*3.1.2 Two-step method*

This is the most widely used method for preparing nanofluids. This gives a largescale production of nanofluids, whereas the single-step method is limited, in which dry powders are dispersed into a fluid. The second step is processing with the help of intensive magnetic force agitation, high-shear mixing, ultrasonic agitation, ball milling and homogenizing [4].

The main drawback in the two-step method is large agglomerations, whereas single-step method has limited agglomerations. The single-step method has the

advantages in terms of controlling the particle size, reducing the particles agglomeration, and producing nanofluids containing metallic nanoparticles. The disadvantage is that it is difficult to prepare nanofluids with a high particle volume concentration [4].

The volume concentration is evaluated from the following relation in percentage:

$$\text{op} = \frac{\text{volume of nanopartical}}{\text{volume of nanopartical} + \text{volume of water}} \times 100\tag{1}$$

or

$$\wp = \frac{\left(\text{\${m}/\text{\$}\_{\rho}\$}\right)\_{\text{nonparametral}}}{\left(\text{\${m}/\text{\${}\_{\rho}\$}}\right)\_{\text{nonparametral}} + \left(\text{\${m}/\text{\${}\_{\rho}\$}}\right)\_{\text{water}}} \times \mathbf{100} \tag{2}$$

Due to difficulties of thermal conductivity measurement, it is estimated by the following equation:

$$K\_{\eta f} = K\_f \left[ \frac{2 + K\_{pf} + 2 \mathcal{Q} (K\_{pf} - \mathbf{1})}{2 + K\_{pf} - \mathcal{Q} (K\_{pf} - \mathbf{1})} \right] \tag{3}$$

where

$$K\_{pf} = \frac{K\_p}{K\_f} \tag{4}$$

(80 nm) with distilled water at concentrations (φ) of 0.3, 0.6, and 0.9% by volume in a horizontal pipe have been studied experimentally and numerically [1]. All tests are conducted with the Reynolds number range of 2900–9820 and uniform heat

**Figure 5** shows the comparison between numerical and experimental results for water and ferrofluid with volume concentration (0 (water), 0.3, 0.6, and 0.9%). An agreement between the results was noticed, and the maximum division was 25, 29, 19, and 7% for nanofluid concentrations of 0, 0.3, 0.6, and 0.9%, respectively. This division could be related to the losses associated with the experimental part which are not taken into account theoretically, and one deals with it as a singlephase flow. However, both results have the same behavior. **Figure 6** shows the contours of temperature at the positions Z = 0, 0.22, 0.44, 0.66, 0.88, 1.1, 1.32, and 0.15 m for a volume concentration of 0.6% and Re = 5890. Such contours of temperature manifest increase in temperatures with decreasing ferrofluid concen-

on the finite volume technique using commercial CFD software. The system geometry shown in **Figure 4** consists of a copper tube with a diameter of 1.4 cm and a length of 150 cm length. The fluid flows in the tube and is subjected to a uniform heat flux. The number of mesh element in this study is 305,492.

*Nanofluids and Computational Applications in Medicine and Biology*

*DOI: http://dx.doi.org/10.5772/intechopen.88577*

*Comparison of numerical and experimental results for distilled water and ferrofluid.*

*Temperature contours in K at locations of Z = 0.22 m (left) and 1.32 m (right) along the test section for*

*ferrofluid of volume concentration = 0.6% with Re =5890.*

. The numerical treatment of the present problem is based

flux 11,262–19,562 W/m2

tration or with decreasing velocity.

**Figure 5.**

**Figure 6.**

**99**

In addition, thermal conductivity measurement techniques for nanofluids are transient hot-wire technique, transient plane source, thermal constant analyzer technique, thermal comparator, steady-state parallel-plate method, cylindrical cell method, temperature oscillation technique, 3ω method, and laser flash method.

### **3.2 The effect of nanofluid on heat transfer in a horizontal pipe**

The enhancement of the distilled water heat transfer characteristics and the metal oxide nanofluid (ferrofluid)-type (Fe3O4) nanoparticles of average diameter

**Figure 4.** *Geometry shape (experimental and numerical) and mesh generated.*

*Nanofluids and Computational Applications in Medicine and Biology DOI: http://dx.doi.org/10.5772/intechopen.88577*

(80 nm) with distilled water at concentrations (φ) of 0.3, 0.6, and 0.9% by volume in a horizontal pipe have been studied experimentally and numerically [1]. All tests are conducted with the Reynolds number range of 2900–9820 and uniform heat flux 11,262–19,562 W/m2 . The numerical treatment of the present problem is based on the finite volume technique using commercial CFD software. The system geometry shown in **Figure 4** consists of a copper tube with a diameter of 1.4 cm and a length of 150 cm length. The fluid flows in the tube and is subjected to a uniform heat flux. The number of mesh element in this study is 305,492.

**Figure 5** shows the comparison between numerical and experimental results for water and ferrofluid with volume concentration (0 (water), 0.3, 0.6, and 0.9%). An agreement between the results was noticed, and the maximum division was 25, 29, 19, and 7% for nanofluid concentrations of 0, 0.3, 0.6, and 0.9%, respectively. This division could be related to the losses associated with the experimental part which are not taken into account theoretically, and one deals with it as a singlephase flow. However, both results have the same behavior. **Figure 6** shows the contours of temperature at the positions Z = 0, 0.22, 0.44, 0.66, 0.88, 1.1, 1.32, and 0.15 m for a volume concentration of 0.6% and Re = 5890. Such contours of temperature manifest increase in temperatures with decreasing ferrofluid concentration or with decreasing velocity.

**Figure 5.**

advantages in terms of controlling the particle size, reducing the particles agglomeration, and producing nanofluids containing metallic nanoparticles. The disadvantage is that it is difficult to prepare nanofluids with a high particle volume

The volume concentration is evaluated from the following relation in

volume of nanopartical <sup>þ</sup> volume of water � 100 (1)

*water*

� 100 (2)

(3)

(4)

<sup>φ</sup> <sup>¼</sup> volume of nanopartical

*m ρ* � � �

*nanopartical*

Due to difficulties of thermal conductivity measurement, it is estimated by the

*Kpf* <sup>¼</sup> *Kp Kf*

In addition, thermal conductivity measurement techniques for nanofluids are transient hot-wire technique, transient plane source, thermal constant analyzer technique, thermal comparator, steady-state parallel-plate method, cylindrical cell method, temperature oscillation technique, 3ω method, and laser flash method.

The enhancement of the distilled water heat transfer characteristics and the metal oxide nanofluid (ferrofluid)-type (Fe3O4) nanoparticles of average diameter

**3.2 The effect of nanofluid on heat transfer in a horizontal pipe**

*Geometry shape (experimental and numerical) and mesh generated.*

� � �

<sup>2</sup> <sup>þ</sup> *Kpf* <sup>þ</sup> <sup>2</sup><sup>∅</sup> *Kpf* � <sup>1</sup> � � <sup>2</sup> <sup>þ</sup> *Kpf* � <sup>∅</sup> *Kpf* � <sup>1</sup> � � " #

*nanopartical* þ *<sup>m</sup> <sup>ρ</sup>*

*φ* ¼

*m ρ* � � �

*Knf* ¼ *Kf*

concentration [4].

*Applications of Nanobiotechnology*

following equation:

where

**Figure 4.**

**98**

percentage:

or

*Comparison of numerical and experimental results for distilled water and ferrofluid.*

#### **Figure 6.**

*Temperature contours in K at locations of Z = 0.22 m (left) and 1.32 m (right) along the test section for ferrofluid of volume concentration = 0.6% with Re =5890.*
