Experimental Study of the Freezing Point of γ-Al 2 O 3 /Water Nanofluid

Abstract

Nanofluids are colloidal suspensions made of nanometer-sized particles dispersed in a conventional fluid. Their unusual thermal properties explain intensive investigations for several thermal and industrial applications. In this work, an experimental investigation was performed to measure the freezing point and to study the supercooling point made of alumina γ-Al₂O₃ nanoparticles with 30 nm diameter size and deionized water. Particles' volume fraction used in this work is ranging from 1% to 4%. The T-historic method based on the measurement of the point of inflexion was performed to measure the thermal properties such as the freezing point and the latent heat of solidification of the nanofluids for different concentrations. The results show that the supercooling degree decreases for the high particles volume concentrations and that the agglomeration does not influence the temperature of the freezing point. However, it makes the freezing process longer.

1. Introduction

Nanofluids are liquids suspensions containing nanoparticles or nanofibers dispersed in a conventional liquid. Recent researches showed an interesting thermal capacity compared to the conventional liquids [1, 2]. Research efforts have mostly been concerned with the characterization of thermal and physical properties of nanofluids. Many experimental studies focused on the measurement of thermal conductivity [3, 4] and the measurement of dynamic viscosity [5, 6] usually for a range of temperature between 20°C and 60°C. Nguyen et al. [7] showed a singular phenomenon of hysteresis for high temperatures and high concentrations. Aladag et al. [8] studied the rheological behavior of alumina/water and aqueous nanotube of carbon nanofluids at low temperature (less than 10°C). Their results show the nanofluids are not Newtonian and that the experimental results of dynamic viscosity are much higher than those from the theoretical models.

Several experimental investigations have revealed an enhancement of the thermal performance in exchangers [9, 10] and an impressive enhancement of the convective heat transfer coefficient in horizontal tubes [11], whereas many factors such as clustering of particles, agglomeration, sedimentation, and the dissociation of the surfactant on the effective thermal properties of nanofluids have an important effect on the results.

The behavior of this type of fluid in a range of temperature below 20°C is not much studied. Some papers show that the behavior of these fluids at low temperature is no longer Newtonian. Khaled and Vafai [12] investigated the effect of the surfactant on the heat transfer, and his experimental results show an influence of the surfactant by more than 20% on the number of Nusselt obtained.

The complexity of the regulation of air conditioning and refrigeration systems especially food industry requires exchangers and buckles with negative temperatures. However, from the point of view of refrigerator performance, the most commonly used fluids such as water, ethylene glycol, and oil have relatively low thermal conductivity. The high conductivity of nanofluids can be a good solution.

Very few reports studied the thermal properties at low temperature, especially at the freezing and supercooling points. Wu et al. [13] investigated infrared instrument to evaluate the freezing rate of alumina (Al₂O₃)/water nanofluid for very low volume concentrations (less than 0.05%). They found that the addition of the nanoparticles decreases strongly the degree of supercooling and reduces the freezing time. Khodadadi and Hosseinizadeh [14] numerally simulated the thermal energy storage of aqueous CuO nanoparticles at low volume concentration (0.1% and 0.2%). Their results show that freezing time decreases when the particles, volume concentration increases.

The main purpose of this work is to study experimentally the behavior of alumina γ-Al₂O₃/water nanofluids for the freezing process and to measure the thermal properties using T-history curves for a range of volume fraction of 1–4%.

The T-history method (modified) used in this study is based on the inflection point as the boundary between phase change and solid-state periods [15, 16]. Hong et al. [17] showed 40% discrepancy between the original T-history and the modified T-history method when analyzing the experimental data.

Three different tests are investigated in this present work.

The first test involves putting the nanofluid (initially at 20°C) in a cold room stabilized at temperature −16°C. The acquisition is made at a pace of 45 s.

In the second test, initially the temperature of alumina/water nanofluids and the cold room is the same as 20°C. Then, the temperature is decreased gradually and simultaneously to −15°C.

The third test reproduces the second for nanofluids samples with the same volume concentration and more or less clustering of nanoparticles.

The first part of this paper presents the T-history method and the experimental setup. The second part analyzes the results of the behavior of alumina/water nanofluids at the freezing point.

2. Method of the Historic of the Curves

As shown in Figure 1, the temporal evolution (T-history curve) of cooling process of water consists of three phases. The first one corresponds to the cooling of the liquid phase solution (sensible heat). The second phase ishorizontal flat parts where the state changes from liquid to solid (latent heat). Finally, the third phase corresponds to the cooling of the ice (solid) solution (sensitive heat). If the T-history curve maintains at a constant temperature in the latent heat range, the selection of range is very easy. Unfortunately, most of T-history curves show typical phenomena (supercooling).

Figure 1:

T-history curve of water and evolution of temperature with time.

There are three main temperatures on the T-history curves.

There is the initial temperature of the horizontal flat parts “plateau” T_s which cannot be determined intuitively because of the supercooling process.

There is the equilibrium freezing temperature T_m where the phase change occurs. Rahman et al. [18] defined it as the temperature in which the slowest cooling rate is observed.

The final temperature of the plateau T_i is defined by the end of latent heat range. This temperature can be calculated using the inflexion point method.

In this present work, the equilibrium temperature of freezing process T_m is evaluated directly from the acquisition data when no difference between two consecutives measurement is observed. The final temperature T_i is obtained using the slope method (Figure 2(a)).

Figure 2:

(a) Evolution of first derivative (°C/s) with time, (b) infection point (end of plateau) for water.

Figure 2(b) shows the slope (derivative in °C/s) of the cooling curve for water as a function of cooling time. When the amount of ice formation decreases, the slope started to increase and reached the highest value of plateau. The end of freezing is defined when the cooling rate is the highest. So T_i is the highest slope value corresponding to the end of the plateau.

The slope decreases to a minimum before ice crystal formation starts. This minimum corresponds to T_s, the supercooling temperature.

The latent heat of solidification is evaluated as the amount of energy required in the second phase (horizontal flat parts) which starts at the beginning of the supercooling process and finishes at the end of the plateau.

3. Determination of the Latent Heat of Solidification

The energy equations including the phase change of water in a tube placed in a room at constant temperature T_a are, respectively as follows.

For the liquid sensible heat range between t₀ and t_s,

(m_{t} {(C_{p})}_{t} + m_{nf} {(C_{p})}_{nf}) (T_{0} - T_{s}) = K S_{t} A_{1},

(1)

with

A_{1} = ȫ_{t_{0}}^{t_{s}} (T_{nf} - T_{a}) d t .

(2)

During the solidification state between t_s and t_i,

\begin{matrix} (m_{t} {(C_{p})}_{t} + \frac{m_{nf} ({(C_{p})}_{nf} + {(C_{p})}_{nfice})}{2}) (T_{m} - T_{i}) + m_{nf} H \\ = K S_{t} A_{2}, \\ A_{2} = \int_{t_{s}}^{t_{i}} (T_{nf} - T_{a}) d t . \end{matrix}

(3)

The latent heat solidification of the fluid is given by

H = \frac{[B (T_{m} - T_{i})]}{m_{nf}},

(4)

with

\begin{matrix} B & = (m_{t} (C_{p}) + m_{nf} {(C_{p})}_{nf}) (T_{0} - T_{s}) (\frac{A_{1}}{A_{2}}) \\ - (m_{t} {(C_{p})}_{t} + \frac{m_{nf} ({(c_{p})}_{nf} + {(c_{p})}_{nfice})}{2}) . \end{matrix}

(5)

A₁ and A₂ correspond to the area below the curve in the considering period shown in Figure 1.

4. Description of the Experimental Setup

The experimental setup for the cooling process is shown in Figure 3. Identical test tubes for three samples of nanofluids for each concentration and for reference fluid (pure water) are placed in an insulated cold room which was previously at −16°C. The test tubes racks were disposed on a table in the middle of the cold room (Figure 3). This room has got a ground area of 12 m² and a height of 2.5 m. It is cooled by a double-flux distributor situated at the ceiling and connected to a refrigerator.

Figure 3:

Experimental setup.

The Pt100 sensors are placed axially and at midheight for each test tube to measure the temperature variation. To visualize the temporal evolution of temperatures, the sensors Pt100 are joined to a power station acquisition Agilent 34970 A permitting a temperature precision of 0.1°C.

5. Validation of the Installation

The experimental setup is validated using water at PH = 5. Each tube contains 15 mL of sample. The tubes have the following characteristics: m_t = 0.03 kg, v_t = 20 mL, and C_pt = 800 J/kgK.

Initially at ambient temperature (20°C), the samples are placed in the center of the cold room stabilized at −16°C with a precision of 0.2°C. The temporal evolution of temperatures in the center of each sample is raised by the power station of acquisition which is made at a pace of 45 s. The results are calculated from the average temperature of three samples. Figure 1 shows the T-history curve for pure water.

Regarding the relative uncertainty on all the measurements (mass, temperature, time, and C_p), and the (1) to (8), the latent heat of water (Table 1) is obtained with a relative uncertainty of 15%.

Table 1:

Characteristic of T-history curve and heat latent results.

	0%	1%	2%	3%	4%

T₀ (°C)	19.5	19.4	19.6	19.6	19.7
T_a (°C)	−16.0	−16.0	−16.0	−16.0	−16.0
T_s (°C)	−0.2	−0.4	−0.3	−0.3	−0.5
T_m (°C)	0	−0.1	-0.0	-0.0	−0.1
T_i (°C)	−5.3	−5.9	−6.0	−6.1	−6.5
H (kJ/kg)	332 ± 32	315 ± 47	276 ± 41	238 ± 36	293 ± 44

6. Results

6.1. Nanofluids Properties

The nanofluids used in this work are composed of demineralized water with pH = 5, alumina nanoparticles (γ-Al₂O₃), and 1% (mass concentration) of surfactant. The mass concentration of the nanofluids was initially 49.9% and has been diluted to get samples with volume concentrations of 1%, 2%, 3%, and 4%. The relation bellow allows the transition between mass and volume concentrations:

φ_{v} = \frac{φ_{w} (ρ_{f} / ρ_{p})}{(1 - φ_{w} (1 - ρ_{f} / ρ_{p}))} .

(6)

The characteristics and the thermal properties of the base fluid (pure water) and the solid nanoparticles (γ-Al₂O₃) used in this study are presented in Table 2.

Table 2:

Thermophysical properties of different phases (water/Al₂O₃ nanoparticles).

Property	Base fluid (water)	Nanoparticles Al₂O₃

C_p (J/kg·K)	4182	773
ρ (kg/m³)	998.2	3880
k (W/m·K)	0.6	36
Particles diameter (nm)	—	30

6.1.1. The Density

We supposed that the density of the particles is constant in the range of temperature used, and we take into account the variation of the water density according to the temperature. We neglected the presence of surfactant, and the relation used is the following:

ρ_{nf} = (1 - φ_{ν}) ρ_{f} + φ_{ν} ρ_{p} .

(7)

6.1.2. The Specific Heat

The specific heat of nanofluids was obtained from the equation given by Xuan and Roetzel [19] who supposed that the nanoparticles are immiscible in water,

{(C_{p})}_{nf} = (1 - φ_{v}) {(C_{p})}_{f} + φ_{v} {(C_{p})}_{p} .

(8)

The same relation is used in solid phase considering the specific heat of ice for the base fluid.

6.1.3. Dispersion of Nanoparticles

To control the dispersion of alumina/water nanofluids, we investigated an experimental test based on measuring the size of nanoparticles by dynamic light scattering by using a Zetasizer Nano S (Malvern Instruments). This method can detect the presence of agglomerates [20]. Figure 4 illustrates the particles size distributions of alumina (γ-Al₂O₃)/water nanofluids. The particles’ size distribution possesses just one peak which shows that our nanofluids are stables. The average particles size is around 400 nm, and it is greater than the initial particles size. It is because there is particles agglomeration.

Figure 4:

Evolution of Al₂O₃ nanoparticles size with the intensity distribution (%).

6.2. Test 1 (Freezing Process of Nanofluid)

In this test, we put the tubes racks of the samples of alumina/water nanofluids initially at the ambient temperature (20°C) at the center of the cold room stabilized at −16°C. Figure 5 shows the T-history curves of alumina/water nanofluids and of pure water. We can notice that the solidification phase for different concentration of alumina/water nanofluids is nearly similar to water solidification phase. The freezing point is close to T_c = 0°C. Therefore, Figure 6 shows that the freezing degree decreases when the particles volume concentration increases.

Figure 5:

T-history curve of 4 nanofluids (1%, 2%, 3%, and 4%), evolution of temperature with time (Test 1).

Figure 6:

Precision of melting fusion of nanofluid (plateau).

However, the difference between the samples is still very low; the freezing temperatures of the samples vary on a range of 0°C to −16°C. In addition to this, the sensors Pt100 have a precision of 0.1°C. So it is hard to evaluate objective conclusions with regard to the variation of the freezing temperature for volume fraction range of 1% to 4% of alumina/water nanofluids.

If we compare only the T-history curve of alumina/water nanofluid at 4% volume fraction with pure water (Figure 6), we will notice that the points of measurement of alumina/water nanofluids (dotted line in Figure 5) are not in the range of uncertainty of pure water, and vice versa. The results in Table 1 show that the latent heat of solidification decreases with increasing the concentration of particle.

6.3. Test 2 (Supercooling Point of Nanofluids)

Initially the temperature of the nanofluids and the cold room was stabilized at 20°C (ambient temperature). The test tubes racks were disposed on a table in the middle of the room. Then, the temperature decreased gradually and simultaneously to −15°C. Figure 7 shows the T-history curves of alumina/water nanofluids and of pure water. Unlike the first test, in this second test, we can observe the supercooling process for all the samples. We noticed that the supercooling degree decreases when the volume fraction of Al₂O₃ nanoparticles increases. However, it is not possible to establish a correlation between the supercooling degree observed and the percentage of volume concentration of the nanofluids. It is due to the uncertainty of measurements and the phenomena of agglomeration and sedimentation of the nanofluids. In fact, it is difficult to evaluate the homogeneity and the dispersion rate of agglomeration or sedimentation of every solution.

Figure 7:

T-history curve of 4 nanofluids (1%, 2%, 3%, and 4%), evolution of supercooling (Test 2).

The supercooling temperature obtained for this test is $T_{s} (0 %) = - 7.8$ °C; $T_{s} (1 %) = - 3.4$ °C; $T_{s} (2 %) = - 2.4$ °C; $T_{s} (3 %) = - 0.6$ °C; $T_{s} (4 %) = - 4.2$ °C.

6.4. Test 3 (Sedimentation of Nanofluid)

This third experience consisted in observing the impact of the sedimentation of the Al₂O₃ nanoparticles on the freezing phase and the supercooling point. We have let six samples of the same volume fraction (3%) stand for 16 hours and 30 minutes. Then three samples have been agitated just before starting the cooling process (Test 2). The cold room was stabilized at −5°C.

The T-history curves for the six samples of Al₂O₃ nanoparticles (Figure 8) show that the impact of agglomeration on the freezing point is insignificant. However, the supercooling time increases strongly with agglomeration. In fact, the agitation allows a good dispersion for the Al₂O₃ nanoparticles, but their agglomeration encourages germination.

Figure 8:

T-history curve of 4 nanofluids (1%, 2%, 3%, and 4%), impact of sedimentation (Test 3).

7. Conclusion

Three experimental tests were performed to measure the freezing point and to study the supercooling point made of alumina γ-Al₂O₃ nanoparticles with 30 nm diameter size and deionized water. The results show that the solidification phase for different concentration of alumina/water nanofluids is nearly similar to water solidification phase, and the freezing and supercooling degrees decrease when the particles volume concentration increases and that is not possible to establish a correlation between the supercooling degree observed and the percentage of volume concentration of the nanofluids due to the uncertainty of measurements and to the phenomena of agglomeration and sedimentation in the nanofluids. In addition to this, we found that the impact of agglomeration on the freezing point is insignificant and that the supercooling time increases strongly with agglomeration.

The difference observed in the first test between water and alumina nanofluids with 4% volume fraction shows that for high-volume fraction of Al₂O₃ nanoparticles, the solidification phase could be different from water.

The heat latent of solidification seems less important for nanofluids in comparison to water.

Finally the impact of the surfactant and the dispersion of nanoparticles must be better dominated to analyze in a more precise way the cooling process.

Footnotes

Nomenclature

Acknowledgments

The head of Pole Cristal of Dinan, Frederic Bazantay, is gratefully acknowledged for his contribution to this study. Malvern Company is gratefully acknowledged for its help in DLS measurement.

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