*3.2. Stability of Hybrid Nanofluid*

toring.

The morphology and dispersion of the hybrid nanoparticles are presented in Figure 3. A good suspension of the hybrid nanoparticles was observed. The UV–visible, viscosity, and visual methods were used to check the stability of the prepared hybrid nanofluids. As it is widely used for studying the stability of nanofluids [7,8], the absorbance of our hybrid nanofluids was measured using UV–visible spectrophotometry in order to assess

**Figure 2.** Optimum sonication time of hybrid nanofluids via electrical conductivity and pH moni-

their stability status. Figure 4 displays the viscosity and absorbance of the hybrid nanofluid (0.5 vol%) for 2580 min (43 h). The absorbance was around 3.2 with a peak wavelength of 261 nm, while the viscosity (at 15 ◦C) was around 2.0 mPas for the monitored period. These parameters (absorbance and viscosity) depicted the stability of the nanofluid, as a straight line relatively parallel to the horizontal was noticed for each parameter. An absorbance range of 3.0–3.8 with wavelengths of 287–264 nm was measured for the hybrid nanofluids at varying volume concentrations (0.1–1.5%). It can be noticed that the absorbance increased with a rise in the volume concentration, which was in agreement with previous studies [43,44]. It was observed that the increased suspension of the bi-nanoparticles into DIW altered the values of both the absorbance and the wavelength. A careful visual inspection of the samples (even titling the sample vial) was also done and no sedimentation was noticed after a month upon inspection (Figure 5). **Figure 1.** Optimum dispersion fraction of sodium dodecyl sulphate (SDS) in hybrid nanofluids via electrical conductivity and pH monitoring. 0.4 0.5 0.6 0.7 0.8 0.9 1.0 800 1000 Dispersion fraction Electrical conductivity (Point of inflection 8.1 8.2 8.3 8.4

8.5

pH

8.6

8.7

8.8

8.9

*Nanomaterials* **2021**, *11*, x FOR PEER REVIEW 7 of 20

pH

Electrical conductivity

1200

1400

∝S/cm)

1600

**Figure 2.** Optimum sonication time of hybrid nanofluids via electrical conductivity and pH monitoring. **Figure 2.** Optimum sonication time of hybrid nanofluids via electrical conductivity and pH monitoring.

*Nanomaterials* **2021**, *11*, x FOR PEER REVIEW 8 of 20

**Figure 3.** Morphology of the hybrid nanofluid using TEM. **Figure 3.** Morphology of the hybrid nanofluid using TEM.

**Figure 4.** Stability monitoring of 0.5 vol% hybrid nanofluid using viscosity and absorbance.

**Figure 3.** Morphology of the hybrid nanofluid using TEM.

**Figure 4. Figure 4.** Stability monitoring of 0.5 vol% hybrid nanofluid using viscosity and absorbance. Stability monitoring of 0.5 vol% hybrid nanofluid using viscosity and absorbance. *Nanomaterials* **2021**, *11*, x FOR PEER REVIEW 9 of 20

**Figure 5.** Visual stability of the hybrid nanofluids. **Figure 5.** Visual stability of the hybrid nanofluids.

#### *3.3. Electrical Conductivity of Hybrid Nanofluid 3.3. Electrical Conductivity of Hybrid Nanofluid*

The capability of an aqueous solution to allow the passage of an electric current with the application of a potential difference has been termed "electrical conductivity". The dispersion of nanoparticles into base fluids (having known electrical conductivity values) to form nanofluids resulted in improved electrical conductivity in the base fluids due to the increased presence and mobility of electric charges. The hybrid nanofluids of MWCNT-Fe2O3/DIW, as electrically conducting fluids, have been investigated for their electrical conductivity at varying temperatures and volume concentrations, as illustrated in Figures 6 and 7, respectively. The electrical conductivity of MWCNT-Fe2O3/DIW nanofluids was enhanced significantly as the volume concentration increased (Figure 6). This can be linked to an increase in the electric charges in the MWCNT-Fe2O3/DIW The capability of an aqueous solution to allow the passage of an electric current with the application of a potential difference has been termed "electrical conductivity". The dispersion of nanoparticles into base fluids (having known electrical conductivity values) to form nanofluids resulted in improved electrical conductivity in the base fluids due to the increased presence and mobility of electric charges. The hybrid nanofluids of MWCNT-Fe2O3/DIW, as electrically conducting fluids, have been investigated for their electrical conductivity at varying temperatures and volume concentrations, as illustrated in Figures 6 and 7, respectively. The electrical conductivity of MWCNT-Fe2O3/DIW nanofluids was enhanced significantly as the volume concentration increased (Figure 6). This can be linked to an increase in the electric charges in the MWCNT-Fe2O3/DIW

nanofluids as the volume concentration rose. The electrical conductivity was noticed to be linearly dependent on the volume concentration of the nanofluids. Subject to a tempera-

observation is well illustrated in Figure 7, in which the electrical conductivity was improved linearly as the temperature increased. Consequently, the electrical conductivity of the nanofluids was directly proportional to the volume concentration and temperature, which was consistent with earlier studies reported in the literature for mono-particle and hybrid nanofluids [14,38,45–48]. At 55 °C and 1.5 vol%, maximum electrical conductivity (4139 μS/cm) was obtained which was considerably higher than the values of 19.0 μS/cm (for Fe3O4/water nanofluid at 0.6 vol% and 60 °C) and 1127–1265 μS/cm (Al2O3-MWCNT (80:20)/DIW nanofluid at 0.1 vol% and 50 °C) reported by Bagheli et al. [49] and Giwa et al. [38], respectively. However, Giwa et al. [48] published a range of 640–4570 μS/cm for Al2O3-Fe2O3 (75:25)/DIW nanofluid (at 0.75 vol% and 50 °C), which had a maximum value slightly higher than that reported for MWCNT-Fe2O3 (20:80)/DIW nanofluid in the present work. The electrical conductivity values were found to be strongly connected to the types of nanoparticles and the mixture ratios used in formulating the hybrid nanofluids.

nanofluids as the volume concentration rose. The electrical conductivity was noticed to be linearly dependent on the volume concentration of the nanofluids. Subject to a temperature increase, a slight enhancement of electrical conductivity was noticed (Figure 6). This observation is well illustrated in Figure 7, in which the electrical conductivity was improved linearly as the temperature increased. Consequently, the electrical conductivity of the nanofluids was directly proportional to the volume concentration and temperature, which was consistent with earlier studies reported in the literature for mono-particle and hybrid nanofluids [14,38,45–48]. At 55 ◦C and 1.5 vol%, maximum electrical conductivity (4139 µS/cm) was obtained which was considerably higher than the values of 19.0 µS/cm (for Fe3O4/water nanofluid at 0.6 vol% and 60 ◦C) and 1127–1265 µS/cm (Al2O3-MWCNT (80:20)/DIW nanofluid at 0.1 vol% and 50 ◦C) reported by Bagheli et al. [49] and Giwa et al. [38], respectively. However, Giwa et al. [48] published a range of 640–4570 µS/cm for Al2O3-Fe2O<sup>3</sup> (75:25)/DIW nanofluid (at 0.75 vol% and 50 ◦C), which had a maximum value slightly higher than that reported for MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluid in the present work. The electrical conductivity values were found to be strongly connected to the types of nanoparticles and the mixture ratios used in formulating the hybrid nanofluids.

In Figure 8, the relative electrical conductivity of MWCNT-Fe2O3/DIW nanofluids at varying volume concentrations is presented. The continued suspension of Fe2O<sup>3</sup> and MWCNT nanoparticles into DIW demonstrated a considerable increase in the relative electrical conductivity, while an increment in temperature slightly enhanced this property. The obtained result was in line with the work of Adio et al. [14], in which the relative electrical conductivity of MgO-EG nanofluids was enhanced with an increase in the nanofluid volume concentration. However, for their study, the temperature only increased relative electrical conductivity up to 30 ◦C, after which it declined. The obtained relative effective conductivity of MWCNT-Fe2O3/DIW nanofluids ranged from 3.95 to 17.76 for all the concentrations (vol.) at 55 ◦ *Nanomaterials* **2021**, *11*, x FOR PEER REVIEW C. 10 of 20

**Figure 6.** Electrical conductivity of hybrid nanofluids against volume concentration at different temperatures. **Figure 6.** Electrical conductivity of hybrid nanofluids against volume concentration at different temperatures.

**Figure 7.** Electrical conductivity of hybrid nanofluids against temperature at different volume

In Figure 8, the relative electrical conductivity of MWCNT-Fe2O3/DIW nanofluids at varying volume concentrations is presented. The continued suspension of Fe2O3 and MWCNT nanoparticles into DIW demonstrated a considerable increase in the relative electrical conductivity, while an increment in temperature slightly enhanced this property. The obtained result was in line with the work of Adio et al. [14], in which the relative electrical conductivity of MgO-EG nanofluids was enhanced with an increase in the nanofluid volume concentration. However, for their study, the temperature only increased relative electrical conductivity up to 30 °C, after which it declined. The obtained

concentrations.

temperatures.

**Figure 6.** Electrical conductivity of hybrid nanofluids against volume concentration at different

**Figure 7.** Electrical conductivity of hybrid nanofluids against temperature at different volume concentrations. **Figure 7.** Electrical conductivity of hybrid nanofluids against temperature at different volume concentrations. relative effective conductivity of MWCNT-Fe2O3/DIW nanofluids ranged from 3.95 to 17.76 for all the concentrations (vol.) at 55 °C.

**Figure 8.** Relative electrical conductivity of hybrid nanofluids against volume concentration at different temperatures. **Figure 8.** Relative electrical conductivity of hybrid nanofluids against volume concentration at different temperatures.

The electrical conductivity enhancement recorded by the addition of the hybrid nanoparticles to DIW at varying temperatures and volume concentrations is provided in Figure 9. In relation to DIW, the electrical conductivity of MWCNT-Fe2O3/DIW nanofluid was augmented significantly as the volume concentration rose but with a small enhancement as the temperature surged. It can be observed in Figure 9 that a relatively linear correlation existed between the enhancement of electrical conductivity and nanofluid volume concentration. A similar trend was noticed for the electrical conductivity enhancement with temperature, though with slight improvement. This result was found to agree The electrical conductivity enhancement recorded by the addition of the hybrid nanoparticles to DIW at varying temperatures and volume concentrations is provided in Figure 9. In relation to DIW, the electrical conductivity of MWCNT-Fe2O3/DIW nanofluid was augmented significantly as the volume concentration rose but with a small enhancement as the temperature surged. It can be observed in Figure 9 that a relatively linear correlation existed between the enhancement of electrical conductivity and nanofluid volume concentration. A similar trend was noticed for the electrical conductivity enhancement with temperature, though with slight improvement. This result was found to agree with

with previous works on the electrical conductivity enhancement of nanofluids [44,47,50]. However, some studies reported either independence from temperature in the enhance-

imum enhancement was recorded at 55 °C for all samples of the hybrid nanofluids. There-

In comparison to previous studies, Bagheli et al. [49] (Fe3O4/water nanofluid; 60 °C and 0.5 vol%), Sundar et al. [47] (nanodiamond-nickel/water nanofluid; 0.1 vol% and 65 °C), Kumar et al. [44] (MWCNT/water nanofluid; 0.6 vol% and 50 °C), Mehrali et al. [43] (nitrogen-doped graphene/water nanofluid; 60 °C and 0.06 wt%), Adio et al. [14] (EGbased MgO nanofluid; 0.5 vol% and 25 °C), Giwa et al. [38] (Al2O3-MWCNT (80:20)/DIW nanofluid; 0.1 vol% and 50 °C), and Giwa et al. [48] (Al2O3-Fe2O3 (75:25)/DIW nanofluid; 0.75 vol% and 50 °C) measured enhancements of 360%, 853.15%, 1814.96%, 190.57%, 6000%, 134.12–255.34%, and 163.37–1692.16%, respectively, for the electrical conductivity of different mono-particles and hybrid nanofluids. The nanofluid types, size of nanoparticles, volume/weight concentration or fraction, mixing ratio (for hybrid nanofluid), and temperature used in the various studies may be responsible for the variation in the results. However, a comparison of the works of Kumar et al. [44] and Bagheli et al. [49] with those of Giwa et al. [38] and Giwa et al. [48] supported the finding in the present study for MWCNT-Fe2O3/DIW nanofluid with regard to the augmentation of electrical conductivity

because of the hybridization of bi-nanoparticles.

fore, at 55 °C and 1.5 vol%, an enhancement of 1676.4% was attained.

previous works on the electrical conductivity enhancement of nanofluids [44,47,50]. However, some studies reported either independence from temperature in the enhancement or a reduction in electrical conductivity with a temperature increase [43,47,51]. Maximum enhancement was recorded at 55 ◦C for all samples of the hybrid nanofluids. Therefore, at 55 ◦ *Nanomaterials* **2021** C and 1.5 vol%, an enhancement of 1676.4% was attained. , *11*, x FOR PEER REVIEW 12 of 20

**Figure 9.** Electrical conductivity enhancement of hybrid nanofluids against volume concentration at different temperatures. **Figure 9.** Electrical conductivity enhancement of hybrid nanofluids against volume concentration at different temperatures.

*3.4. Viscosity of Hybrid Nanofluid*  An examination of the influence of the studied temperatures and volume concentrations on the viscosity of MWCNT-Fe2O3/DIW nanofluids was carried out. The viscosity of the hybrid nanofluids under varying volume concentrations and temperatures is shown in Figures 10 and 11, respectively. An appreciation of the volume concentration of MWCNT-Fe2O3 (20:80)/DIW nanofluid was observed to enhance the viscosity in a linear pattern (Figure 10). This was because of the higher density of the hybrid nanoparticles in relation to DIW. An increment in the volume concentration due to the amount of hybrid nanoparticles suspended in DIW was noticed to enhance the viscosity of the nanofluid. Nanofluid viscosity was also observed to be dependent on the temperature, as depicted in Figure 11. The increasing change in the temperature was found to lessen the viscosity of the nanofluids. From Figures 10 and 11, it can be observed that the influence of temperature on the viscosity of the hybrid nanofluids was more than that of volume concentration. Thus, the viscosity was dependent on both variables. The obtained results agreed In comparison to previous studies, Bagheli et al. [49] (Fe3O4/water nanofluid; 60 ◦C and 0.5 vol%), Sundar et al. [47] (nanodiamond-nickel/water nanofluid; 0.1 vol% and 65 ◦C), Kumar et al. [44] (MWCNT/water nanofluid; 0.6 vol% and 50 ◦C), Mehrali et al. [43] (nitrogen-doped graphene/water nanofluid; 60 ◦C and 0.06 wt%), Adio et al. [14] (EGbased MgO nanofluid; 0.5 vol% and 25 ◦C), Giwa et al. [38] (Al2O3-MWCNT (80:20)/DIW nanofluid; 0.1 vol% and 50 ◦C), and Giwa et al. [48] (Al2O3-Fe2O<sup>3</sup> (75:25)/DIW nanofluid; 0.75 vol% and 50 ◦C) measured enhancements of 360%, 853.15%, 1814.96%, 190.57%, 6000%, 134.12–255.34%, and 163.37–1692.16%, respectively, for the electrical conductivity of different mono-particles and hybrid nanofluids. The nanofluid types, size of nanoparticles, volume/weight concentration or fraction, mixing ratio (for hybrid nanofluid), and temperature used in the various studies may be responsible for the variation in the results. However, a comparison of the works of Kumar et al. [44] and Bagheli et al. [49] with those of Giwa et al. [38] and Giwa et al. [48] supported the finding in the present study for MWCNT-Fe2O3/DIW nanofluid with regard to the augmentation of electrical conductivity because of the hybridization of bi-nanoparticles.

#### [38], Sharifpur et al. [53], and Giwa et al. [54], for the viscosity–temperature and viscosity– *3.4. Viscosity of Hybrid Nanofluid*

volume concentration relationships. In the present study, the viscosity of MWCNT-Fe2O3/DIW nanofluids ranged from 0.65 to 1.36 mPas for the ranges of volume concentration and temperature investigated. This was slightly higher than the range of 0.51 to 1.11 mPas and 0.57 to 1.13 mPas published by Gangadevi and Vinayagam [55] and Giwa et al. [48] for Al2O3-CuO/water nanofluid (0.2 vol% and at 20–60 °C) and Al2O3-Fe2O3/DIW nanofluid (0.75 vol% and at 20–50 °C). An examination of the influence of the studied temperatures and volume concentrations on the viscosity of MWCNT-Fe2O3/DIW nanofluids was carried out. The viscosity of the hybrid nanofluids under varying volume concentrations and temperatures is shown in Figures 10 and 11, respectively. An appreciation of the volume concentration of MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluid was observed to enhance the viscosity in a linear pattern (Figure 10). This was because of the higher density of the hybrid nanoparticles in relation to DIW. An increment in the volume concentration due to the amount of hybrid nanoparticles suspended in DIW was noticed to enhance the viscosity of the nanofluid. Nanofluid viscosity was also observed to be dependent on the temperature, as depicted in Figure 11. The increasing change in the temperature was found to lessen the viscosity of

with the works of Nadooshan et al. [34], Mehrali et al. [43], Adio et al. [45,52], Giwa et al.

the nanofluids. From Figures 10 and 11, it can be observed that the influence of temperature on the viscosity of the hybrid nanofluids was more than that of volume concentration. Thus, the viscosity was dependent on both variables. The obtained results agreed with the works of Nadooshan et al. [34], Mehrali et al. [43], Adio et al. [45,52], Giwa et al. [38], Sharifpur et al. [53], and Giwa et al. [54], for the viscosity–temperature and viscosity–volume concentration relationships. In the present study, the viscosity of MWCNT-Fe2O3/DIW nanofluids ranged from 0.65 to 1.36 mPas for the ranges of volume concentration and temperature investigated. This was slightly higher than the range of 0.51 to 1.11 mPas and 0.57 to 1.13 mPas published by Gangadevi and Vinayagam [55] and Giwa et al. [48] for Al2O3-CuO/water nanofluid (0.2 vol% and at 20–60 ◦C) and Al2O3-Fe2O3/DIW nanofluid (0.75 vol% and at 20–50 ◦ *Nanomaterials* **2021**, *11*, x FOR PEER REVIEW C). 13 of 20

**Figure 10.** Viscosity of hybrid nanofluids against volume concentration at different temperatures. **Figure 10.** Viscosity of hybrid nanofluids against volume concentration at different temperatures. in this work increased from 1.152 (0.1 vol%) to 1.357 (1.5 vol%).

**Figure 11. Figure 11.** Viscosity of hybrid nanofluids against temperature at different volume concentrations. Viscosity of hybrid nanofluids against temperature at different volume concentrations.

**Figure 11.** Viscosity of hybrid nanofluids against temperature at different volume concentrations.

*Nanomaterials* **2021**

As shown in Figure 12, the relative viscosity of MWCNT-Fe2O3/DIW nanofluids was compared with DIW for the studied volume concentrations. An increment in the concentration of the bi-nanoparticles was found to enhance the relative viscosity of the nanofluid. A seemingly linear correlation was observed between volume concentration and relative viscosity. In addition, the relative viscosity of MWCNT-Fe2O3/DIW nanofluids was noticed to increase as the temperature increased. The observed trend agreed with the data published by Nadooshan et al. [34] (Fe3O4-MWCNT/EG nanofluid), Adio et al. [45] (Al2O3-glycerol nanofluid), and Zawawi et al. [56] (hybrid nanofluids). However, Dardan et al. [26] reported the reverse of the trend noticed in the present work, as the relative viscosity of Al2O3-MWCNT/EO nanofluid was reduced with temperatures at 35–50 ◦C, for measurements spanning 25–50 ◦C. At 55 ◦C, the relative viscosity of the nanofluids examined in this work increased from 1.152 (0.1 vol%) to 1.357 (1.5 vol%). , *11*, x FOR PEER REVIEW 14 of 20

**Figure 12.** Relative viscosity of hybrid nanofluids against volume concentration at different temperatures. **Figure 12.** Relative viscosity of hybrid nanofluids against volume concentration at different temperatures.

The percentage enhancement of the hybrid nanofluid viscosity compared with DIW under varying temperatures and volume concentrations is illustrated in Figure 13. It can be noticed that a rise in the volume concentration of MWCNT-Fe2O3 (20:80)/DIW nanofluids resulted in substantial viscosity enhancement when compared with DIW. Relatively linear enhancement of the viscosity was noticed for MWCNT-Fe2O3 (20:80)/DIW nanofluids, as the concentration and temperature rose when compared with DIW. For this work, the highest viscosity enhancement of 35.7% was estimated for the hybrid nanofluids compared to DIW. Previous studies have recorded viscosity enhancements of 58% (MWCNT; 1 vol%) [57], 20.5% (Al2O3-TiO2/PAG; 0.1 vol%) [56], 43.52% (MWCNT-CuO/EO; 1 vol%) [58], 46% (Al2O3-MWCNT/EO; 1.0 vol%) [26], 24.56% (Al2O3-MWCNT/DIW; 0.1 vol%) [38], 20% (ZnO-MWCNT/EO; 0.8 vol%) [37], 36.4% (CuO-MgO-TiO2/DIW; 0.5 vol%) [36], and 43.64% (Al2O3-Fe2O3/DIW; 0.75 vol%) [48] for mono-particle and hybrid nanofluids, when compared with the respective base fluids. The results from the present work showed a relatively lower viscosity enhancement in relation to earlier studies, which can be attributed to the types of hybrid nanoparticles and base fluids utilized in preparing MWCNT-Fe2O3 (20:80)/DIW nanofluids. MWCNT nanoparticles are known to have significantly lower density in comparison to metal oxide-based nanoparticles. The percentage enhancement of the hybrid nanofluid viscosity compared with DIW under varying temperatures and volume concentrations is illustrated in Figure 13. It can be noticed that a rise in the volume concentration of MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluids resulted in substantial viscosity enhancement when compared with DIW. Relatively linear enhancement of the viscosity was noticed for MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluids, as the concentration and temperature rose when compared with DIW. For this work, the highest viscosity enhancement of 35.7% was estimated for the hybrid nanofluids compared to DIW. Previous studies have recorded viscosity enhancements of 58% (MWCNT; 1 vol%) [57], 20.5% (Al2O3-TiO2/PAG; 0.1 vol%) [56], 43.52% (MWCNT-CuO/EO; 1 vol%) [58], 46% (Al2O3-MWCNT/EO; 1.0 vol%) [26], 24.56% (Al2O3-MWCNT/DIW; 0.1 vol%) [38], 20% (ZnO-MWCNT/EO; 0.8 vol%) [37], 36.4% (CuO-MgO-TiO2/DIW; 0.5 vol%) [36], and 43.64% (Al2O3-Fe2O3/DIW; 0.75 vol%) [48] for mono-particle and hybrid nanofluids, when compared with the respective base fluids. The results from the present work showed a relatively lower viscosity enhancement in relation to earlier studies, which can be attributed to the types of hybrid nanoparticles and base fluids utilized in preparing MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluids. MWCNT nanoparticles are known to have significantly lower density in comparison to metal oxide-based nanoparticles.

*Nanomaterials* **2021**, *11*, x FOR PEER REVIEW 15 of 20

**Figure 13.** Viscosity enhancement of hybrid nanofluids against volume concentration at different temperatures. **Figure 13.** Viscosity enhancement of hybrid nanofluids against volume concentration at different temperatures.

#### *3.5. Correlation Development 3.5. Correlation Development*

correlations.

Formulated classical models and theoretical correlations for estimating various thermal properties of different nanofluids have been demonstrated by numerous studies to be inadequate for their estimation [20,36,51,53,59]. They are found to either underestimate or overestimate the measured data of the thermal properties of nanofluids. Research progress showed that there is a need to formulate correlations to effectively estimate the thermal properties of MWCNT-Fe2O3 (20:80)/DIW nanofluid. The uniqueness of the physicochemical properties of the diverse nanoparticles and base fluids used to prepare hybrid nanofluids and the fitting of the experimental data to estimate the thermal properties are Formulated classical models and theoretical correlations for estimating various thermal properties of different nanofluids have been demonstrated by numerous studies to be inadequate for their estimation [20,36,51,53,59]. They are found to either underestimate or overestimate the measured data of the thermal properties of nanofluids. Research progress showed that there is a need to formulate correlations to effectively estimate the thermal properties of MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluid. The uniqueness of the physicochemical properties of the diverse nanoparticles and base fluids used to prepare hybrid nanofluids and the fitting of the experimental data to estimate the thermal properties are now becoming more important and relevant.

now becoming more important and relevant. Curve fittings of the experimental data of the relative electrical conductivity and relative viscosity garnered for MWCNT-Fe2O3 (20:80)/DIW nanofluids were performed. The formulas developed from the data of relative electrical conductivity and viscosity as dependencies of temperature and volume concentration are expressed in Equations (8) and (9), respectively. For the electrical conductivity correlation, R2 = 0.968, coefficient of corelation (R) = 0.984, root mean square error (RMSE)= 0.16, and mean absolute percentage error (MAPE) = 11.085, while for the viscosity correlation (linear regression), R2 = 0.966, R = 0.983, RMSE = 0.166, and MAPE = 8.721. These variables revealed relatively high coefficients of determination and correlation coefficients with significantly low errors for both Curve fittings of the experimental data of the relative electrical conductivity and relative viscosity garnered for MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluids were performed. The formulas developed from the data of relative electrical conductivity and viscosity as dependencies of temperature and volume concentration are expressed in Equations (8) and (9), respectively. For the electrical conductivity correlation, R<sup>2</sup> = 0.968, coefficient of corelation (R) = 0.984, root mean square error (RMSE) = 0.16, and mean absolute percentage error (MAPE) = 11.085, while for the viscosity correlation (linear regression), R<sup>2</sup> = 0.966, R = 0.983, RMSE = 0.166, and MAPE = 8.721. These variables revealed relatively high coefficients of determination and correlation coefficients with significantly low errors for both correlations.

$$\frac{\sigma\_{\text{lutf}}}{\sigma\_{bf}} = 2.757 + 0.032T + 9.287\varphi \tag{8}$$

$$\frac{\mu\_{\text{hf}f}}{\mu\_{bf}} = 1.031 + 0.0025T + 0.1386\varphi \tag{9}$$

ߤ ߤ = 1.031 + 0.0025ܶ + 0.1386߮ (9) The correlation from the work of Ganguly et al. [60] and that derived using Equation (8) for the relative electrical conductivity of MWCNT-Fe2O3 (20:80)/DIW at 35 °C are plotted in Figure 14. It is obvious that the existing correlation, as published in the literature, overestimated the experimental data of the electrical conductivity of MWCNT-Fe2O3 (20:80)/DIW nanofluid. This was because the existing correlation was formulated using data from a different nanofluid (Al2O3/water) to that utilized (MWCNT-Fe2O3/water) in The correlation from the work of Ganguly et al. [60] and that derived using Equation (8) for the relative electrical conductivity of MWCNT-Fe2O<sup>3</sup> (20:80)/DIW at 35 ◦C are plotted in Figure 14. It is obvious that the existing correlation, as published in the literature, overestimated the experimental data of the electrical conductivity of MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluid. This was because the existing correlation was formulated using data from a different nanofluid (Al2O3/water) to that utilized (MWCNT-Fe2O3/water) in this study, hence, it could not adequately predict the property. The correlation relating the experimental and predicted data of the relative electrical conductivity of MWCNT-Fe2O<sup>3</sup>

this study, hence, it could not adequately predict the property. The correlation relating

(20:80)/DIW nanofluid is presented in Figure 15. A straight line was noticed to relate the predicted and experimental values, showing a good correlation between both data sets. The MOD for the correlation was ±3.48%. Fe2O3 (20:80)/DIW nanofluid is presented in Figure 15. A straight line was noticed to relate the predicted and experimental values, showing a good correlation between both data sets. The MOD for the correlation was ±3.48%. the predicted and experimental values, showing a good correlation between both data sets. The MOD for the correlation was ±3.48%.

the experimental and predicted data of the relative electrical conductivity of MWCNT-Fe2O3 (20:80)/DIW nanofluid is presented in Figure 15. A straight line was noticed to relate

the experimental and predicted data of the relative electrical conductivity of MWCNT-

**Figure 14.** Developed correlations for electrical conductivity compared to an existing correlation at different temperatures. **Figure 14.** Developed correlations for electrical conductivity compared to an existing correlation at different temperatures. **Figure 14.** Developed correlations for electrical conductivity compared to an existing correlation at different temperatures.

**Figure 15.** Correlation of experimental and predicted data (electrical conductivity). **Figure 15.** Correlation of experimental and predicted data (electrical conductivity). **Figure 15.** Correlation of experimental and predicted data (electrical conductivity).

A plot of the fitted relative viscosity correlation for this work and those formulated in previous studies at 35 °C is presented in Figure 16 [26,61,62]. It shows that none of the existing correlations for estimating the viscosity of mono-particle and hybrid nanofluids could fit the obtained experimental data. They all overestimated the relative viscosity of the investigated MWCNT-Fe2O3/DIW nanofluid. The obtained relative viscosity of A plot of the fitted relative viscosity correlation for this work and those formulated in previous studies at 35 °C is presented in Figure 16 [26,61,62]. It shows that none of the existing correlations for estimating the viscosity of mono-particle and hybrid nanofluids could fit the obtained experimental data. They all overestimated the relative viscosity of the investigated MWCNT-Fe2O3/DIW nanofluid. The obtained relative viscosity of A plot of the fitted relative viscosity correlation for this work and those formulated in previous studies at 35 ◦C is presented in Figure 16 [26,61,62]. It shows that none of the existing correlations for estimating the viscosity of mono-particle and hybrid nanofluids could fit the obtained experimental data. They all overestimated the relative viscosity of the investigated MWCNT-Fe2O3/DIW nanofluid. The obtained relative viscosity of MWCNT-Fe2O3/DIW nanofluid was overestimated using the experiment-derived cor-

relation for Fe2O3/DIW nanofluid [62]. This revealed a reduction (49.8%) in the viscosity of MWCNT-Fe2O<sup>3</sup> (20:80)/DIW nanofluid because of the hybridization of Fe2O<sup>3</sup> nanoparticles with MWCNT nanoparticles. With the evident reduction in the viscosity of MWCNT-Fe2O3/DIW nanofluid, the use of this hybrid nanofluid is favorable for engineering applications in terms of lower pumping power. A linear relationship was found to occur between the experimental and predicted data, as presented in Figure 17. An MOD of ±0.01% was found. tion for Fe2O3/DIW nanofluid [62]. This revealed a reduction (49.8%) in the viscosity of MWCNT-Fe2O3 (20:80)/DIW nanofluid because of the hybridization of Fe2O3 nanoparticles with MWCNT nanoparticles. With the evident reduction in the viscosity of MWCNT-Fe2O3/DIW nanofluid, the use of this hybrid nanofluid is favorable for engineering applications in terms of lower pumping power. A linear relationship was found to occur between the experimental and predicted data, as presented in Figure 17. An MOD of ±0.01% was found. tion for Fe2O3/DIW nanofluid [62]. This revealed a reduction (49.8%) in the viscosity of MWCNT-Fe2O3 (20:80)/DIW nanofluid because of the hybridization of Fe2O3 nanoparticles with MWCNT nanoparticles. With the evident reduction in the viscosity of MWCNT-Fe2O3/DIW nanofluid, the use of this hybrid nanofluid is favorable for engineering applications in terms of lower pumping power. A linear relationship was found to occur between the experimental and predicted data, as presented in Figure 17. An MOD of ±0.01% was found.

MWCNT-Fe2O3/DIW nanofluid was overestimated using the experiment-derived correla-

MWCNT-Fe2O3/DIW nanofluid was overestimated using the experiment-derived correla-

**Figure 16.** Developed correlations for viscosity compared to existing correlations at different temperatures. **Figure 16.** Developed correlations for viscosity compared to existing correlations at different temperatures. **Figure 16.** Developed correlations for viscosity compared to existing correlations at different temperatures.

**Figure 17.** Correlation of experimental and predicted data (viscosity). **Figure 17.** Correlation of experimental and predicted data (viscosity). **Figure 17.** Correlation of experimental and predicted data (viscosity).

**4. Conclusions** 

**4. Conclusions** 
