Introduction

In recent years, several studies have been carried out on the thermophysical properties of nanofluids, which offer a promising outlook for improving heat transfer efficiency as a new cooling liquid (Sergis and Hardalupas 2011; He et al. 2009; Yu et al. 2008; Trisaksri and Wongwises 2009). Results show augmentation in the thermal conductivity of conventional heat transfer liquids when ultra fine particles of metal, metal-oxide, or carbon are added to the base fluid (Özerinç et al. 2010; Kleinstreuer and Feng 2011). Further, experimental reports reveal the influence of various factors such as nanoparticles characteristics and suspension homogeneity on thermal conductivity enhancement of nanofluid (Ghadimi et al. 2011). Indeed, preparation and stability of nanofluids are the key parameters in experiments and future applications of nanofluids. However, there are some discrepancies among experimental results on the correlation between the stability and thermal conductivity enhancement.

The first dramatic enhancement of thermal conductivity by improving the dispersion of nanoparticles in the host fluid was reported by Eastman et al. (2001). Further studies on the stability of nanofluid by Hong et al. (2005, 2006) illustrated the significant influence of ultrasonication on increasing the stability and thermal conductivity of nanofluid right after sonication. However, the increased time after sonication caused aggregation of nanoparticles and increment of cluster size. This phenomenon reduced the stability and thermal conductivity of the nanofluid. In contrast, recent studies have shown enhancement of thermal conductivity with aggregation of nanoparticles and formation of nanoclusters in nanofluid (Evans et al. 2008; Timofeeva et al. 2007; Gharagozloo and Goodson 2010).

The importance of nanofluid stability motivates researchers to use various techniques and instruments to improve the dispersion of nanoparticles in the host fluid and measure the stability of nanofluid. Nevertheless, there are limited stability investigations in literature compared with the thermophysical properties of nanofluids. The most common method for developing the nanoparticles dispersion and improving the stability of nanofluid is ultrasonication. Duangthongsuk and Wongwises applied 2-h ultrasonic vibration for the preparation of TiO2 water-based nanofluids to break down the nanoparticle aggregate (Duangthongsuk and Wongwises 2010). Wang et al. (2009) used ultrasonic cleanser, 100 W, for at least 15 min for the preparation of alumina water-based nanofluids. Literature shows that nanofluid sonication breaks down the nanoparticle aggregate, which improves the stability of the nanofluid (Li et al. 2007; Wu et al. 2009). However, excessive sonication time can have negative impact on the stability of nanofluids (Lee et al. 2008, 2007). There are discrepancies between experimental studies regarding the influence of ultrasonication time on stability and thermal conductivity of nanofluids. Hong and Yang (2005) reported large enhancement of thermal conductivity of Fe nanofluids at different concentrations by increasing the time of sonication. Study by Kwak and Kim (2005) on CuO-ethylene glycol has shown that the first hours of sonication (up to 9 h) introduce smaller nanoparticles and stable nanofluid, but further hours of sonication increases the size of nanoparticles and decreases the stability. Moreover, a recent study on ZnO-ethylene glycol reported particle size reduction and thermal conductivity enhancement with rising sonication time (up to 60 h) although growth of particle size and reduction of thermal conductivity were observed with further sonication time (Kole and Dey 2012). Reduction in the stability of alumina nanofluids after long sonication time (after 5 h) has also been reported by Lee et al. (2008).

Since there is no coherent study on the influence of ultrasonication on stability and thermal conductivity of nanofluids by increasing the nanoparticle loading, we conducted this study to investigate the influence of ultrasonication (power and time) on stability and thermal conductivity of nanofluids at different concentrations. In addition, we studied the correlation between stability and thermal conductivity of nanofluids. TiO2 water nanofluid without the addition of any surfactant was used for the current experiments. TiO2 is a low toxic, stable, and inexpensive photocatalyst material, which provides a safe and wide range of experimental studies. UV–Vis spectrophotometer measurement which was first employed by Jiang et al. (2003) for estimating the stability of carbon nanotube suspension was used to estimate the stability of nanofluids. This method has shown a good reliability for measuring the stability of nanosuspensions (Jiang et al. 2003; Hwang et al. 2007; Kim et al. 2007).

Since investigating the effect of all factorial combinations of the variables is time consuming and requires numerous experiments, response surface methodology (RSM) with three-levels, three factors Box–Behnken design (BBD) was used to optimize ultrasonic time, ultrasonic power and concentration of nanofluid as the process of variables. Comparing to the classical approach, RSM not only reduces the number of experiments but also is a useful approach to assess and investigate the effects of different factors on responses by varying them simultaneously or as a combination (Adinarayana and Ellaiah 2002; Liu et al. 2004).

Methodology

Nanofluid preparation

A two-step method nanofluid preparation, surfactant free, was used for producing TiO2 water nanofluids. The TiO2 nanoparticle with an average particle size of 25 nm was purchased from Sigma-Aldrich Company. An ultrasonic disruptor, Sonic vibra cell (1,200 W, 20 kHz), was used for sonication of TiO2 water nanosuspension.

Stability measurement

A UV–Vis spectrophotometer (Varian Cary 50-probe) was employed to determine the relative stability of nanofluids. This method quantitatively evaluates the colloidal stability by measuring the concentration of nanoparticles in the suspension versus sedimentation time (Jiang et al. 2003).

Experimental procedure

The main goal of this study is to investigate the influence of sonication (power and time) on the stability of nanofluids by means of UV–Vis spectrophotometer at different concentrations in short-term (after 1 week) and long-term (after 1 month) intervals. Meanwhile, we measured the thermal conductivity of nanofluids right after preparation to optimize the influence of sonication and TiO2 volume concentration on the thermal conductivity of nanofluids at 25 °C. Moreover, we implemented statistical analysis, RSM method, and Box–Behnken to find out the optimum condition for maximum thermal conductivity and high stability of nanofluids.

Experimental design and statistical analysis

The experiment was designed by means of RSM modeling combining with three-level BBD. BBD is an independent quadratic design which needs fewer combinations of the variables to estimate a potentially complex response function than a full factorial design (Yetilmezsoy et al. 2009). In this study, BBD with three independent variables (x 1: ultrasonic power, x 2: ultrasonic time, x 3: TiO2 volume concentration) at three-levels was performed. The coded values of the variable for statistical calculation were determined by the following equation:

$$ X_{i} \, = \, (x_{i} - x_{ 0} )/\Updelta x $$
(1)

where X i is a coded value of the variable, x i is the actual value of the variable, and x 0 is the actual value of the ith test variable at the center point. The range and levels of individual variables are presented in Table 1. The whole experiment design consisting of 17 experimental runs is shown in Table 2. The five replicates at the center point were added to provide a measure of process stability and inherent variability.

Table 1 Independent variables and their levels used in the response surface design
Full size table
Table 2 Box–Behnken design matrix and experimental record responses
Full size table

In the first step of RSM, a proper approximation is implemented to find the relationship between the dependent variable and the set of independent variables. In the next step, the behavior of the system is defined by the following quadratic polynomial equation (Myers et al. 2009; Can et al. 2006).

$$ Y \, = \, \beta_{ 0} \, + \, \sum\limits_{i = 1}^{k} {\beta_{i} X_{i} + } \sum\limits_{i = 1}^{k} {\beta_{ii} X_{i}^{2} + } \sum\limits_{i = 1}^{k} {\sum\limits_{j = i + 1}^{k} {\beta_{ij} X_{i} X_{j} + \varepsilon } } $$
(2)

where \( \varepsilon \) is the random error, X i ,…,X k are input factors that influence the predicted response Y, \( \beta_{0} \) is the constant and \( \beta_{i} \), \( \beta_{ii} \) and \( \beta_{ij} \) are the linear, quadratic, and interaction effects. The fitted equation is expressed as contour plots in order to visualize the relationship between the response and experimental levels of each factor and to infer the optimum conditions. Design Expert (version 8.0.7.1) software package was used to analyze the experimental data. A P value of less than 0.05 was considered significant.

Results and discussion

The effect of independent variables, ultrasonic power, ultrasonic time, and TiO2 volume concentration on stability (after 1 week and 1 month) and thermal conductivity of TiO2 water nanofluids was investigated using RSM according to BBD. By applying multiple regression analysis on the experimental data, the response and the test variables are given in Table 2. The following second-order polynomial equations were derived to explain the UV measurements (stability after 1 week and 1 month) and thermal conductivity of nanofluids.

UV after 1 week:

$$ (Y_{ 1} )^{ - 1} = 2.47 - 0.099X_{1} + 0.72X_{2} - 0.39X_{3} - 0.43X_{12} - 0.37X_{23} + 0.47X_{2}^{2} + 0.23X_{3}^{2} $$
(3)

UV after 1 month:

$$ (Y_{2} )^{ - 1} = 3.12 + 0.034X_{1} - 0.064X_{2} + 0.014X_{3} - 0.78X_{12} - 0.93X_{13} - 0.18X_{23} + 0.082X_{1}^{2} + 0.65X_{2}^{2} + 0.9X_{3}^{2} $$
(4)

Thermal conductivity:

$$ Y_{3} = 0.61 + 3.75 \times 10^{-3} X_{1} - 2.375 \times 10^{-3} X_{2} + 3.125 \times 10^{-3} X_{3} + 7.5 \times 10^{-4} X_{12} + 1.25 \times 10^{-3}X_{13} - 1.382 \times 10^{-3} X_{1}^{2} + 2.868 \times 10^{-3} X_{3}^{2} $$
(5)

where X 1 is the power of sonication, X 2 is the time of sonication, X 3 is the TiO2 volume concentration, X 12 is the interaction between power and time of sonication, X 13 is the interaction between power and volume concentration, and X 23 is the interaction between time and volume concentration.

The analysis of variance (ANOVA) is a requisite to check the significance of the model (Sen and Swaminathan 2004). Hence, the analysis of variance was implemented to explore the significance and fitness of the models. Table 3 shows the ANOVA of the response surface model. According to the ANOVA results, the large F value and the small P value (<0.05) indicate the validity of the model. In addition, the lack of fit (LOF) measures the failure of the model to represent data in the experimental domain at points which are not included in the regression (Khajeh 2011). The non-significant value of LOF (>0.05) indicates that the quadratic model is statistically significant for the response. The goodness of fit of the model was tested by determination coefficient (R 2). In this case, all the three responses show a very high value of determination coefficient. Furthermore, the values of the adjusted determination coefficient were also very high, which confirms that the models are highly significant (Liu et al. 2004; Adinarayana and Ellaiah 2002). At the same time, a high degree of precision and a good deal of reliability of the experimental values were explained by a low value of the coefficient of variation (CV).

Table 3 ANOVA for response surface quadratic model
Full size table

Figure 1 shows that the models were successful in capturing the correlation between the factors and the responses. The points around the diagonal line indicate a satisfactory fit of the model. As it is seen in Fig. 1, in all the three responses, replications at the center of the design show a very good agreement with each other, which confirms the reliability of the experiments.

Fig. 1
figure 1

Actual versus predicted values for a UV after 1 week, b UV after 1 month, and c thermal conductivity

Full size image

Figure 2 shows the contour plots for UV after 1 week and 1 month, which represent the short term and long term stability of nanofluids at 0.1, 0.55, and 1 % TiO2 volume concentrations. Figure 2 illustrates that at low concentration (0.1 vol%), after 1 week and 1 month, low power and short time of sonication results in the maximum UV values which represent the best stability. This incident can also be explained by the significant quadratic term X 12 in Eq. 3. This effect on stability will continue after 1 week even by increasing nanoparticle loading. This indicates that at low volume concentration, the nanofluids with short-term stability were also stable in long term. It is also clear that increasing the power and time of sonication reduces the UV values. This supports the previous studies, where long-time and high power sonication decreased the stability of nanofluids (Lee et al. 2008; Li et al. 2007). However, by increasing the particle loading, the stability would follow the diagonal direction, which ends up at high power and long time of sonication for 1 vol%. As it is shown in Fig. 2e, the high stability is more significant for UV after 1 month (long term stability). In fact, at higher concentrations, longer and stronger sonication is needed to breakdown the agglomerated particles and produce a stable nanofluid. Moreover, the comparison between the UV results after 1 week and after 1 month shows that the optimum UV area changes and nanofluids with short-term stability may not be stable in long term.

Fig. 2
figure 2

Contour plots showing the effect of time and power of sonication on UV measurements after 1 week; a 0.1, b 0.55, c 1 vol%, and after 1 month; d 0.1, e 0.55, and f 1 vol%

Full size image

In addition, by comparing the UV trend after 1 week and 1 month, it can be obtained that the short-term stability of TiO2 nanofluids is more dependent on time of sonication, while the long-term stability relies more on power of sonication.

Figure 3 portrays the contour plots for thermal conductivity of TiO2 water nanofluids. It demonstrates the effect of time and power of ultrasonication on the thermal conductivity of nanofluids by increasing the volume fraction from 0.1 to 1 %. As it can be seen from Fig. 3, all the three parameters have a considerable influence on the thermal conductivity of titania nanofluid. Increasing the power and time will gradually enhance the thermal conductivity of titania nanofluid.

Fig. 3
figure 3

Contour plots showing the effect of time and power of sonication on thermal conductivity of TiO2 water nanofluids at a 0.1, b 0.55, and c 1 vol% concentration

Full size image

It is possible that stronger and longer ultrasonication of nanofluids increases the Brownian motion which results in the thermal conductivity enhancement. By increasing the time and power of sonication, nanoparticles are agitated and their collisions inside the water increase. This improves the heat transport from one particle to another and the thermal conductivity of nanofluid. Moreover, from the comparison of the three contour plots, it can be observed that a higher loading of TiO2 nanoparticles augments the thermal conductivity of nanofluids, which is in agreement with the previous studies on thermal conductivity of nanofluids (Turgut et al. 2009; Murshed et al. 2005; Duangthongsuk and Wongwises 2009).

Although stability is essential in preparation and application of nanofluids, comparison between the UV and thermal conductivity data (Figs. 2, 3) shows that the nanofluids with higher stability does not necessarily have higher thermal conductivity. Especially, at low volume concentrations, optimizing stability and thermal conductivity follows an opposite trend (Figs. 2a, d, 3a).

Growing thermal conductivity along with long-term stability can be observed by comparing Figs. 2e and 3b. Furthermore, stability of nanofluid after 1 month can surprisingly coexist with the enhanced thermal conductivity of TiO2 nanofluid at 1 vol% (Figs. 3c, 2f).

Therefore, it is possible that nanoparticles' agglomeration and formation of nanocluster would be responsible for thermal conductivity enhancement at low volume concentrations. In this case, the stability of this nanofluid cannot be guaranteed after 1 month. Recent studies on the thermal conductivity of nanofluids have also confirmed that the enhancement of thermal conductivity is caused by the growth of nanoparticle size and formation of nanocluster (Evans et al. 2008; Gharagozloo and Goodson 2010).

Conclusion

The study focused on the influence of power and time of sonication on stability and thermal conductivity of TiO2 water nanofluids at different nanoparticle loadings. A UV–Vis spectrophotometer was employed to determine the relative stability of nanofluids after 1 week and 1 month. Implementing the contour plots in RSM based on the BBD was helpful to study the effect of time of sonication, power of sonication, and TiO2 volume concentration as three independent variables. The UV–Vis spectrophotometer measurements revealed that nanofluids with short-term stability may not be stable in long term. Results show that the stability of nanofluids after 1 week relies more on the time of sonication, while the power of sonication was found more significant for stability after 1 month. In addition, at low volume concentration, short time and low power sonication established the highest stability without any increase in the thermal conductivity. However, increasing the power and time of sonication at low volume concentration deteriorated the stability. On the other hand, by increasing the volume concentration, higher stability was more likely to be obtained at longer and stronger sonication.

Thermal conductivity enhancement was observed with increasing the time and power of sonication as well as increasing TiO2 volume concentration. It is possible that increasing the sonication time and power enhances the Brownian motion of TiO2 nanoparticles, which improves the thermal conductivity of nanofluids.

We have also observed that higher thermal conductivity of TiO2 water nanofluids was not necessarily obtained at higher stability. Hence, authors suggest that other factors such as clustering effect due to aggregation and growth of nanoparticle size are responsible for thermal conductivity enhancement. Further research and investigation is needed to understand the influence of sonication on the enhancement of thermal conductivity.

In conclusion, we suggest that stability and thermal conductivity enhancement of nanofluid should be pursued together in optimization of heat transfer characteristic. The discrepancies among the reported results in this area may be stemmed from the lack of attention to the interaction between the maximum thermal conductivity and stability in the optimization of nanofluid preparation.