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Prediction of Thermo-Physical Properties of TiO_{2}-Al_{2}O_{3}/Water Nanoparticles by Using Artificial Neural Network

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## Abstract

**:**

_{2}-Al

_{2}O

_{3}/water nanofluid. TiO

_{2}-Al

_{2}O

_{3}/water in the role of an innovative type of nanofluid was synthesized by the sol–gel method. The results indicated that 1.5 vol.% of nanofluids enhanced the thermal conductivity by up to 25%. It was shown that the heat transfer coefficient was linearly augmented with increasing nanoparticle concentration, but its variation with temperature was nonlinear. It should be noted that the increase in concentration may cause the particles to agglomerate, and then the thermal conductivity is reduced. The increase in temperature also increases the thermal conductivity, due to an increase in the Brownian motion and collision of particles. In this research, for the sake of predicting the thermal conductivity of TiO

_{2}-Al

_{2}O

_{3}/water nanofluid based on volumetric concentration and temperature functions, an artificial neural network is implemented. In this way, for predicting thermal conductivity, SOM (self-organizing map) and BP-LM (Back Propagation-Levenberq-Marquardt) algorithms were used. Based on the results obtained, these algorithms can be considered as an exceptional tool for predicting thermal conductivity. Additionally, the correlation coefficient values were equal to 0.938 and 0.98 when implementing the SOM and BP-LM algorithms, respectively, which is highly acceptable.

## 1. Introduction

_{2}/water nanofluid has been studied by Esfe et al. [34]. As indicated in the results, the regression coefficient of the model for the Nusselt number’s data is 99.94%. Azizi et al. [35] employed ANN to estimate the water holdup in different layouts of oil-water two-phase flow. In another use of ANN, Azizi et al. [36] investigated the estimation of void fraction in pipes with different inclination. ANN-based methods have this potential to give high precision estimation which can be beneficial in real practice since the actual experiment is not only so expensive but also very time-consuming.

_{2}nanopowder was obtained. Zhang et al. [39] used the sol–gel microemulsion method. They synthesized TiO

_{2}nanoparticles by hydrolysis of tetraizo titanium Prop Oxide with 80 Tween-Span in a microemulsion and then calcined it is at different temperatures. The results show that the particles are spherical. In some cases, the surfactant is used in the sol–gel process. Pavasupree et al. [40] synthesized semi-porous TiO

_{2}nanoparticles by adding hydrochloride clarinylamine (LAHC) as a surfactant to the precursor solution. The resulting powders were calcined for 4 h at 400 °C. In the same way, Colon et al. [41] increased the specific surface area of the particles by adding activated carbon to the solution. The XRD results showed only the presence of the anatase phase in the powders. Li et al. [37] aged the gel for 12 h at 100 °C after drying it. The results showed that aging help to remove organic compounds and influence atomic penetration and crystalline anatase. In 2014, SiO

_{2}nanoparticles were synthesized by Oliveira et al. They used the polypropylene matrix in their research. Their results showed that the production of inorganic nanoparticles in a polymer solution does not require solvent through the reaction in the molten phase [42]. Moreover, the influence of adding Al

_{2}O

_{3}and TiO

_{2}nanoparticles into the drilling mud was studied by Ghasemi et al. [43]. The size of Al

_{2}O

_{3}and TiO

_{2}nanoparticles were 20 and 60 nm, respectively, and a concentration of 0.05 wt. %. Based on the obtained results of temperature and pressure effects, the drilling mud rheological properties such as plastic viscosity are decreased by increasing the temperature, nonetheless, the pressure rise augments these properties. Additionally, the influences of pressure in low temperature outweighs in high temperatures. Also, the effective electrical conductivity of Al

_{2}O

_{3}nanoparticles was experimentally measured by Ganguly et al. [44]. For examining the influences of temperature variations and volume fraction on the electrical conductivity of Al

_{2}O

_{3}nanofluids, experiments have been carried out as a function of these parameters. As indicated in the results, the electrical conductivity increases significantly with augmenting volume fraction and temperature. Nonetheless, the effective conductivity’s reliance on the volume fraction is much higher than the temperature. Furthermore, some investigations have been intensively carried out for increasing the nanofluids’ thermal conductivity with the help of applying different kinds of nanoparticles [45,46].

_{2}-Al

_{2}O

_{3}nanoparticles in water that can be employed as a coolant fluid with its improved thermal properties. This is accomplished by conducting experiments on various volumes of nanoparticles in water. In this study, special attention has been paid to the temperature effect on the nanofluid’s thermal conductivity. The temperature’s influence on the thermal conductivity of TiO

_{2}nanofluid has not been reported yet. Furthermore, the current investigation discloses the influence of temperature and nanoparticle concentrations on the thermal properties of hybrid nanofluids. With the help of the experimental results obtained by this study, researchers can acquire exceptional information regarding the displacement of nanofluid and its properties, in which appropriate theoretical models can be achieved in the future.

## 2. Test section

#### Synthesis of TiO_{2}-Al_{2}O_{3} Nanoparticles and Characterization

_{2}-Al

_{2}O

_{3}nanoparticles prepared in various percentages of Al

_{2}O

_{3}(10–60). Two different solution samples were prepared for this nanofluid. In the first sample, 0.1105 mol (2 g) of TiCl

_{4}was dissolved in a solution that contains 10 mL of methyl acetate, 10 mL of ethanolamine and 100 mL of ethanol, and stirred for one hour at room temperature. Finally, a uniform suspension was produced. Then, AlCl

_{3}was added to the solution in various weights (0–100%) and the resulting solution was stirred for one hour at 80 °C. The second sample solution was made up of 30 mL of n-hexane, 20 mL of ethanol, 4 mL of methyl acetate and 5 mL of ammonium hydroxide. The second sample was added to the first sample and the solution was mixed simultaneously to obtain the hydrogel. By adding the second sample, the viscosity of the hydrogel increased. After the addition of the sample was complete, the solution was stirred at room temperature for 48 h and then kept at room temperature for 12 h. After 12 h, with the help of water, the obtained gel was washed to remove the chloride salts and then separated solids from it. The solids were washed three times with distilled water and then placed in an oven for 3 h at 900 °C. Figure 1 shows the schematic of nanocomposite synthesis.

_{2}). Therefore, adding more alumina will keep TiO

_{2}away from its main. With the help of the TCi Thermal Conductivity analyzer made by Canada’s C-Therm, the thermal conductivity of the nanocomposite has been calculated experimentally. Also, the Brookfield Viscometer was used to measure the viscosity of prepared nanofluid. Based on the manufacturer and the obtained results, the proposed approach for measuring thermal conductivity brings an uncertainity of ±2% with the deviation of 4% for each measurement. The repeatability and accuracy of the viscometer used are ±0.2% and ±1% in the full-scale range (FSR) of measurements, respectively. One noteworthy approach in the field of thermal analysis is differential scanning calorimetry (DSC). This approach can be found in ASTM E1269. The ASTM E1269 is the standard defined procedure for measuring specific heat capacity through DSC approach. In this research, the improved modulated-DSC approach is used to obtain the specific heats. In modulated-DSC, a sinusoidal temperature fluctuation is employed instead of a linear ramp. This novel technique is capable to calculate the heat capacity and the heat flow of the samples, simultaneously.

## 3. Results and Discussion

_{2}O

_{3}particles in the nanocomposite, the thermal conductivity of the nanocomposite was very close to that of Al

_{2}O

_{3}. Based on Figure 4, the thermal conductivity coefficient was calculated to be 11.7 W/mK within the range of 300–360 K.

^{2}+ p11 × x × y + p02 × y

^{2}+ p30 × x

^{3}+ p21 × x

^{2}× y + p12 × x × y

^{2}+ p03 × y

^{3}+ p40 × x

^{4}+ p31 × x

^{3}× y + p22 × x

^{2}*y

^{2}+ p13 × x × y

^{3}+ p04 × y

^{4}+ p50 × x

^{5}+ p41 × x

^{4}× y + p32 × x

^{3}× y

^{2}+ p23 × x

^{2}× y

^{3}+ p14 × x × y

^{4}+ p05 × y

^{5}

p10 = 3.494 × 10^{−1} (1.966 × 10^{−1}, 5.022 × 10^{−1}) |

p01 = 7.815 × 10^{−3} (−1.715 × 10^{−2}, 3.279 × 10^{−2}) |

p20 = −3.843 × 10^{−1} (−8.201 × 10^{−1}, 5.145 × 10^{−2}) |

p11 = −1.749 × 10^{−2} (−2.926 × 10^{−2}, −5.721 × 10^{−3}) |

p02 = −1.736 × 10^{−4} (−1.623 × 10^{−3}, 1.276 × 10^{−3}) |

p30 = 4.467 × 10^{−1} (−2.094 × 10^{−1}, 1.103) |

p21 = 8.337 × 10^{−3} (−1.159 × 10^{−3}, 1.783 × 10^{−2}) |

p12 = 4.972 × 10^{−4} (7.729 × 10^{−5}, 9.171 × 10^{−4}) |

p03 = 1.163 × 10^{−6} (−3.839 × 10^{−5}, 4.071 × 10^{−5}) |

p40 = −3.24 × 10^{−1} (−7.665 × 10^{−1}, 1.186 × 10^{−1}) |

p31 = −4.751 × 10^{−3} (−1.065 × 10^{−2}, 1.146 × 10^{−3}) |

p22 = −4.931 × 10^{−5} (−2.011 × 10^{−4}, 1.025 × 10^{−4}) |

p13 = −7.265 × 10^{−6} (−1.401 × 10^{−5}, −5.195 × 10^{−7}) |

p04 = 1.758 × 10^{−8} (−4.95 × 10^{−7}, 5.302 × 10^{−7}) |

p50 = 8.486 × 10^{−2} (−2.493 × 10^{−2}, 1.946 × 10^{−1}) |

p41 = 2.198 × 10^{−3} (5.41 × 10^{−4}, 3.855 × 10^{−3}) |

p32 = −2.4 × 10^{−5} (−6.092 × 10^{−5}, 1.293 × 10^{−5}) |

p23 = 5.426 × 10^{−7} (−5.136 × 10^{−7}, 1.599 × 10^{−6}) |

p14 = 3.898 × 10^{−8} (−1.76 × 10^{−9}, 7.971 × 10^{−8}) |

p05 = −2.131 × 10^{−10} (−2.756 × 10^{−9}, 2.33 × 10^{−9}) |

p00 = 4.794 × 10^{−1} (3.199 × 10^{−1}, 6.388 × 10^{−1}) |

^{2}+ p11 × x × y + p02 × y

^{2}+ p30 × x

^{3}+ p21 × x

^{2}× y + p12 × x × y

^{2}+ p03 × y

^{3}+ p40 × x

^{4}+ p31 × x

^{3}× y + p22 × x

^{2}× y

^{2}+ p13 × x × y

^{3}+ p04 × y

^{4}+ p50 × x

^{5}+ p41 × x

^{4}× y + p32 × x

^{3}× y

^{2}+ p23 × x

^{2}× y

^{3}+ p14 × x × y

^{4}+ p05 × y

^{5}

p00 = 1.043 × 10^{−3} (1.442 × 10^{−4}, 1.941 × 10^{−3}) |

p10 = −1.066 × 10^{−4} (−9.675 × 10^{−4}, 7.544 × 10^{−4}) |

p01 = 4.699 × 10^{−5} (−9.37 × 10^{−5}, 1.877 × 10^{−4}) |

p20 = −5.178 × 10^{−4} (−2.973 × 10^{−3}, 1.937 × 10^{−3}) |

p11 = 4.561 × 10^{−5} (−2.071 × 10^{−5}, 1.119 × 10^{−4}) |

p02 = −3.333 × 10^{−6} (−1.15 × 10^{−5}, 4.832 × 10^{−6}) |

p30 = 4.982 × 10^{−4} (−3.198 × 10^{−3}, 4.195 × 10^{−3}) |

p21 = 2.274 × 10^{−5} (−3.076 × 10^{−5}, 7.625 × 10^{−5}) |

p12 = −2.283 × 10^{−6} (−4.649 × 10^{−6}, 8.235 × 10^{−8}) |

p03 = 6.58 × 10^{−8} (−1.57 × 10^{−7}, 2.886 × 10^{−7}) |

p40 = −2.457 × 10^{−4} (−2.739 × 10^{−3}, 2.248 × 10^{−3}) |

p31 = −1.03 × 10^{−5} (−4.352 × 10^{−5}, 2.292 × 10^{−5}) |

p22 = −3.773 × 10^{−7} (−1.233 × 10^{−6}, 4.781 × 10^{−7}) |

p13 = 4.347 × 10^{−8} (5.466 × 10^{−9}, 8.147 × 10^{−8}) |

p04 = −4.355 × 10^{−10} (−3.324 × 10^{−9}, 2.453 × 10^{−9}) |

p50 = 4.998 × 10^{−5} (−5.686 × 10^{−4}, 6.685 × 10^{−4}) |

p41 = 1.876 × 10^{−6} (−7.46 × 10^{−6}, 1.121 × 10^{−5}) |

p32 = 6.451 × 10^{−8} (−1.435 × 10^{−7}, 2.725 × 10^{−7}) |

p23 = 2.166 × 10^{−9} (−3.785 × 10^{−9}, 8.116 × 10^{−9}) |

p14 = −2.81 × 10^{−10} (−5.105 × 10^{−10}, −5.151 × 10^{−11}) |

p05 = 1.276 × 10^{−13} (−1.42 × 10^{−11}, 1.445 × 10^{−11}) |

Goodness of fit: |

SSE: 2.306 × 10^{−9} |

R-square: 0.9991 |

Adjusted R-square: 0.9979 |

RMSE: 1.24 × 10^{−5} |

## 4. Conclusions

_{2}-Al

_{2}O

_{3}nanocomposite was synthesized. For the synthesis of nanocomposites, the sol–gel method and TiCl

_{4}and AlCl

_{3}compounds were used. The results of the analysis showed that all synthesized samples had dimensions in the nano range. After the synthesis of the nanocomposites, they were characterized by TEM. Adding alumina had a significant effect on the TiO

_{2}crystal size. The main reason for this is the formation of a homogeneous mixture of Ti-O-Al bonds during the sol–gel process. DSC (differential scanning calorimetry) was used to measure the specific heat capacity of the nanofluid. The nanocomposite showed a higher thermal capacity than its components at 300 K. A TC-Thermal Conductivity Analyzer (C-Therm Canada) was used to measure the thermal conductivity of the nanofluid-containing nanocomposite. The results showed that the average thermal conductivity was 11.7 W/mK. It should be noted that as the concentration of nanofluid increases, the agglomeration of particles also increases; as a result, the thermal conductivity of the nanofluid decreased. An increase in temperature also increases the thermal conductivity coefficient. Based on the experimental data, the relationships among concentration, temperature, thermal conductivity and viscosity were obtained. Finally, neural networks were used to predict the electrical properties of the nanofluid. For this purpose, a neural network with a multilayer perceptron structure was used to develop a model for estimating the thermal properties of nanofluids. In the end, the neural network was able to predict thermal properties by a correlation coefficient of 98%.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 5.**Variations in thermal conductivity coefficient of nanofluid with temperature and concentration of nanoparticles.

**Figure 6.**(

**a**) Contour plots, (

**b**) 3D, and (

**c**) proposed model for the thermal conductivity coefficient (Temperature is in °C and phi (Volumetric Concentration (%)).

**Figure 8.**Contour graphs (3D) describing the model’s (

**a**to

**c**) viscosity (Vis) distribution. (T (temperature) and phi (Volumetric Concentration (%)).

**Figure 10.**Correlation coefficient data based on investigating the predicted and experimental thermal conductivity ratio.

**Figure 11.**Results based on the correlation coefficient of thermal conductivity ratio. (

**a**) Training, (

**b**) Validation, (

**c**) Test, (

**d**) totally).

Parameter | Range |
---|---|

Temperature (°C) | 10–70 |

Volumetric Concentration (%) | 0.25–6 |

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## Share and Cite

**MDPI and ACS Style**

Sadeghzadeh, M.; Maddah, H.; Ahmadi, M.H.; Khadang, A.; Ghazvini, M.; Mosavi, A.; Nabipour, N. Prediction of Thermo-Physical Properties of TiO_{2}-Al_{2}O_{3}/Water Nanoparticles by Using Artificial Neural Network. *Nanomaterials* **2020**, *10*, 697.
https://doi.org/10.3390/nano10040697

**AMA Style**

Sadeghzadeh M, Maddah H, Ahmadi MH, Khadang A, Ghazvini M, Mosavi A, Nabipour N. Prediction of Thermo-Physical Properties of TiO_{2}-Al_{2}O_{3}/Water Nanoparticles by Using Artificial Neural Network. *Nanomaterials*. 2020; 10(4):697.
https://doi.org/10.3390/nano10040697

**Chicago/Turabian Style**

Sadeghzadeh, Milad, Heydar Maddah, Mohammad Hossein Ahmadi, Amirhosein Khadang, Mahyar Ghazvini, Amirhosein Mosavi, and Narjes Nabipour. 2020. "Prediction of Thermo-Physical Properties of TiO_{2}-Al_{2}O_{3}/Water Nanoparticles by Using Artificial Neural Network" *Nanomaterials* 10, no. 4: 697.
https://doi.org/10.3390/nano10040697