Synthesis of new dihybrid nanofuid of TiO2/MWCNT in water–ethylene glycol to improve mixture thermal

Author's personal copy Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-020-10392-9

Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture thermal performance: preparation, characterization, and a novel correlation via ANN based on orthogonal distance regression algorithm Yicheng Li1,2 · Iman Moradi3 · Mahdi Kalantar4 · Elmira Babadi3 · Omid Malekahmadi4 · Amirhosein Mosavi5,6 Received: 11 October 2020 / Accepted: 30 October 2020 © Akadémiai Kiadó, Budapest, Hungary 2020

Abstract Nanofluid refers to the mixture of fluid and solid nanoparticles. If this mixture contains more than one NP or fluid, it is called “hybrid nanofluid”; further, if HN contains more than one NP and also more than one fluid, it is called “dihybrid nanofluid.” In this research, first, titanium dioxide NP was dispersed in the water–ethylene glycol basefluid and formed an HN. Then, thermal conductivity of HN was measured. After that, MWCNT NP was added to the HN and formed a DHN. Further, TC of DHN measured. Both HN and DHN TCs were compared, and the results revealed that by adding MWCNT, thermal conductivity enhanced about 30.83% (from 25.65% of HN to 56.48% of DHN). On the other hand, to analyze the phase structure, and to observe the microstructure, X-ray diffraction analysis, energy-dispersive X-ray analysis, and field emission scanning electron microscopy were examined. The measured TC for both samples was at volume fractions up to 1.0% and temperatures up to 50 °C. After an experimental study, two novel correlations were calculated by the curve-fitting method for HN and DHN, individually. In the end, to predict the other Vf and temperature, an artificial neural network has been modeled for both HN and DHN. Keywords Nanofluid · Thermal conductivity · Multi-walled carbon nanotube · Titanium dioxide · Ethylene glycol · Artificial neural network

Introduction

* Amirhosein Mosavi amirhosein.mosavi@tdtu.edu.vn 1

Automotive Engineering Research Institute, Jiangsu University, Zhenjiang 212013, China

2

The Hubei Key Laboratory of Transportation Internet of Things, Wuhan University of Technology, Wuhan 430063, China

3

Department of Mechanical Engineering, Najaf Abad University, Isfahan, Iran

4

Department of Mining and Metallurgical Engineering, Yazd University, Yazd, Iran

5

Environmental Quality, Atmospheric Science and Climate Change Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

6

Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Nanofluid refers to the mixture of fluid and solid NPs. These NPs can be metals, oxides, polymers, etc. The basefluid can be water, EG, oil, etc. [1, 2]. The first use of nanofluids to produce high thermal conductivity fluids happened in 1995,

by Lee et al. The main use of nanofluids was in the industrial applications as the heat exchanger, solar cell [3–5], etc.

However, their potential in better heat transfer led scientists and engineer researchers to develop these applications.

Nowadays, nanofluids are used in food, medicine, electronics, etc. [6–9]. The increase in TC, which is called thermal conductivity enhancement (TCE), happens in varied circumstances such as 1. an increase in the temperature and Vf., 2. change of the NPs, and 3. reduction in the NPs’ size. Jalal Alsarraf et al. [10] reported 31.08% enhancement of water basefluid TC by adding 4.5 mg/ml graphene (G). Liu et al.

[11] reported a 25.27% enhancement of water basefluid TC by adding 4.5 mg/ml graphene oxide (GO).

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If the nanofluid mixture contains only one NP or fluid, it is called “mono nanofluid (MN)” [12], while for more than one NP or fluid, it is called “HN” [13]; further, if HN contains more than one NP and also more than one fluid, it is called “DHN.” The main reason to disperse more than one NP or to mix more than one fluid is to achieve more advantages and reduce disadvantages. The advantages are more efficiency in energy, more conservation in energy, more saving in energy, etc. The disadvantages are instability, less electro-physical properties of one NP, etc. Iman Kazemi et al. [14] reported 36.12% enhancement of TC by adding 1.0 vol% G–silicon dioxide ­(SiO2) to water nanofluid.

Nguyen et al. [15] reported 26.93% enhancement of TC by adding 1.0 vol% GO–SiO2 to water nanofluid. The nanofluids field of study includes not only the TC measurement [14, 15], but also viscosity measurement [16–20], radiation estimation [21], molecular dynamic (MD) simulations [22, 23], mixed convection [24], etc.

The remarkable mechanical and thermo-electrical features of carbon nanotubes (CNTs) are the reasons that attracted the attention of scientists [25]. CNTs inside the polymer matrix with ultra-high thermal conductivity and high dimensionality provide an effective mesh for heat flow.

Overall, the application of thermal management to CNTs has made them very promising materials in various fields [26]. Serious attention was paid to the discovery of multilayer carbon nanotubes (MWCNTs) with super-microscopic structural properties, chemical, thermal, electrical, and mechanical properties in 1991 by Ijima. Significant efforts in technology applications to translate the superior properties of MWCNT into macroscale structures by researchers are addressing the dimensionality and property gap between MWCNT and ongoing engineering materials [27]. MWCNTs can be reinforcing nanofillers with very high strength properties, high rigidity, high aspect ratio, and low-density composition. Prominent mechanical properties of MWCNTs include tensile strength of 11–63 GPa and Young’s modulus of 270–950 GPa [28]. In 2009, the TC study of MWCNT nanofluids in EG basefluid was performed by Xie and Chen.

The results of their experiments demonstrated that the TC increases with the loading of the nanotube and increasing the temperature. Du et al. [29] reported a 33.23% enhancement of TC by adding 1.0 vol% MWCNT to F ­ e3O4/water nanofluid. Karimipour et al. [30] reported 37.05% enhancement of TC by adding 1.0 vol% MWCNT to CuO/water nanofluid.

Due to titanium, which is the number nine element in the Earth’s crust, ­TiO2 is used in many different applications.

These include solar cells and photocatalysts, self-cleaning coatings and paints, and anti-corrosion materials as the most common titanium compound [31]. Recently, nanofibers, nanotubes, spherical nanocrystals, and nanoparticles with elongated nanotubes are T ­ iO2 nanostructured materials that

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have a typical dimension of less than 100 nm. Production of ­TiO2 nanoparticles had reached 201,500 tons in 2015 and was projected to reach at least two million tons per year, because ­TiO2NPs can be easily accessed due to their largescale industrial production and T ­ iO2 is considered a safe material for humans and animals, according to fundamental research that may make future changes to nanotoxicology.

The use of ultrafine T ­ iO2 particles was introduced by Masuda et al. in 1993 to change the thermal conductivity and viscosity of the basefluid.

Artificial neural networks (ANNs) are computer-aided design programs and digital models of the human brain that simulate the human brain processing [32]. ANNs can be trained not just by programming but just like people through experience with appropriate learning examples. ANN features are as follows: 1. able to learn from history, 2. structural generalization, 3. in the last two decades, it has been an attractive tool for nonlinear multivariate modeling. In 2009, Yilmaz and Ozer simulated a hypothesis for biological system learning mechanisms in neural networks and expanded this learning by learning rules through specific training algorithms. In 2009 by Pham et al., it was stated that learning to perform complex tasks such as process control, process prediction, system identification, and pattern recognition is done in a set of neurons of each neural network.

In this research, first, T ­ iO2 NP was dispersed in the water–EG basefluid and formed an HN. Then, TC of HN was measured at varied Vf. from 0.2 to 1.0% and varied temperature from 25 to 50 °C. After that, MWCNT NP was added to the HN and formed a DHN. Further, TC of the DHN was measured at the same condition of HN sample. The maximum measured TCEs of the HN and the DHN were 25.65% and 56.48%, respectively. The results revealed that by adding MWCNT, thermal conductivity enhanced by about 30.83%.

After an experimental study, two novel correlations were calculated by the curve-fitting method for the HN and the DHN, individually. In the end, to predict the other domain (more or less than the mentioned temperature and Vf.), an artificial neural network (ANN) has been modeled for both HN and DHN. The novelty of this work is the ANN modeling with the orthogonal distance regression algorithm for the dihybrid nanofluid.

Materials and methods Materials As can be seen in Fig. 1, multi-walled carbon nanotube and titanium dioxide were used as NPs. Also, water and ethylene glycol were used as basefluids. Further, carboxyl

Author's personal copy Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture t…

Fig. 1 3D schematic view of MWCNT and ­TiO2

[C]

[Ti] [O] Y X

Titanium dioxide

Chemical formula Molar mass (g/mol) Density (g/cm3)

Basefluids

Nanoparticles

Water

EG

MWCNT

TiO2

H 2O 18.0153 ~ 1

C2H6O2 62.07 ~ 1.1

C 12.011 ~ 2.6

TiO2 79.866 ~ 4.2

methyl cellulose (CMC) was used as a surfactant. All the materials, with the highest purity, were purchased from Sigma-Aldrich. Properties of the NPs and the basefluids are shown in Table 1.

For phase structure analysis of MWCNT, X-ray diffraction and energy-dispersive X-ray tests were done by D8 ADVANCE Bruker X-ray diffractometer and NOVA NanoSEM, individually. Further, to observe MWCNT morphology, NOVA NanoSEM was used for a field emission scanning electron microscope.

Fig. 2 Preparation steps

Multi-walled carbon nanotube

Methods

Table 1 Properties of the basefluids and the NPs Properties

Z

TiO2

Nanofluid preparation First, the water–EG mixture was prepared at a ratio of 1:1.

Then, to prepare the HN, T ­ iO2 dispersed into the mixture of water–EG. After that, to prepare the DHN, MWCNT was added to the HN sample. The ratio of MWCNT in the DHN sample was 1:1 with T ­ iO2. For each sample, volume fractions were 0.2, 0.4, 0.6, 0.8, and 1.0% and the temperatures were 25, 30, 35, 40, 45, and 50 °C. The agglomerations between NPs must be broken to make a stable suspension [29]. So, first, the surfactant was added to the mixture, and then, pH meter was used to reach a suitable PH. After that, HN and DHN samples were stirred in a magnetic stirring for almost 180 min, individually. In the end, a 400 W sonication (24 kHz) was used for almost 10 min to make a homogeneous solution that can be seen in Fig. 2. To make sure that this solution was stable, the solution was examined after 2 weeks [30].

MWCNT

Homogeneous solution

Water–EG

Heterogeneous solution

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Thermal conductivity measurement

Thermal conductivity ratio =

knf kbf

(1)

MWCNT + TiO2 Intensity/a.u.

After the preparation of basefluid, HN, and DHN samples, a KD2 Pro Thermal apparatus was used to study the thermal conductivity. The uncertainty of this apparatus is almost 7–10% [30]. Thus, to make sure that the uncertainty is in the range of mentioned error in the manual, the apparatus calibrated with water (distilled), EG, and glycerin. The results were checked with the manual and then basefluid, HN, and DHN samples containers for each vol%, placed in the temperature Bath, and the temperature reached at the mentioned ones, individually. In the end, stainless steel KS1 sensor, which is a single-needle connection of apparatus, has entered into the HN and the DHN containers, and the TC was noted individually [29]. To make sure that the data are correct, each test was done up to five times. Figure 3 shows the measurement device.

The TCR and the TCE formulas [11] are:

(101) (004)

(105) (211) (200)

TiO2

(213)

(002) (100)

15

30

45

(004)

2θ

60

MWCNT 75

90

Fig. 4 XRD of MWCNT, T ­ iO2, and MWCNT/TiO2 composite

Results and discussion Materials

k − kbf ∗ 100 Thermal conductivity enhancement (%) = nf kbf (2) where “k” is the TC of nanofluid, “nf” is the nanofluid, and “bf” is the basefluid.

Phase and structural analysis XRD XRD patterns of MWCNT–COOH and T ­iO2 are shown in Fig. 4. A sharp characteristic peak at the (002) plane at 2θ = 25.98° with 3.423 Ǻ d-spacing interlayer spacing (Bragg’s law Cu Kα: wavelength of 1.541° Å) is nota-

Fig. 3 Measurement device

Temperature control

Circulator

Tank Pump

Body

Heater Circulating water at fixed temperature

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KD2 Pro device

Author's personal copy Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture t…

ble in the pattern. On the graph, low-intensity points at the (100) and (004) planes, at 2θ = 42.71° and 2θ = 53.26°, can be seen individually. These peaks revealed the crystalline structure of carbon nanotube [29, 30].

For ­TiO2 NP, characteristic sharp points at the (101), (004), (200), (105), (211), and (213) planes, at 2θ = 25.48°, 2θ = 38.06°, 2θ = 48.39°, 2θ = 54.19°, 2θ = 55.32°, and 2θ = 63.06°, can be seen individually. These peaks revealed the tetragonal structure of the sample. The diffraction is well-paired with the 96-900-9087 PDF card.

Microstructural observations FESEM and EDX Figure 5 reveals the FESEM pattern of carbon nanotube with scales of 5000 nm and 500 nm. Nano-

tubes have 1D structure. As image shows, these functionalized carbon nanotubes are under 100 nm, which is called the “Nano-scale.” The image also shows that these nanotubes have flattened surfaces and bundles of tangled tubes. Moreover, due to the oxygenated functional groups, it has a rough surface structure [29, 30].

After that, the energy-dispersive X-ray (2-point) was analyzed, and the chemical composition of MWCNT was resolved, which is displayed in Fig. 6 and noted in Table 2.

As can be seen, the MWCNT had pollutants such as nitrogen (N) that can be eliminated by acid functionalization.

MWCNT at points A and B consists of almost 94.58 and 95.91 at.% C, 4.19 and 2.94 at.% O and 1.23 and 1.15 at.% N, individually.

Fig. 5 FESEM of MWCNT, ­TiO2, and MWCNT/TiO2 composite

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C

N

1.0

O

0.390

0.4 0.2 0.2 Point A

ASHRAE handbook, water–EG Experimental data, water–EG

0.385 TC/W m–1 K–1

0.6

cps/eV/a.u.

0.8

0.380

0.375

0.370

Point B 0.1

0.2

0.3

0.4

0.5

0.365

0.6

25

30

35

40

45

50

45

50

Temperature/°C

keV

(a) Fig. 6 EDX of MWCNT 0.65

Table 2 EDX data for MWCNT

Point A C O N Total Point B C O N Total

[mass%]

[mass%]

at.%

[mass%]

93.09 5.49 1.42 100

93.09 5.49 1.42 100

94.58 4.19 1.23 100

12.01 1.91 1.32

94.81 3.87 1.32 100

94.81 3.87 1.32 100

95.91 2.94 1.15 100

12.57 1.71 1.44

Nanofluid preparation Thermal conductivity Validation As mentioned, the KD2 apparatus was calibrated with water and EG, and then, the results were compared with the ASHRAE handbook [33]. The maximum error was 0.52% at 50 °C. This is an acceptable error based on the ASHRAE handbook. After that, the TC of basefluid was noted (Fig. 7).

Volume fraction and temperature effect For the TC measurement, two parameters should be determined to set the range of the test. These two parameters are volume fraction and temperature. In this research, the Vf was set between 0.2 and 1.0% and the temperature was set between

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TC/W m–1 K–1

0.60

El AN Series unn. C norm. C Atom. C Error (1 Sigma)/

0.55

ASHRAE handbook, water–EG ASHRAE handbook, water

0.50 0.45 0.40 0.35

25

30

35

40

Temperature/°C

(b) Fig. 7 a Validation of basefluid by ASHRAE handbook [33] and b validation of water–EG compared to water validation

25 and 50 °C [34]. First, the TC of the ­TiO2 dispersed in the water–EG basefluid (HN) was measured. Then, the TC of the MWCNT–TiO2 dispersed in the water–EG basefluid (DHN) was measured. In Figs. 8 and 10, the TC is shown for different temperatures [35]. Also, in Figs. 9 and 11, the TC is shown for different volume fractions [36].

Further, the TC of both the HN and the DHN is shown in Fig. 12 to reveal the effect of adding MWCNT into T ­ iO2/ water–EG HN. It can be seen that after increasing the Vf and the temperature, the TC increases. However, the trend of TC increment is not similar for volume fraction and temperature. As shown in these figures, in more volume fractions, temperature has a greater effect [37]. For example, from 25 to 50 °C, the thermal conductivity increase was as follows:

Author's personal copy Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture t…

0.50

0.52

T = 25 °C T = 30 °C T = 35 °C T = 40 °C T = 45 °C T = 50 °C

TC/W m–1 K–1

0.46 0.44

EG-Water TiO2 0.2% ϕ TiO2 0.4% ϕ TiO2 0.6% ϕ TiO2 0.8% ϕ TiO2 1.0% ϕ

0.48

TC/W m–1 K–1

0.48

0.42 0.40

0.44

0.40

0.38 0.36

0.0

0.2

0.4

0.6

0.8

0.36

1.0

25

30

Volume fraction/ϕ

35 40 Temperature/°C

1.30

1.28 T = 25 °C T = 30 °C T = 35 °C T = 40 °C T = 45 °C T = 50 °C

TCR

1.16

45

50

TiO2 0.2% ϕ TiO2 0.4% ϕ TiO2 0.6% ϕ TiO2 0.8% ϕ TiO2 1.0% ϕ

1.25 1.20 TCR

1.20

50

(a)

(a)

1.24

45

1.12

1.15 1.10

1.18 1.05

1.14 1.10

1.00

0.2

0.4

0.6

0.8

1.0

Volume fraction/ϕ

(b) Fig. 8 For HN: volume fractions at different temperatures a TC and b TC ratio

For HN 0.2% vol., 4.498% (0.378–0.395 W ­m−1 ­K−1) For HN 1.0% vol., 15.476% (0.42–0.485 W ­m−1 ­K−1) It shows that 0.8% increment in vol. leads to 10.978% increase in the TC For DHN 0.2% vol., 7.017% (0.399–0.427 W ­m−1 ­K−1) For DHN 1.0% vol., 20.319% (0.502–0.604 W ­m−1 ­K−1) It shows that 0.8% increment in vol. leads to 13.302% increase in the TC. Thermal conductivity enhancement The temperature parameter has an effect on NPs’ interaction. An increase in temperature leads to the increment of interaction between NPs. The “Brownian motion (BM)” refers to this condition that by increasing the volume fraction, suspended NPs

25

30

35

40

Temperature/°C

(b) Fig. 9 For HN: temperatures at different volume fractions a TC and b TC ratio

increase and lead to an increment in surface-to-volume ratio.

The TCE of the HN and the DHN is shown in Figs. 13 and 14, respectively. At the most volume fraction and temperature, BM increment leads to higher enhancement percentage compared to the lowest temperature and volume fraction.

For example, from 25 to 50 °C, the thermal conductivity enhancement was: For HN 0.2% vol., 44.57% (1.613–2.332%) For HN 1.0% vol., 98.77% (12.903–25.648%) It shows that 0.8% increment in Vol. leads to a 54.2% increase in the TCE. For DHN 0.2% Vol., 46.35% (7.258–10.622%).

For DHN 1.0% Vol., 61.61% (34.946–56.477%).

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0.64

0.70 T = 25 °C T = 30 °C T = 35 °C T = 40 °C T = 45 °C T = 50 °C

0.56 0.52 0.48 0.44 0.40 0.36

EG –Water DHN 0.2% ϕ DHN 0.4% ϕ DHN 0.6% ϕ DHN 0.8% ϕ DHN 1.0% ϕ

0.65

TC/W m–1 K–1

TC/W m–1 K–1

0.60

0.60 0.55 0.50 0.45 0.40

0.0

0.2

0.4 0.6 Volume fraction/ϕ

0.8

0.35

1.0

25

30

35

40

45

50

45

50

Temperature/°C

(a)

(a)

1.61 1.54 1.47 1.40 1.33

1.54 1.47

1.26

1.40 1.33

1.19

1.26

1.12

1.19

1.05

DHN 0.2% ϕ DHN 0.4% ϕ DHN 0.6% ϕ DHN 0.8% ϕ DHN 1.0% ϕ

1.61

TCR

TCR

1.68

T = 25 °C T = 30 °C T = 35 °C T = 40 °C T = 45 °C T = 50 °C

1.12 0.2

0.4

0.6

0.8

1.0

Volume fraction/ϕ

1.05

25

It shows that 0.8% increment in Vol. leads to a 15.26% increase in the TCE. Further, the HN and the DHN TCEs were compared, and the results revealed that by adding MWCNT, thermal conductivity enhanced by about 30.83% (from 25.65% of the max. TCE of the HN to 56.48% of the max. TCE of the DHN). Thus, the TCE improved significantly by adding carbon nanotubes.

TCEs from different solid(s) or fluid(s) are presented in Tables 3 and 4.

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35

40

Temperature/°C

(b) Fig. 10 For DHN: volume fractions at different temperatures a TC and b TC ratio

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(b) Fig. 11 For DHN: temperatures at different volume fractions a TC and b TC ratio

Numerical study Correlation After the TC measurement, with the available experimental data, it is possible to do numerical study. Thus, to estimate a novel correlation, the curve fitting method with the “Levenberg–Marquardt” algorithm was applied on the 3D graph of TCR [48]. The novel correlations estimated for the HN and the DHN have almost 0.9 R-squared that is acceptable. The suggested correlations can calculate the TC ratio of ­TiO2/water–EG and MWCNT–TiO2/ water–EG in the specific domain of the temperature and

Author's personal copy Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture t…

70 TiO2 CNT + TiO2

DHN 0.2% ϕ DHN 0.4% ϕ DHN 0.6% ϕ DHN 0.8% ϕ DHN 1.0% ϕ

60

0.60

50

0.54

40 TCE/%

TC/W m–1 K–1

0.66

0.48

30 20

0.42 0.36 0 5

45 Tem 40 5 per atu 3 re/° C

30

25

6

0.

4

0.

2

0.

0.

10

1.

0

0

8 n/ϕ ctio

25

30

ra ef

m

lu Vo

35

40

45

50

Temperature/°C

Fig. 14 For DHN: TCE at different volume fractions Fig. 12 3D graph of TC to compare HN and DHN Table 3 TCE of other nanoparticles: mono nanofluid 30

Nanoparticle

Basefluid

TC enhancement %

References

G

Water

15

GO

Water

10

MWCNT

Water

CuO

Water

ZnO MgO Fe3O4 SiO2

Water Water Water Water

10.3% at 0.02 vol% 25% at 0.1 mass% 27% at 0.2 vol% 31.08 at 4.5 mg ­mL−1 19.9% at 0.5 mass% 25.27 at 4.5 mg ml −1 64.0 at 3.0 mass% 38.0 at 0.6 vol% 11.3 at 1.0 vol% 37 at 4.0 vol% 19.16% at 1.0 vol% 21 at 5.0 vol% 22 at 0.02 vol% 32.76% at 1.0 vol% 12.24% at 1.0 vol%

[38] [39] [40] [10] [41] [11] [42] [26] [43] [44] [30] [45] [46] [29] [14]

TiO2 0.2% ϕ TiO2 0.4% ϕ TiO2 0.6% ϕ TiO2 0.8% ϕ

25

TCE/%

20

TiO2 1.0% ϕ

5 0

25

30

35

40

45

50

Temperature/°C Fig. 13 For HN: TCE at different volume fractions

volume fraction. Both parameters of TC, volume fraction and temperature, can affect the outcome of the equations [49]. Figures 15 and 16 display the 3D graph of TCR and the fitted correlation for the HN and the DHN. The novel correlations are:

For HN:

For DHN:

knf = 1 + (0.13621 ∗ T 0.93372 ∗ V 1.35848 ) kbf knf = 1 + (0.34561 ∗ T 0.68042 ∗ V 1.01254 ) kbf

(3)

(4)

Table 4 TCE of other nanoparticles: hybrid nanofluid Nanoparticle(s)

Basefluid(s)

TC enhancement %

References

G–SiO2 GO–SiO2 MWCNT–CuO MWCNT–Fe3O4 MWCNT–Ag TiO2 MWCNT–TiO2

Water Water Water Water Water Water–EG Water–EG

36.12 at 1.0 vol% 26.93% at 1.0 vol% 37.05% at 1.0 vol% 33.23% at 1.0 vol% 37.3 at 0.03 vol% 25.65% at 1.0 vol% 56.48% at 1.0 vol%

[14] [15] [30] [29] [47] This work This work

To verify the correlation efficiency, Figs. 17 and 18 display the graphs of both experimental data and correlation line. As

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1.30 1.30

TiO2

Solid Line: correlation of TiO2/water–EG nanofluid

Exp. data for T = 25 °C Exp. data for T = 30 °C Exp. data for T = 35 °C Exp. data for T = 40 °C Exp. data for T = 45 °C Exp. data for T = 50 °C

1.25

1.25

1.20

TCR

1.20

TCR

1.15

1.10

1.10

1.05

1.05 1.00

1.15

50 5 Tem 4 0 per 4 35 atu re/° C

30

0.

6

0.

4

0.

25

0.

me

1.

0

0.6

0.8

1.0

Fig. 17 For HN: validation of novel correlation by experimental results 1.6

Solid Line: correlation of CNT-TiO2/water–EG nanofluid

Exp. data for T = 25 °C Exp. data for T = 30 °C Exp. data for T = 35 °C Exp. data for T = 40 °C Exp. data for T = 45 °C Exp. data for T = 50 °C

1.5

CNT + TiO2

1.5

TCR

1.4

1.4

TCR

0.4

Volume fraction/ϕ

Fig. 15 For HN: curve-fitting on 3D graph of TCR​

1.6

0.2

t

c fra

lu Vo

2

1.00

8 /ϕ ion

1.3

1.3 1.2

1.2

1.1

1.1 1.0 0 5 45 40 Tem per 35 atu re/° C

30

25

0.

6

0.

4

0.

2

0.

8 /ϕ ion

0

1.0

0.2

0.4

0.6

0.8

1.0

Volume fraction (ϕ)

t

rac

f me

1.

Fig. 18 For DHN: validation of novel correlation by experimental results

lu Vo

Fig. 16 For DHN: curve-fitting on 3D graph of TCR​

is obvious, the error is ignorable, and the correlation can be used to calculate the data in future studies. As is obvious, the correlation line cannot fit exactly on the experimental data, due to the 7–10% uncertainty of the KD2 device [50]. Thus, the error of the correlation line, compared to experimental Data, is not the same for all temperatures and volume fractions. With this correlation, it is also possible to calculate all the temperatures and volume fractions in this specific range.

Deviation margin that verifies the correlation [51] is:

Deviation margin (%) =

13

kExp − kPred kExp

× 100

(5)

where “Exp” and “Pred” refer to the experimental and the predicted results, respectively.

Error determination of novel correlation by experimental results is revealed in Figs. 19 and 20.

The maximum margin of deviation of the correlations is: For the HN, 1.51958% (0.70334 positive to 0.81624 negatives).

For the DHN, 1.9569% (1.02328 positive to 0.93362 negatives).

The HN and the DHN margins of deviation are revealed in Figs. 21 and 22. These figures show the error of correlation

Author's personal copy Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture t…

1.24

T = 25 °C T = 30 °C T = 35 °C T = 40 °C T = 45 °C T = 50 °C

Maximum positive error : 0.70334%

1.16 1.12 1.08 1.04

Maximum negative error : 0.81624%

1.04

1.08

1.12

1.16

1.20

Margin of deviation/%

Correlation outputs

1.20

1.0 0.5 0.0 –0.5 –1.0

1.24

1.36 1.28 1.20

1.0

1.44

Maximum negative error = – 0.934%

1.52

Fig. 20 For DHN: error determination of novel correlation by experimental results

compared to experimental data for whole quantity of temperatures. In the modeling of TC, certainty is crucial.

Correlations from different solid(s) or fluid(s) are presented in Tables 5 and 6.

Artificial neural network After the TC measurement, with the available experimental data, it is possible to train an artificial neural network (ANN) model [15, 30]. A total of one thousand data marks were set (that were for the test, validation, and train divisions):

Maximum positive error = + 1.023%

– 0.5

0.2

1.20 1.36 1.28 Experimental data

1.0

0.0

Maximum negative error : 0.93362% 1.12

0.8

0.5

– 1.0

1.12 1.04 1.04

T = 25 °C T = 30 °C T = 35 °C T = 40 °C T = 45 °C T = 50 °C

Maximum positive error : 1.02328%

1.44

0.4 0.6 Volume fraction/ϕ

Fig. 21 For HN: margin of deviation

Margin of deviation/%

Correlation outputs

1.52

Maximum negative error = – 0.816% 0.2

Experimental data

Fig. 19 For HN: error determination of novel correlation by experimental results

Maximum positive error = + 0.703%

0.4 0.6 Volume fraction/ϕ

0.8

1.0

Fig. 22 For DHN: margin of deviation Table 5 Correlation of other nanoparticles: mono nanofluid Nanofluid

Correlation

References

G–Water

knf = 0.7596 + 0.0748 × T (0.39×wt0.1835) kbf 0.224 knf = 0.863 + 0.0412 × T (0.41×wt ) kbf knf = 1 + (0.04712 ∗ T 0.36401 ∗ V 0.7393 ) kbf knf = 1 + (0.03542 ∗ T 0.57325 ∗ V 0.49394 ) kbf knf −kbf = 0.764481464u + 0.018688867T kbf

[10]

GO–Water CuO–Water Fe3O4–Water Al2O3–Water

[11] [30] [29] [52]

− 0.462147175

To control the certainty and dependability, 150 marks are placed for testing.

To control and adjust the training, 150 marks are placed for validation.

700 marks are placed for training output.

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Y. Li et al.

Table 6  Correlation of other nanoparticles: hybrid nanofluid

Nanofluid

Correlation

References

GO–SiO2/water

knf kbf knf kbf knf kbf knf kbf

[15]

MWCNT–CuO/water MWCNT–Fe3O4/water MWCNT/water–EG ZnO/water–EG

=

(0.13658+đ?œ™) − 7.20304 ∗ đ?œ™ (0.13956−0.00262∗T) 0.32529 0.41196

= 1 + (0.1034 ∗ T

∗V

[30]

)

= 1 + (0.08134 ∗ T 0.35753 ∗ V 0.19655 )

[29]

= 0.9212+1.0975đ?œ™0.319 exp(0.01286T) ( ) 0.29216 knf −kbf = 1.8454−5.2302đ?œ™ ∗ 100 k T 0.29216 −3.457

[53] [54]

bf

TC/W m–1 K–1 1.0

TC/W m–1 K–1 1.0

0.4850

0.6040

0.4582 0.4449

0.6

0.4315 0.4181

0.4

0.4048

0.5784

Volume fraction/Ď•

Volume fraction/Ď•

0.4716 0.8

0.8

0.5527 0.5271

0.6

0.5015 0.4759

0.4

0.4503

0.3914 0.2

25

30

35

40

45

50

0.4246

0.3780

0.2

25

Temperature/°C (a)

30

35

40

45

50

Temperature/°C (a) TC/W m–1 K–1

1.0

TC/W m–1 K–1

1.0

0.4860

0.6030 0.5779

0.8

0.4590 0.4455

0.6

0.4320 0.4185 0.4050

0.4

Volume fraction/Ď•

Volume fraction/Ď•

0.4725 0.8

0.5527 0.5276

0.6

0.5025 0.4774 0.4523

0.4

0.4271

0.3915 0.2

0.3780 25

30

35

40

0.3990

45

50

Temperature/°C (b)

0.4020

0.2 25

30

35

40

45

50

Temperature/°C (b)

Fig. 23  For HN: color-fill contour of a experimental data and b trained data

Fig. 24  For DHN: color-fill contour of a experimental data and b trained data

Two mentioned parameters, temperature and volume fraction, are used as input to model the ANN. Further, the “Orthogonal Distance Regression (ODR)� algorithm is employed. After that, a two-layer feed-forward net with 36 sigmoid hidden neurons and linear output neurons are

trained. The models estimated for the HN and the DHN have almost 0.999 R-squared that is satisfactory.

The suggested models can predict the TC of ­TiO 2/ water–EG and MWCNT–TiO2/water–EG beyond the mentioned specific domain of the temperature and volume fraction.

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Author's personal copy Synthesis of new dihybrid nanofluid of ­TiO2/MWCNT in water–ethylene glycol to improve mixture t…

1.24

Error determination of the ANN model by experimental results is revealed in Figs. 25 and 26.

The maximum margin of deviation of the models is:

Maximum positive error : 0.75358%

Correlation outputs

1.20

For the HN, 1.44797% (0.75358 positive to 0.69439 negatives).

For the DHN, 1.89808% (0.84674 positive to 1.05134 negatives).

1.16 1.12 1.08 1.04

Maximum negative error : 0.69439%

1.04

1.08 1.12 1.16 Experimental data

1.20

1.24

Fig. 25 For HN: error determination of ANN model by experimental results

These deviations revealed that after training the data, the HN and the DHN deviations decreased almost 0.07161% and 0.05882%, individually.

The artificial NN modeling fitted the most excellently line on the experimental data of each nanofluid. Thus, the reduction can be seen in the gaps. The comparison between the gaps of the HN and the DHN is not possible since they are different nanofluids and have different TC trends. There are other numerical models such as EANN [55], lattice Boltzmann [56] and so on [57–62].

Conclusions 1.52

Maximum positive error : 0.84674%

Correlation outputs

1.44 1.36 1.28 1.20 1.12 1.04 1.04

Maximum negative error : 1.05134%

1.12

1.20 1.28 1.36 Experimental data

1.44

1.52

Fig. 26 For DHN: error determination of ANN model by experimental results

In this research, first, ­TiO 2 NP was dispersed in the water–EG basefluid and formed an HN [63–65]. Then, TC of HN was measured at varied volume fractions of 0.2, 0.4, 0.6, 0.8, and 1.0% and varied temperatures of 25, 30, 35, 40, 45, and 50 °C. After that, to enhance the TC, MWCNT NP was added to the HN and formed a DHN. Further, TC of the DHN was measured at the same condition of the HN sample.

After an experimental study, two novel correlations were calculated by the curve-fitting method [66–74] for HN and DHN, individually. In the end, to predict the other domain (more or less than the mentioned temperature and Vf.), an artificial neural network [75–81], or MD & Nanofluid simulations [82–85] have been modeled. A comparative study between achieved data and those trained by novel correlation reveals a fine certainty.

The results are as follows: • A stable and homogeneous nanofluid has been prepared.

• By dispersing NPs to basefluid, heat transfer enhanced.

A comparative contour between experimental data and those modeled by the ANN is revealed in Figs. 23 and 24. In these graphs, (a) section refers to experimental data, while the (b) section refers to the trained model. At the (a), solid lines are wavy, since, in the (b), they are smooth. The main reason is that 30 data (6 temp. * 5 Vol. fraction) were calculated for experimental tests, while for the trained model, 1000 data were used. It can be seen that, by using these models, the TC can be predicted in the whole domain and also beyond it.

Also, after increasing temperature and Vf, the TC enhanced.

• Thermal conductivity studied for hybrid nanofluid: Titanium dioxide was dispersed in water–ethylene glycol.

Thermal conductivity studied for dihybrid nanofluid: Multi-walled carbon nanotube–titanium dioxide was dispersed in water–ethylene glycol.

• XRD, EDX, and FESEM tests were done to phase and structural analysis, and microstructural observation of MWCNT.

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• The maximum TCE of T ­ iO2/water–EG was calculated

25.65% at 1.0% Vf and 50 °C. The maximum TCE of MWCNT–TiO2/water–EG was calculated 56.48% at 1.0% Vf and 50 °C. Thus, the effect of adding MWCNT in the enhancement of the heat transfer was 30.83%.

• Two novel correlations with 0.9 R-squared were suggested to calculate the TC of HN and DHN, individually.

1.51958% (0.70334–0.81624) and 1.9569% (1.02328– 0.93362) deviations for HN and DHN were computed.

• The artificial neural network (ANN) model with 0.999 R-squared has been applied for HN and DHN, respectively. 1.44797% (0.75358–0.69439) and 1.89808% (0.84674–1.05134) deviations for HN and DHN were computed. These deviations revealed that after training the data, the HN and the DHN deviations decreased almost 0.07161% and 0.05882%, individually.

Acknowledgement The work presented in this paper was supported

by National Natural Science Foundation of China (61906076), Natural Science Foundation of Jiangsu Province (BK20190853), China Postdoctoral Science Foundation (2018M642181), Hubei Key Laboratory of Transportation Internet of Things Open Foundation (WHUTIOT-2019002).

Availability of data The data that support the findings of this study are available from the corresponding author upon reasonable request.

Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest.

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