Introduction

In recent years, various studies have been done to evaluate the thermophysical properties of water to develop its application in various industries. One of the most convenient methods of reduction of water freezing point is the addition of EG. The mixture of EG and water is known as an efficient antifreeze in cold regions. In fact, this mixture has a lower TC in comparison with the pure water.

Nanofluids are a new class of heat transfer fluid incorporating a small quantity of nanosized particles that are uniformly and stably suspended in common liquids such as water and engine oil [1]. Nanofluids have many applications in various fields such as chemical and environmental engineering [2,3,4,5]. Previous studies have revealed that the TC of nanofluids is higher than that of the base fluids [6]. In addition, it has been reported that the TC of nanofluids is highly sensitive to several factors such as size, shape, aspect ratio, NP concentration, temperature, base fluid, pH, and surfactant type and also many studies have focused on thermal convection improvement as desired change and also rheological changes to check viscosity increase as unwanted phenomena after adding nanoparticles to base fluids [6,7,8,9,10,11,12,13,14,15,16,17,18,19]. The presence of dispersed NPs within the range of 1–100 nm in nanofluids can significantly enhance the TC and the viscosity of base fluids [20]. Hence, nanofluids have been noted by many scholars and scientists because of their advantageous for several modern uses, and researchers have believed that they are the modern heat transfer fluids [21,22,23].

Several researchers have focused on the TCE of nanofluids with base fluids like water, EG, and EG–water mixture. Syam Sundar et al. [24] studied the thermophysical aspects of Fe3O4/EG–water nanofluid at ratios 60:40, 40:60, and 20:80 and reported the highest TCE of 2.94% which was for the 60:40 mixture. Vajjha and Das [25] investigated the TCE of mixture of 60:40 EG–water containing CuO and Al2O3 NPs. Reddy and Rao [26] reported the TC of TiO2/EG–water nanofluid samples in the temperature range of 30–70 °C and the volume concentration range of 0.2–1.0%. They noticed that the TC of this type of nanofluid could increase up to about 7%. Suganthi et al. [27] examined the TC of ZnO/EG–water (50:50) nanofluid and reported the maximum TCE of 17.26% for the nanofluid with volume concentration of 2%. Teng and Yu [28] showed that the TCE of nanofluid Al2O3/EG–water (45:55) nanofluid with volume concentration of 3% is about 11.6%. Hemmat Esfe et al. [29,30,31] depicted that the TCE of 40:60 EG–water nanofluid containing CuO, MgO and Cu/TiO2 NPs is 36.97%, 35%, and 44%, respectively. Afrand et al. [32] examined the TC of Fe3O4/water nanofluid in the temperature range of 20–55 °C and volume concentration range of 0.1–3%. In an experimental investigation, Sundar et al. [33] studied the TC of Fe2O4/EG–water nanofluid and found that the maximum TCE belongs to the 20:80 EG–water mixture with NP concentration of 2%. They also reported that the TC augments by boosting both the NP concentration and temperature. Soltanimehr and Afrand [1] investigated the influence of operational parameters on the TC of MWCNT/EG–water nanofluid. The outcomes of their research showed that the maximum TCE of this nanofluid is about 34.7%. Keyvani et al. [34] studied the TCE of CeO2/water nanofluid. The findings revealed that the highest TCE is about 22% which belonged to the nanofluid with NP concentration of 2.5% at 50 °C. Some was performed on thermal behavior of nanofluids with CeO2 NPs and different base fluids [35,36,37,38].

Table 1 presents a brief summary of other researches work. In these works, water or ethylene glycol was used as the base fluid. According to the results of these studies, increasing NP concentration in water or ethylene glycol enhances the TC of the base fluid.

Table 1 TCE of various nanofluids
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One of the main requirements of nanofluids is their long-term stability. The preparation method of a nanofluid is very important because of its direct impact on its thermophysical properties such as the TC. Literature survey shows that numerous inconsistencies exist in the available data regarding the nanofluids stability. Indeed, the key factor which affects the nanofluid stability is aggregation of NPs due to the existence of van der waals attractive forces. In fact, the instability of nanofluids is the main disadvantage for industrial applications [45,46,47]. Nanoparticles tend to aggregate since surface area and surface activity of these particles are high [48]. To achieve stable nanofluids, researchers use physical or chemical techniques such as the addition of surfactant, surface adjustment of the suspended particles or inducing a strong external force on the NP clusters. Among these techniques, the use of surfactant is one of the most efficient methods [49, 50]. Surfactants can be anionic, cationic, non-ionic and amphoteric [51]. Various scholars have used surfactants to make stable nanofluids. Leong et al. [52] studied the stability and TC of the carbon nanotube/EG–water nanofluid with/without a surfactant. Table 2 summarizes some of the examples of surfactants.

Table 2 Common surfactants used by researchers
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Kim et al. [53] applied the SDS and CTAB for dispersing carbon nanotubes in water and the concentration of each surfactant was nearly 0.3 mass%. Li et al. [54] focused on spreading the performance of aqueous copper nanofluids. They investigated CTAB, SDBS, and Polyoxyethylene (10) nonyl phenyl ether (TX-10). Their work showed that the optimum concentration for TX-10, CATB, and SDBS is 0.43%, 0.05%, and 0.07%, respectively. Hemmat Esfe et al. [55] applied Cetyltrimethylammonium Bromide (CTAB) to warrant high stability and good dispersion of different nanofluids.

To have better insight, Table 3 shows the comparison of different surfactant and nanofluid combinations reported in the literature.

Table 3 Comparison of different surfactants and nanofluids
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In this study, for the first time, the TC of cerium oxide/ethylene glycol–water (50:50) nanofluid has been evaluated. Stable nanofluid samples containing cerium oxide NPs in EG–water base fluid were prepared through a two-step method. The stability and the TC of prepared samples are examined in the temperature range of 20–50 °C and volume concentration range of 0.015–0.135%. Characterization of CeO2 NPs was conducted using the XRD, FTIR, FESM/EDAX, and elemental mapping techniques. Cetyltrimethylammonium bromide (CTAB) was applied as surfactant to improve the stability of suspended NPs. Although it seems that adding surfactant is an efficient and economical approach to increase the nanofluids stability, the existence of surfactant can increase the thermal resistance and weakens the heat transfer performance of nanofluids. The dispersion behavior of nanofluid samples was examined to confirm nanofluid stability via different methods. The TC of the prepared samples was evaluated using the KD2-Pro at temperatures between 20 and 50 °C. In this research, a very small amount of CTAB was utilized to reduce the disadvantage of this method. Table 4 shows the review of the TCE of nanofluids with mixture of EG–water as base fluid. According to the results, the CeO2/EG–water nanofluids with lower solid volume concentrations and at the same operating temperature range show better TCE in comparison with other nanofluids.

Table 4 TCE of nanofluids with mixture of EG–water as base fluid
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Experimental

Characterization of nanoparticles

The CeO2 NPs (purity ~ 99% and average diameter of 8–10 nm) were purchased from TECNAN company (Spain). Table 5 gives some physical properties of these NPs.

Table 5 Some physical properties of CeO2 NPs
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XRD Investigation

The crystal structure of the CeO2 NPs was evaluated using a X’Pert Pro diffractometer (PANalytical, UK) equipped with a copper anode and a Cu K\(\alpha\) radiation source (\(\lambda\) = 0.71 Å). Figure 2 shows the XRD pattern of CeO2 NPs. It is seen that the exact similarity of applied CeO2 NP with the reference COD card (96-900-9009) which refer to the cerianite mineral. Miller indices, which related to the orientation of a surface or a crystal plane also, are given in Fig. 1.

Fig. 1
figure 1

XRD pattern of CeO2 NPs

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The Sherrer formula [Eq. (1)] was applied for the estimation of the average crystallite size [61]. In this case, the average crystallite size of CeO2 NPs is about 121 Å.

$$d = \frac{0.94\lambda }{B (2\theta )\cos \theta }$$
(1)

where \(d\) is the average crystalline size (nm), \(\theta\) is the angle at maximum peak, \(\lambda\) stands for the wavelength of the incident X-ray and \(B\) denotes the full width at the half maximum intensity.

FESEM and EDAX examination

Field emission scanning electron microscopy (FESEM) was performed using ZEISS SIGMA 500 VP FESEM (ZEISS company, Germany), and the obtained results are presented in Fig. 2a. It is seen that the average diameter of NPs is on the order of 15 nm, which is in good agreement with the XRD analysis. As shown in Fig. 2b, the energy-dispersive X-ray analysis (EDAX) spectrum of CeO2 demonstrates peaks of Ce and O. Energy-dispersive X-ray analysis (EDAX) and Mapping was measured by Oxford instrument, England.

Fig. 2
figure 2

FESEM image of CeO2 NPs at ×50,000 magnification (a) and EDAX spectrum of CeO2 NPs

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To verify FESEM, the dynamic light scattering (DLS) analysis was done by ZENZS 3690 NANO SERIES, UK in two mass concentration of CeO2 NPs. Figure 3 shows the particle distribution of CeO2 in the base fluid. The findings revealed that the average particle size of CeO2 NPs is about 8.392 nm and 7.780 nm at solid volume concentration of 0.035% and 0.135%.

Fig. 3
figure 3

Particle distribution of nanofluid a 0.035% and b 0.135%

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Dispersing and nanofluid preparation

To study the TC of nanofluids, the procedure of nanofluid preparation should be studied. According to the previous studies, there are two methods for preparing a nanofluid including the single-step method and the two-step technique [26]. In this work, as the most common approach, the two-step technique is used to prepare the nanofluids. In this technique, NPs, nanofibers, nanotubes, or other nanomaterials are initially provided through chemical or physical procedures. In the next step, the nanosized powders are spread into a base fluid by using intensive magnetic force agitation, high-shear mixing, ultrasonic agitation, homogenizing, and ball milling. [18].

In this work, the considered base fluid was the 50:50 EG–water mixture. Table 6 gives some thermophysical properties of deionized water and EG. The certain amount of CTAB was added to the base fluid and sonicated for about 5 h by ultrasonic probe sonicator to get a 0.1% mass concentration solution. The required amount of CeO2 is then calculated using Eq. (2). In fact, sonication of the nanofluid samples was done to gain better dispersion of NPs by removing the agglomerations of NPs.

$$\varphi = \left[ {\frac{{\left( {\frac{W}{\rho }} \right)_{{{\text{CeO}}_{2} }} }}{{\left( {\frac{W}{\rho }} \right)_{{{\text{CeO}}_{2} }} + \left( {\frac{W}{\rho }} \right)_{\text{base fluid}} }}} \right] \times 100$$
(2)

where \(\varphi\) is the NP concentration, \(W\) is the mass and \(\rho\) is the density.

Table 6 Some thermophysical properties of water and EG
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FTIR

The FTIR was applied to assess the formation of surfactant. In the FTIR spectrum, which is presented in Fig. 4, one peak at 3016 cm−1 is observed in the νas (N–CH3) feature for the surfactants [62]. The absorption band at 2918 cm−1 was the characteristic peak for C–H stretch. Indeed, the νas (CH3) feature located in a frequency lower than 2956 cm−1 indicates the crystalline structure and a crystalline phase occurs when the νsym (CH2) frequency is lower than 2849 cm−1 [63,64,65]. The C–H stretching vibration- sym appeared at 2849 cm−1. Two features of 1462 and 1472 cm−1 are related to the CH2 scissoring region [66, 67]. CH2 Wagging Region for the CTAB molecules occurs between 1300 and 1400 cm−1 [68]. Also, the peak at 1398 cm−1 is within the region of course. δ sym(N–CH3) and ν(C–N) are also noticed at 1398 and 909 cm−1, respectively, and they are in good agreement with the data in the literature [57]. Meanwhile, the peak appeared at 725 cm−1 was due to the C–H out-of-plane deformation vibration [69]. Therefore, the tail was also detected as a triplet peak at 0.90 mg L−1.

Fig. 4
figure 4

FTIR spectra of CTAB

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Critical micelle concentration (CMC)

CMC is one of the main parameters for the evaluation of surfactants. In fact, CMC is the concentration in which surfactant mixture starts to form micelles in large scale. Electrical conductivity method is the simplest approach to define CMC. For this purpose, various concentrations of CTAB were prepared and the electrical conductivity of samples was measured. The results are depicted in Fig. 5. The sharp change in the slope indicates the CMC point of CTAB.

Fig. 5
figure 5

Electrical conductivity versus surfactant concentration

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Stability investigation

The value of zeta potential is proportional to the stability of colloidal dispersions. Consequently, high-zeta-potential nanofluids, regardless of the type of surface charge, remain well stable, while low-zeta-potential nanofluids are unstable. According to the literature, the zeta potential values less than − 25 mV or more than + 25 mV can be considered as the stable fluids [70, 71]. For analyzing the agglomeration of NPs, the Zetasizer Nano Z (MALVERN ZENZS 3690 NANO SERIES, UK) was applied to study the zeta potential values of the samples. It was found that the zeta potential of the nanofluids with NP concentration of 0.015% and 0.135% are + 54.1 mV and + 59.9 mV, respectively (See Fig. 6). In the observation process, the prepared samples were examined in terms of the sedimentation of particles (Fig. 7), and it was found that the prepared nanofluids samples are stable for minimum 3 weeks.

Fig. 6
figure 6

Zeta potential for a 0.015% and b 0.135%

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Fig. 7
figure 7

Images of the dispersed nanofluids a after 2 days and b after 10 days

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TC evaluation

To study the TC of CeO2/EG–water nanofluid, five nanofluid samples with volume concentrations of 0.015%, 0.035%, 0.07%, 0.105%, and 0.135% are prepared using a cationic surfactant (CTAB) and the ultrasonic vibrator. To evaluate the TC of all nanofluids, a KD2-Pro thermal properties analyzer (Decagon devices, USA) was used. In this instrument, the well-known hot wire method is used. The samples were placed inside a glass vessel (15 mL) where the sensor was fixed vertically to reduce the error of measurement. The samples were maintained at several temperatures using a constant temperature water bath. After the temperature of the sample reached the required temperature, the sample was kept at that temperature for further 30 min to ensure temperature equilibrium before each measurement. The accuracy of the KD-2 device was tested by measuring the TC of 50:50 EG–water mixture and comparing the results with those of the ASHRAE [72] and Sundar et al. [33]. (See Fig. 8.) The obtained results showed that the device works properly and the error of the device is less than 3%.

Fig. 8
figure 8

Comparison of this experimental values and data available in the literature for EG–water 50:50% [29, 57]

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Results and discussion

Figure 9 illustrates the variations of TC of CeO2/EG–water nanofluid versus temperature for various NP concentrations. It is clear that the TC of nanofluid enhances by rising both the volume concentration and temperature. In addition, it is seen that the TCE is higher at higher temperatures.

Fig. 9
figure 9

TC of CeO2/EG–water nanofluid versus temperature in different solid volume concentrations

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Figure 10 demonstrates the TCE of nanofluid samples in various temperatures and volume concentrations. According to the findings, the highest TCE is 36.13% which belongs to the NP with volume concentration of 0.135% at 50 °C.

Fig. 10
figure 10

TCE of the studied CeO2/EG–water nanofluid samples

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Figure 11 depicts the variations of the TCR (i.e., ratio of nanofluid TC and base fluid TC) versus NP concentration and temperature. The obtained results reveal that the TCR augments by boosting the volume concentration of NPs. Brownian motion and collisions between particles in high temperature are the main reasons for this observation. The results also demonstrate that the TCR intensifies with growing volume concentrations of NPs. Furthermore, the maximum TCR (i.e., 1.3613) is observed at 50 °C and volume concentration of 0.135%.

Fig. 11
figure 11

TCR versus NP concentration and temperature

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New correlation

According to the best knowledge of the authors, there is not an accurate and simple correlation for estimation of the TCE and TC of dispersed CeO2 in 50:50 EG–water mixture. Equations (3) and (4) are proposed for the estimation of TCE and TC of CeO2/EG–water nanofluid, respectively.

$${\text{Thermal conductivity enhancement}} = 0.152057T + 78.1569\varphi (\% ) + 2.01932 T.\varphi (\% ) + 4.02839$$
(3)
$${\text{Thermal conductivity}} = 0.00143474T + 0.25939\varphi (\% ) + 0.00882305T.\varphi (\% ) + 0.366217$$
(4)

These correlations are valid in the volume concentration range of 0.015–0.135% and temperature range of 20–50 °C. According to the coefficient of volume concentration in both equation, it can be concluded that the volume concentration of CeO2 NPs has more influence on TCE and TC values as compared with the temperature. Figure 12 shows the predicted values of TCE and TC versus the actual values. The high value of R2 indicates the accuracy of equations in the prediction of TCE and TC.

Fig. 12
figure 12

Predicted versus actual values for TCE (up) and TC (down)

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Conclusions

In this study, the stable CeO2/EG–water nanofluid was successfully prepared and the stability of prepared samples was evaluated. The TC of the prepared nanofluid samples with 0.015%, 0.035%, 0.07%, 0.105%, and 0.135% solid volume concentrations were evaluated in the temperature range of 20–50 °C. The findings confirmed that the TCR of the nanofluid could improve by boosting both the temperature and NP volume concentration. Additionally, it was found that the TC of CeO2/EG–water nanofluid improves up to 36.13% when temperature and solid volume concentration are at the highest value. In addition, a new correlation was proposed for predicting the TC and TCE of nanofluid.

Future work

It is suggested that the rheological behavior of this nanofluid also be examined in order to be able to evaluate its efficiency using hydrothermal analysis of heat exchangers containing this nanofluid.