina nanofluids can provide better performance than base fluids under laminar flow regime,

μbf

of nanofluid to thermal conductivity base fluids must be more than 1259 as shown in Figure 4a. Figure 6 shows the optimization of the preparation of nanofluid, starting with the measurement of the stability of nanofluid, if it fast agglomerates necessary additional treatment, for

128μVL WπΔP � �<sup>1</sup>=<sup>3</sup>

∞ μ 1 3

ΔTbf > ΔTnf (23)

is equal to two, the ratio thermal conductivity

<sup>Δ</sup><sup>P</sup> <sup>¼</sup> <sup>128</sup><sup>μ</sup> <sup>V</sup>

<sup>Δ</sup><sup>T</sup> <sup>¼</sup> <sup>Q</sup>

WπLNu

bulk fluid temperature should be smaller than the temperature using base fluids:

knf kbf >

whereas the tested MWCNT nanofluids are very unfavorable.

If a ratio nanofluid viscosity to the base fluid <sup>μ</sup>nf

high stability by adding surfactant or surface modifier.

LrU<sup>2</sup>

<sup>π</sup>d<sup>4</sup> <sup>¼</sup> <sup>128</sup>μVL

<sup>2</sup><sup>d</sup> (19)

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

<sup>π</sup>Wd<sup>3</sup> (20)

<sup>k</sup> (22)

(21)

287

(24)

The pressure drop due to viscous effects represents an irreversible pressure loss, and it is called pressure loss ΔpL in circular tube that can be determined from the pressure drop using the Darcy-Weisbach equation below:

$$
\Delta p\_L = f \frac{L}{D} \frac{\rho l I^2}{2} \tag{15}
$$

But mass flow rate is m ¼ rAU, and the pressure drop from Eq. (15) is

$$
\Delta p = f \frac{L}{D} \frac{\rho \left(\frac{\dot{m}}{\text{ALI}}\right)^2}{2} = f \frac{L}{D} \frac{4 \dot{m} \rho}{\pi D^2} = f \frac{L}{D^3} \frac{4 \dot{m} \rho}{\pi} \tag{16}
$$

Performance evaluation criteria by Lee [33] obtained a boundary line for laminar flow using thermal conductivity and viscosity of nanofluids to compared than base fluid. The method has been used to analyze the performance of nanofluid in a microchannel heat sink. A microchannel heat sink as a passive method can be a cooling device by dissipating heat into the surrounding air. The microchannel heat sink consists of N number of circular channels, each with diameter d, as shown in Figure 4. The total channel width W is constant (W ¼ N � d).

Assume a constant heat flux boundary condition for all channel, and the flow is hydrodynamically and thermally fully developed. The heat transfer flow rate for convection heat transfer as Newton's law of cooling is

$$Q = hA\Delta T\tag{17}$$

The difference in temperature between the surface wall temperature and the local bulk fluid temperature is

$$Q = T\_w - T\_m = \frac{Q}{N\pi dLh} = \frac{Q}{\binom{w}{d}dL} \frac{1}{kN\mu} \tag{18}$$

Figure 4. A schematic of a microchannel heat sink.

The pressure drop for a channel with length L as follows:

$$
\Delta P = f \frac{L \rho \mathcal{U}^2}{2d} \tag{19}
$$

For laminar flow, f ¼ 64=ℜ

<sup>Δ</sup><sup>p</sup> <sup>¼</sup> <sup>32</sup>μLVavg

The pressure drop due to viscous effects represents an irreversible pressure loss, and it is called pressure loss ΔpL in circular tube that can be determined from the pressure drop using the

> <sup>Δ</sup>pL <sup>¼</sup> <sup>f</sup> <sup>L</sup> D rU<sup>2</sup>

Performance evaluation criteria by Lee [33] obtained a boundary line for laminar flow using thermal conductivity and viscosity of nanofluids to compared than base fluid. The method has been used to analyze the performance of nanofluid in a microchannel heat sink. A microchannel heat sink as a passive method can be a cooling device by dissipating heat into the surrounding air. The microchannel heat sink consists of N number of circular channels, each with diameter d, as shown in Figure 4. The total channel width W is constant

Assume a constant heat flux boundary condition for all channel, and the flow is hydrodynamically and thermally fully developed. The heat transfer flow rate for convection heat transfer as

The difference in temperature between the surface wall temperature and the local bulk fluid

<sup>N</sup>πdLh <sup>¼</sup> <sup>Q</sup> w d dL

<sup>Q</sup> <sup>¼</sup> Tw � Tm <sup>¼</sup> <sup>Q</sup>

But mass flow rate is m ¼ rAU, and the pressure drop from Eq. (15) is

r <sup>m</sup> AU <sup>2</sup> <sup>2</sup> <sup>¼</sup> <sup>f</sup> <sup>L</sup> D 4m r <sup>π</sup>D<sup>2</sup> <sup>¼</sup> <sup>f</sup> <sup>L</sup> D3

<sup>Δ</sup><sup>p</sup> <sup>¼</sup> <sup>f</sup> <sup>L</sup> D

Darcy-Weisbach equation below:

286 Microfluidics and Nanofluidics

(W ¼ N � d).

temperature is

Newton's law of cooling is

Figure 4. A schematic of a microchannel heat sink.

<sup>D</sup><sup>2</sup> (14)

<sup>2</sup> (15)

<sup>π</sup> (16)

kNu (18)

4m r

Q ¼ hAΔT (17)

1

$$
\Delta P = \frac{128\mu \left(\frac{V}{N}\right)L}{\pi d^4} = \frac{128\mu VL}{\pi \mathcal{W}d^3} \tag{20}
$$

The above equation can be written to d as follows:

$$d = \left(\frac{128\mu VL}{\pi W \Delta P}\right)^{1/3} \tag{21}$$

Therefore, at a fixed volume flow rate, fixed pumping power, and a given channel length, the following correlation can be obtained for laminar flow with constant a Nusselt number:

$$
\Delta T = \frac{Q}{W \pi L N \mu} \left(\frac{128 \mu VL}{W \pi \Delta P}\right)^{1/3} \approx \frac{\mu^{\frac{1}{5}}}{k} \tag{22}
$$

If the nanofluid is more efficient than their base fluids, the difference between the wall and bulk fluid temperature should be smaller than the temperature using base fluids:

$$
\Delta T\_{b\circ} > \Delta T\_{n\circ} \tag{23}
$$

and

$$\frac{k\_{nf}}{k\_{bf}} > \left(\frac{\mu\_{nf}}{\mu\_{bf}}\right)^{1/3} \tag{24}$$

Eq. (24) shows that nanofluids are effective as long as the thermal conductivity enhancement is more than the one-third power of the viscosity enhancement for laminar flow regime. The boundary line for the performance of nanofluids in laminar flow regime is shown in Figure 5a. The thermal conductivity and viscosity ratios of Al2O<sup>3</sup> and multiwalled carbon nanotube (MWCNT) nanofluids are measured in the work of Wu et al. [34] plotted in Figure 5. Alumina nanofluids can provide better performance than base fluids under laminar flow regime, whereas the tested MWCNT nanofluids are very unfavorable.

If a ratio nanofluid viscosity to the base fluid <sup>μ</sup>nf μbf is equal to two, the ratio thermal conductivity of nanofluid to thermal conductivity base fluids must be more than 1259 as shown in Figure 4a.

Figure 6 shows the optimization of the preparation of nanofluid, starting with the measurement of the stability of nanofluid, if it fast agglomerates necessary additional treatment, for high stability by adding surfactant or surface modifier.

Figure 5. The boundary line for the performance of nanofluid at fixed volume flow rate and fixed pumping power: (a) laminar flow regime and (b) turbulent flow regime. The alumina and MWCNT nanofluids measured in Wu et al. correlation [32].

Viscosity measurements were performed to determine the viscosity value of nanofluid, for high viscosity nanofluid required special treatment to decrease viscosity, i.e., nanofluid used at the temperature above room temperature. Following the above discussion with an increasing temperature, the viscosity of nanofluid decreases.

6. Conclusion

Figure 6. Optimization fabrication of nanofluid.

future.

The above discussion can be concluded that the application for nanofluid with low viscosity (high temperature) and high thermal conductivity (small volume fraction) is promising for the

Performance Evaluation Criterion of Nanofluid http://dx.doi.org/10.5772/intechopen.74610 289

Nanofluid can be used as a fluid that has a high-performance increase of heat transfer suitable

only for the cooling process, as hot fluids with low particle volume fraction.

When the viscosity of the nanofluid is low, and the thermal conductivity of the nanofluid is high, nanofluids can be used in practical applications.

Figure 6. Optimization fabrication of nanofluid.
