Study of the thermal conductivity of hybrid nanofluids: Recent research and experimental study

Powder Technology 367 (2020) 347–357

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Study of the thermal conductivity of hybrid nanofluids: Recent research and experimental study Gabriela Huminic a,⁎, Angel Huminic a, Florian Dumitrache b, Claudiu Fleacă b, Ion Morjan b a b

Transilvania University of Brasov, Mechanical Engineering Department, 29, Bulevardul Eroilor, 500036, Brasov, Romania National Institute for Laser, Plasma and Radiation Physics, 409, Atomistilor Street, PO Box MG-36, 077125 Magurele, Bucharest, Romania

a r t i c l e

i n f o

Article history: Received 17 October 2019 Received in revised form 12 March 2020 Accepted 23 March 2020 Available online 04 April 2020 Keywords: Fe\ \Si aggregates Thermal conductivity Correlations

a b s t r a c t In this study, new hybrid nanoparticles aggregates containing distinct iron-based and silicon nanophases are used to improve the thermal conductivity of the base fluid. The hybrid aggregates were synthesized using the pyrolysis laser technique and also characterized using XRD and TEM and HR-TEM analysis. The thermal conductivity of the hybrid nanofluid was measured at different temperatures within the range of 20–50 ° C and mass concentrations of 0.25–1.0%. Based on the experimental results, a new correlation for the thermal conductivity variation with both the temperature and mass concentration of the Fe\\Si hybrid nanofluids was developed. The experimental results were compared to experimental data from literature. Also, the correlations proposed by different researchers for thermal conductivity prediction of hybrid nanofluids were compared and analyzed. Results indicated that increased temperature and concentration lead to increases in thermal conductivity. © 2020 Elsevier B.V. All rights reserved.

1. Introduction Hybrid nanofluids are new working fluids with improved properties, intensively studied in last years, which can be useful in many heat transfer applications. Different combinations of nanoparticles such as MgO-MWCNT, SWCNT-MgO, Al2O3-CNT, Al2O3-Ag, Ag-CNT, Cu–TiO2, Fe2O3-CNT, Al2O3-SiO2, and Al2O3-TiO2 into the base fluids (water, ethylene glycol and water-ethylene glycol mixture) were used by researchers in their studies. Because, in the past year, the number of research on the thermo-physical properties of hybrid nanofluids, especially thermal conductivity and viscosity has increased, our attention will be focused only articles published between 2018 and 2019, which will be reviewed below. These studies are necessary to understand the behavior as well as to identify factors that affect the thermo-physical properties of those hybrid nanofluids that lead to the enhancement of heat transfer performance. Esfahani et al. [1] investigated the effects of volume concentration and temperature on thermal conductivity of ZnO-Ag/water hybrid nanofluid and developed a new correlation for predicting the thermal conductivity of nanofluids. The experiments carried out for volume concentration and temperature within the range 0.125–2% and 25–50 °C respectively. They found that the effect of temperature decreases with decreasing volume fraction, the maximum enhancement in thermal ⁎ Corresponding author. E-mail address: [email protected] (G. Huminic).

https://doi.org/10.1016/j.powtec.2020.03.052 0032-5910/© 2020 Elsevier B.V. All rights reserved.

conductivity being notice at a concentration of 2% and temperature of 50 °C. Akhgar, and Toghraie [2] investigated the stability and the thermal conductivity of TiO2-MWCNTs/water-ethylene glycol hybrid nanofluid. The studied volume concentrations of nanoparticles and temperatures were within the range 0.05–1% and 20–50 °C respectively. They showed that the maximum enhancement in the thermal conductivity of nanofluid was of 38.7% and they proposed also two correlations in order to estimate the thermal conductivity of the nanofluid. Sati et al. [3] performed an experimental study on the thermal conductivity of graphene-wrapped carbon nanotubes (GC), ZnO and CuO nanoparticles and GC composites (ZnO/GC, CuO/GC) based nanofluids in distilled water and ethylene glycol different temperatures and they found that GC, ZnO/GC and CuO/GC dispersed distilled water based nanofluids showed an enhancement of 22.6%, 24.1% and 26.0% for 0.015vol.% at 50 °C, respectively. For the same volume concentration and temperature, the enhancement in thermal conductivity for GC, ZnO/GC and CuO/GC dispersed ethylene glycol based nanofluids was of 15.5%, 17.7% and 21.2%. Hamid et al. [4] studied the effect of mixing ratio of TiO2-SiO2 nanofluids on thermal conductivity and viscosity. The experiments performed for five mixing ratio, 20%:80%, 40%:60%, 50%:50%, 60%:40% and 80%:20% and also for 1.0% volume concentration of TiO2-SiO2 nanofluids. They reported that the optimum mixture ratios were 40%:60% and 80%:20% both in terms of thermal conductivity and viscosity. Also, they proposed two correlations for the thermal conductivity

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and viscosity that take into account the mixing ratio between hybrid nanoparticles. The thermal conductivity of the MWCNTs-SiC/water-ethylene glycol hybrid nanofluid was determined by Kakavandi and Akbari [5]. They observed an enhancement in thermal conductivity up to 33% compared to the base fluid at a temperature of 50 °C and a volume concentration of 0.75%. In another study, Trinh et al. [6] reported significant enhancement of 50% in thermal conductivity of ethylene glycol-based nanofluid containing graphene and carbon nanotube (Gr-CNT) hybrid material at a temperature of 50 ° C and a volume concentration of 0.07%. Dalkılıç et al. [7] found that the thermal conductivity increased by 26.29% at 1% vol. fraction for CNT- SiO2 with the mixing ratio of 80%:20% at a volume concentration of 1.0% and temperature of 60 ° C. Investigations on the thermal conductivities of Al2O3-SiO2 and Al2O3TiO2 hybrid nanofluids with water as base fluid were undertaken by Moldoveanu et al. [8,9]. They reported an enhancement up to 23.61% for 0.50 vol% Al2O3 + 2.50 vol% SiO2 and up to 19.2% for 0.50 vol% Al2O3 + 2.50 vol% TiO2 with increasing volume concentrations and temperature. Verma et al. [10] observed an enhancement in thermal conductivity up to 11.28%, 12.88%, 18.44%, 19.23%, 20.82% respectively for MgO/ water, CuO/water, MgO hybrid, CuO hybrid and MWCNT/water compared to the base fluid for 1% volume concentration of nanoparticles. Bagheri and Nadooshan [11] studied the effect of ZnO-MWCNT hybrid nanoparticles on the thermal conductivity of ethylene-glycol mixture and they found that the thermal conductivity increased up to 30% by increasing volume concentration of nanoparticles and temperature. In their research, Leong et al. [12] investigated the effects of weight percentages of the nanoparticles, types of surfactants, pH values of the base fluid solution and sonication times on the thermal conductivity of Cu-TiO2/ ethylene glycol hybrid nanofluids. They reported that the thermal conductivity of Cu-TiO 2 increased with added PVP surfactant compared to SDBS and GA surfactants, with the increase in the sonication time applied during the preparation of the nanofluids and also that the pH of the solution has a direct impact on particle–fluid interactions, the maximum value in thermal conductivy being notice at a pH = 7. Recently, Esfe [13] examined the thermal conductivity characteristics of ethylene glycol -based nanofluids containing SWCNTs-MgO (60%:40%). The results showed that the maximum increase in the thermal conductivity which was greater than 35% at temperature of 50 °C and a volume concentration of 0.55%. Also, they notice that the temperature variation considerably affects the thermal conductivity at high volume concentrations. Rostami et al. [14] conducted an experimental study on the thermal conductivity of graphene oxide‑copper oxide/water-ethylene glycol within the range 0–0.75% (volume concentrations) and 25–50 °C (temperature) and reported an enhancement in thermal conductivity up to 43.4% compared to the base fluid. Mahyari et al. [15] found that the thermal conductivity of water/graphene oxide‑silicon carbide nanofluid increased up to 33.2% at a concentration of 1 vol% and a temperature of 50 °C. In another study, Siddiqui et al. [16] studied the effect of mixing ratio of Cu-Al2O3 nanofluids on thermal conductivity. The experiments performed for three mixing ratio, 30%:70%, 50%:50% and 70%:30% and found that the optimum mixture ratio was 50%:50% due to its improved thermal conductivity and relatively better stability. Safaei et al. [17] also noticed that the thermal conductivity of CoFe2O4/SiO2/water-ethylene glycol hybrid nanofluid is increased with increasing mass concentration up to 37.7%. Aparna et al. [18] observed that the Al2O3-Ag/water hybrid nanofluids with 0.1 volume concentration and temperature of 325K showed 23.82% enhancement in thermal conductivity as compared to the base fluid. Relevant results in this field were presented also and in Refs. [19–31]. From reviewed papers, the following possible mechanisms for improving the thermal conductivity of hybrid nanofluids have been

highlighted: the Brownian motion [1–5,10,11,13,14,17,18], the clusters formation [2], the percolation effect [6], the increase of kinetic energy [4,13], the sonication time [12] and the chain formation of nanoparticles [14,17]. The novelty of the current study relates to the synthesis and characterization of the hybrid nanoparticle aggregates containing distinct iron-based and silicon nanophases as well as preparation of the water-based Fe\\Si hybrid nanofluid which was not studied until now. A novel hybrid nanoparticle aggregates containing distinct iron-based and silicon nanophases are used to improve the thermal conductivity of the base fluid. Experiments were carried out at a temperature range of 20–50°C and mass concentrations of 0.25–1.0%. The thermal conductivity correlations proposed by different researchers were compared and analyzed. A new correlation for the thermal conductivity variation with both the temperature and mass concentration of the Fe\\Si hybrid nanofluids was developed. Finally, the results of experiments were compared to experimental data from literature. 2. Thermal conductivity correlations The thermal conductivity is a measure of the ability of the material to conduct heat. The high values of the thermal conductivity indicate that the material is a good heat conductor (solid), while low values indicate that the material is a poor heat conductor (fluid). Thus, in last year's developed the materials in which the thermal conductivity of a fluid was enhanced by adding small solid particles to that fluid, called nanofluids/hybrid nanofluids. Researchers conducted many experiments to tell how much that increase would be and many correlations have been developed as shown in Tables 1–3. 3. Experimental procedure 3.1. Synthesis of raw nanopowders New hybrid nanoparticle containing metallic/carbidic iron and elemental silicon phases were synthesized using laser pyrolysis technique [32]. The experimental set-up of Fe\\Si nanopowders laser pyrolysis synthesis is shown in Fig. 1. The composite nanostructures were obtained by combining two independent laser pyrolysis processes with two reaction zones close each other and using the same nanoparticle collector, as schematically presented in Fig. 1. The first laser pyrolysis process was designated for iron based nanoparticle synthesis and used a combination between iron pentacarbonyl vapors and ethylene as reactive mixture. The second laser pyrolysis process generates the synthesis of nano-Si particles using silane as Si precursor (premixed with inert argon). In both cases silane and ethylene play a dual role as reactant and as laser energy transfer agent. The obtaining of hybrid aggregates that contains distinct silicon and iron-based nanoparticles was achieved by optimizing the distance between the reaction zones. The freshly nanoparticles emerging as a smoke diluted/surrounded by argon flow from the bright reaction zone were subsequently captured on a porous filter as figured in the same Fig. 1. The main parameters used in this synthesis are introduced in the Table 4, when one can observe that equal gas flows were introduced through the two nozzles in order to preserve the laminarity. 3.2. Characterization of hybrid Fe\\Si nanoparticles The XRD analysis of nanomaterials synthesized by hybrid laser pyrolysis technique and then-exposed to normal environment was evaluated using a High Resolution X-ray Diffractometer (PANalyticalX'Pert MPD Theta–Theta) with a Cu\\K α source (0.15418 nm), while their particular morphology was examined with a Transmission Electron Microscope (Tecnai G2 F30(300 KV)). Energy-dispersive X-ray spectroscopy (EDS) was also performed to estimate the elemental composition

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Fig. 1. The experimental set-up of Fe\ \Si nanopowders laser pyrolysis synthesis using two nearby parallel flows of precursors.

using a scanning electron microscope (FEI Quanta Inspect S) and an element Silicon Drift Detector.

controlled using a thermostat bath Haake C10–P5/U with an accuracy of ±0.04 °C.

3.3. Preparation of the Fe\\Si hybrid nanfluids

4. Results and discussions

In order to obtain homogeneous suspensions, the dry mixture of nanopowder and CMCNa stabilizer was slowly inserted in water under the combined action of the ultrasonic horn disperser (UIP 1000-hd Ultrasonic Homogenizer), and a vibrating thin rod during 5 min. Subsequently, the suspension was subjected to ultrasound treatment for 30min using an external cold water bath, to maintain a temperature around 30 °C. Finally, three different suspensions (250 ml each) containing Fe\\Si nanoparticles (2.5, 5.0 and 10 g/l, respectively) and 3 g/l low viscosity carboxymethyl cellulose sodium salt (CMCNa) were obtained. A reference 3 g/l carboxymethyl cellulose sodium salt (CMCNa) solution was also prepared in similar conditions. For determining the amount of the surfactant three simples were prepared (water+3 g/l CMCNa, water+6 g/l and water+10 g/l). For these simples the thermal conductivity and dynamic viscosity were measured. The thermal conductivity values for these simples decreases with increasing in surfactant concentration and the viscosity increases with increasing surfactant concentration [33]. This is the reason for establishing the amount of the surfactant (3 g/l CMCNa), since most studies have shown that the enhancement of convective heat transfer in thermal systems with hybrid nanofluids is accompanied by an increase in pressure drop, and consequently, by an increase in pumping power determined of the increase in viscosity.

4.1. Thermal conductivity correlations

3.4. Thermal conductivity measurement After the preparation of the new hybrid nanofluids, their thermal conductivities were measured. The measurements for the thermal conductivity were done using KD 2 Pro thermal properties analyzer (Decagon devices, Inc., USA), which operates based on the Transient Hot Wire method. In the first stage, the analyzer accuracy was checked using a test solution provided by the producer (glycerin), and also using the values of water provides by NIST [34], as depicted in Fig. 9. As shown by the error bars, the maximum relative error is smaller than 2.2%, and it decreases with the temperature bellow 1%. The thermal conductivity of each sample was measured at each temperature and the average value was taken into account. The sample temperature was

The empirical correlations based on experimental data for the thermal conductivity of hybrid nanofluids are summarized in Tables 1–3 and illustrate in Figs. 2–4. The empirical correlations were divided according to the base fluid: water, ethylene glycol and water-ethylene glycol respectively. The proposed correlations to predict thermal conductivity are established on the basis experimental data and are valid (most of them) for certain limits of nanoparticles concentration and temperature. It is seen that there are some discrepancies in empirical data, since these equations are based on fitting experimental results for studied hybrid nanofluid. For water (t = 25 °C and 50 °C) (Fig. 2) one can notice a linear trend of the thermal conductivity ratio, khnf/kbf for majority of hybrid nanofluids, excepting GO+SiC and Al2O3 + TiO2 hybrid nanofluids. Moreover, for the same hybrid nanofluid, (i.e CNT + SiO2), different results were obtained, if the mixing ratio between those two solid particles was not the same. Also, can be notice that the thermal conductivity ratio increases with increasing temperature for Al2O3 + TiO2 and Al2O3 + SiO2 respectively, while for Al2O3 + Ag the thermal conductivity ratio decreases with increasing temperature for the same mixing ratio. Although, the thermal conductivity of Al2O3 + Ag hybrid nanofluid increases with increasing temperature, it is can see a slight reduction in the conductivity ratio with increasing temperature. The high values of thermal conductivity ratio were obtained for Al2O3 + Ag (50:50) at 25 °C (1.18) and for GO+SiC at 50 °C (1.335). Compared to the water, only a few empirical correlations for hybrid nanoparticles based on ethylene glycol were developed (Fig. 3). For the same type of hybrid nanofluid, SWCNT+MgO, but in different mixing ratio, can be notice different trends for the thermal conductivity ratio. Thus, for SWCNT+MgO (20:80) the thermal conductivity ratio has a non-linear trend, while for SWCNT+MgO (60:40) the trend is linearly. Also, the values of the thermal conductivity ratio for SWCNT+MgO (60:40) were much higher than those for SWCNT+MgO (20:80) at the same volume concentration of nanoparticles. Significant differences between the thermal conductivity ratios can be notice in the case

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Table 1 Empirical correlations for thermal conductivity of hybrid nanoparticles based on water. Reference/year

Hybrid nanoparticles

Esfe et al. [19]/2015

Ag-MgO (50%:50%)

Correlation 0:1747∙10 þ ϕp knf ¼ kbf 0:1747∙105 −0:1498∙106 ∙ϕp þ 0:1117∙107 ∙ϕ2p þ 0:1997∙108 ∙ϕ3p

ϕ ≤ 0.03/−

Range/deviations

Sundar et al. [20]/2016

ND - Fe3O4 (72%:28%)

0.05 % b ϕ ≤ 0.2% 20 °C ≤ t ≤ 60 °C/−

Sundar et al. [21]/2016

ND –Co3O4 (67%:33%)

knf ¼ a þ b∙ϕ kbf t = 20 °C: a = 1.0149; b = 0.2403; t = 30 °C: a = 1.0188; b = 0.3751; t = 40 °C: a = 1.0157; b = 0.4728; t = 50 °C: a = 1.0168; b = 0.5697; t = 60 °C: a = 1.0150; b = 0.6818 knf ¼ 0:9978∙ð1 þ ϕÞ0:6556 kbf

Esfahani et al. [1]/2018

ZnO–Ag (50%:50%)

knf ¼ 1 þ 0:0008794∙ϕ0:5899 ∙t 1:345 kbf

Dalkılıç et al. [7]/2018

CNT-SiO2 (20:80, 40:60, 60:40, 80:20)%

Mahyari et al. [15]/2019

GO-SiC (50%:50%)

Aparna et al. [18]/2019

Al2O3-Ag (50%:50%)

Moldoveanu et al. [8]/2018 Moldoveanu et al. [9]/2019

Al2O3-SiO2

5

  knf mCNT 0:022254808 ¼ 0:852870218∙t 0:052797513 ∙ð1 þ ϕÞ6:591412917 ∙ kbf mSiO2 m – mass, kg knf ¼ 0:015229∙t ð0:52876þ0:31508∙ϕÞ þ 0:92124 kbf

0.05 % b ϕm ≤ 0.15% 20 °C ≤ t ≤ 60 °C /AD = 1.43% SD = 1.85% 0.125 % b ϕ ≤ 2.0% 25 °C ≤ t ≤ 50 °C/MD = 1.3% 0.001 b ϕ ≤ 0.02 25 °C ≤ t ≤ 60 °C /SD = 12%

0.05 % b ϕ ≤ 1.0% 25 °C ≤ t ≤ 50 °C /MD = 1.79% knf = 0.2154 + (−0.1177 ∙ ϕ) + (0.0012 ∙ T) + (0.0018 ∙ ϕ ∙ T) - for Al2O3-Ag (30%:70%) 0.005 % b ϕ ≤ 0.1% 298 K ≤ T ≤ 325 K/− knf = 0.541 + (−2.8811 ∙ ϕ) + (0.0003359 ∙ T) + (0.0122 ∙ ϕ ∙ T) - for Al2O3-Ag (50%:50%) knf = 0.2239 + (1.0229 ∙ ϕ) + (0.00129 ∙ T) + (−0.0008196 ∙ ϕ ∙ T) - for Al2O3-Ag (70%:30%) knf = 0.474 + 0.006 ∙ t − 0.00005 ∙ t2 + 0.041 ∙ ϕ 1.0 % b ϕ ≤ 3.0% 20 °C ≤ t ≤ 50 °C/− knf = −0.347 + 0.003 ∙ T + 6.639 ∙ ϕ − 109.024 ∙ ϕ2 0.01 b ϕ ≤ 0.03 293 K ≤ T ≤ 323 K/−

Al2O3-TiO2

fMWCNT+Fe3O4 and MgO + fMWCNT respectively, at a temperature of 25 °C. With the increase of temperature these differences become less (50 °C). Regarding the hybrid nanoparticles based on water and ethylene glycol mixture (Fig. 4), the trends are different depending on the hybrid nanofluid studied. The most of hybrid nanofluids have a non-linear trend compared to those based on water. For these hybrid nanofluids, the values of thermal conductivity ratio are quite close, at lower values of volume concentrations (up to 0.5%). Significant differences can one

notice between TiO2 + SiO2 nanofluid and other hybrid nanofluids studied. The reasons for these discrepancies could be attributed of the measurement techniques and clustering of nanoparticles. It is known that the natural convection effect in the transient hot-wire method, adding surfactants and the pH value in order to provide better dispersion and prevents clustering, as well as the mixing ratio between solid particles, can influence the thermal conductivity values. Concerning different trends of the thermal conductivity with increase in nanoparticle concentration (linear and non-linear), it can be

Table 2 Empirical correlations for thermal conductivity of hybrid nanoparticles based on ethylene glycol. Reference/year

Hybrid nanoparticles

Correlation

Range/deviations

Harandi et al. [22]/2016

f-MWCNTs-Fe3O4 (50%:50%)

knf ¼ 1 þ 0:0162∙ϕ0:7038 ∙t 0:6009 kbf

Sundar et al. [21]/2016

ND –Co3O4 (67%–33%)

knf ¼ 0:9978∙ð1 þ ϕÞ0:6556 kbf

Esfe et al. [24]/2017

SWCNT-MgO (20%–80%)

Vafaei et al. [25]/2017

MgO-MWCNTs (−)

knf ¼ 0:90844−0:06613∙ϕ0:3 ∙T 0:7 þ 0:01266 ϕ0:31 ∙T kbf knf ¼ 0:9787 þ expð0:3081∙ϕ0:3097 −0:002∙tÞ kbf

0.1 % ≤ ϕ ≤ 2.3% 25 °C ≤ t ≤ 50 °C /MD = 1.58% 0.05 % ≤ ϕm ≤ 0.15% 20 ° C ≤ t ≤ 60 ° C /AD = 1.43% SD = 1.85% 0 b ϕ ≤ 0.02 303 K ≤ T ≤ 323 K/−

Afrand [26]/2017

MgO-f-MWCNT (50%–50%)

knf ¼ 0:8341 þ 1:1∙ϕ0:243 ∙t −0:289 kbf

Akilu et al. [27]/2017

TiO2-CuO/C (80%–20%)

 0:9371  10:2685 knf ϕ T ¼ 1 þ 6:2299∙ ∙ 100 333 kbf

Esfe et al. [13]/2019

SWCNTs-MgO (60%–40%)

knf ¼ 0:97600 þ 0:10579∙ϕ þ 0:00104∙t þ 0:01017∙ϕ∙t kbf

0.05 % ≤ ϕ ≤ 0.6% 25 ° C ≤ t ≤ 50 ° C /MD = 0.8% 0 b ϕ ≤ 0.006 25 ° C ≤ t ≤ 50 ° C /MD=±1.2% 0.005 ≤ ϕ ≤ 0.02 303.15 K ≤ T ≤ 333.15 K /AD = 0.37% SD = 3.6% 0.015 % ≤ ϕ ≤ 0.55% 25 ° C ≤ t ≤ 50 ° C /SD = 2.38%

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Table 3 Empirical correlations for thermal conductivity of hybrid nanoparticles based on water-ethylene glycol mixture. Reference/year

Hybrid nanoparticles

Correlation

Range

Esfe et al. [28]/2015

Cu-TiO2 (−)

knf −0:000184 þ 4:44∙t∙ϕ ¼ 1:07 þ 0:000589∙t þ t∙ϕ kbf ∙ cos (6.11 + 0.00673 ∙ t + 4.41 ∙ t ∙ ϕ − 0.0414 ∙ sin (t)) − 32.5 ∙ ϕ

Sundar et al. [20]/2016

ND – Fe3O4 (72%:28%)

Sundar et al. [21]/2016

ND –Co3O4 (67%–33%)

knf ¼ a þ b∙ϕ kbf t = 20 °C: a = 1.0149; b = 0.2403; t = 30 °C: a = 1.0188; b = 0.3751; t = 40 °C: a = 1.0157; b = 0.4728; t = 50 °C: a = 1.0168; b = 0.5697; t = 60 °C: a = 1.0150; b = 0.6818 knf ¼ 0:9978∙ð1 þ ϕÞ0:6556 kbf

Water-ethylene glycol (60%:40%) 0.001 ≤ ϕ ≤ 0.02 30 °C ≤ t ≤ 60 °C /MSE=1.3310 ∙ 10−4 Ethylene glycol – water (20:80, 40:60and 60:40) % 0 b ϕ ≤ 0.002 20 °C ≤ t ≤ 60 °C/−

Nabil et al. [29]/2017

TiO2-SiO2 (50%–50%)

knf ¼ kbf

Rostamian et al. [30]/2017

CuO-SWCNTs (50%–50%)

knf ¼ 1 þ ð0:04056∙ðϕ∙tÞÞ−ð0:003252∙ðϕ∙tÞ2 Þ þ ð0:0001181∙ðϕ∙tÞ3 Þ−ð0:000001431∙ðϕ∙tÞ4 Þ kbf

Esfe et al. [31]/2017

SWCNT-ZnO (30%–70%)

knf ¼ 0:8707 þ 0:179∙ϕ0:179 ∙ expð0:09624∙ϕ2 Þ þ ðϕ∙tÞ∙8:883  10−4 þ ϕ0:252 ∙t∙4:435  10−3 kbf

Akhgar and Toghraie [2]/2018

TiO2-MWCNTs (50%:50%)

knf ¼ 0:006∙ϕ1:099 ∙t 1:051 þ 1:014 kbf  1;09   knf ϕ t ¼ 4:055∙ ∙ exp þ 1:013 34 34 kbf

Hamid et al. [4]/2018

TiO2-SiO2 (20:80, 40:60, 50:50, 60:40, 80:20)%

Kakavandi and Akbari [5]/2018

MWCNTs-SiC (50%:50%)

knf ¼ 0:0017∙ϕ0:698 ∙t 1:386 þ 0:981 kbf

Bagheri and Nadooshan [11]/2018

ZnO-MWCNT (25%:75%)

knf 0:8603 þ 4:9806∙ϕ0:2684 ∙0:0260∙T 0:3065 ¼ kbf expð34:9071∙ϕ2 ∙t −1:7738 Þ

Rostami et al. [14]/2019

CuO-GO (50%:50%)

 0:7803 knf t ¼ 0:2051∙ ∙ϕ0:5059 þ 0:9679 t0 kbf

Safaei et al. [17]/2019

CoFe2O4/SiO2 (−)

knf ¼ 0:9789 þ 0:0389∙T 0:4917 ∙ϕ0:7182 m kbf

 1þ

ϕ 100

5:5  0:01 t ∙ 100

 0:0437 knf t ¼ 1:17∙ð1 þ RÞ−0:1151 ∙ 80 kbf R – the mixture ratio

stated that a linear growth is according to theoretical models which concluded a linear relationship between the thermal conductivity and nanoparticles concentration, while a non-linear character of the thermal conductivity with increase in nanoparticles concentration could be an indicator that suspensions not well- dispersed.

Ethylene glycol – water (20:80, 40:60and 60:40) % 0.05 % ≤ ϕm ≤ 0.15% 20 °C ≤ t ≤ 60 °C /AD = 1.43% SD = 1.85% Water – ethylene glycol (60%:40%) 0.5 % ≤ ϕ ≤ 3.0% 20 °C ≤ t ≤ 60 °C /AD = 1.4% SD = 1.4% Ethylene glycol- water (40%:60%) 0.02 % ≤ ϕ ≤ 0.75% 20 °C ≤ t ≤ 50 °C /MD b 4% Ethylene glycol- water (60%:40%) 0.05 % ≤ ϕ ≤ 1.6% 26 °C ≤ t ≤ 50 °C /MD = 2% Ethylene glycol- water (50%:50%) 0.05 % ≤ ϕ ≤ 1.0% 20 °C ≤ t ≤ 50 °C /MD = 1.741% (first Eq.) MD = 2.002% (second Eq.) Water – ethylene glycol (60%:40%) ϕ = 0.01 30 °C ≤ t ≤ 80 °C /MD = 3.46% Water – ethylene glycol (50%:50%) 0.05 % ≤ ϕ ≤ 0.75% 25 °C ≤ t ≤ 50 °C /MD = 1.58% Ethylene glycol- water (40%:60%) 0.0375 % ≤ ϕ ≤ 1.2% 25 °C ≤ t ≤ 50 °C /MD = 1.46% Water-ethylene glycol (50%:50%) 0.1 % ≤ ϕ ≤ 1.6% 25 °C ≤ t ≤ 50 °C MD = 1.68% Water-ethylene glycol (60%:40%) 0.1 % ≤ ϕm ≤ 1.5% 15 °C ≤ t ≤ 65 °C MD = 1.86%

4.2. Characterization of hybrid Fe\\Si nanoparticles The XRD pattern of the as-synthesized nanoparticle aggregates in Fig. 5 shows the presence of two main crystalline phases: Silicon (PDF file: 005–0565) and Iron carbide/cohenite (PDF file: 035–0772) that

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highlights their hybrid particularity. Their mean crystallite size was estimated using FWHM (full width half maximum) of (111) Si and (301) Fe3C peaks based on Scherrer equation as: 16.4 nm and 11.2 nm, respectively. There is no evidence of other iron carbide phases, iron silicides or iron carbo-silicides, but their presence as unorganised phases could not be excluded from XRD analyses. Also, a minor contribution comes from the iron oxide phases: Fe3O4/ γFe2O3 (PDF files: 019–0629/039–1346) by the presence of a very broad peaks centred at 2θ 35.6° and 62.8° corresponding to magnetite-(311) and (440) respectively. The differences in XRD pattern between the crystalline phases of either oxides (Fe3O4 and γFe2O3) at the nanoscale level are difficult to be established due to similar crystalline ordering. The most viable explanation for the presence of oxide phases is the post-synthesis surface oxidation of the iron-based nanoparticles due to exposure to ambient air – synthesis conditions are strictly non-oxidative, as the reactive species are mixed with argon. While the presence of silicon phase can be explained by the silane molecules dehydrogenation, those of the iron carbide may be due to the interaction of freshly formed iron atoms/clusters (provided by Fe(CO)5 decomposition) with carbon-donor species (ethylene and carbon monoxide (via disproportionation to C and CO2), the second

being released from iron pentacarbonyl molecules splitting) in the laser-heated reaction zone. The morphology of the as-synthesized nanoparticles can be visualized in the TEM image from Fig. 6. The great majority of aggregated/agglomerated nanoparticles have a spherical form and appears to be coated by a thin shell, presumably due to oxidation upon air exposure, as certified by XRD for the iron carbide nanoparticles, yet a similar superficial oxidation should happen also for the silicon nanoparticles (low amounts of amorphous silica being difficult to be identified by XRD). In the upper left part of this image, an aggregate presenting elongated and partially fused particles can also be observed, whereas another aggregate from conjoined nanoparticles with less defined shape nanoparticles is visible in the middle-left zone. The nanoparticles in this image have dimensions in the 1–20 nm range, a great part of them entering in the 3–5 nm category, yet also intermediate size of 6–9 nm can be observer, together with a considerable population around 13–15 nm and few having 18–20 nm. The XRD mean crystallite diameter of both phases (cementite and diamond type cubic silicon) is generally compatible with the

Fig. 2. The thermal conductivity ratio variation versus volume concentration for hybrid nanofluids based on water, a) t = 25 °C , b) t = 50 °C.

Fig. 3. The thermal conductivity ratio variation versus volume concentration for hybrid nanofluids based on ethylene glycol, a) t = 25 °C , b) t = 50 °C.

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conductivity was notice at a mass concentration of 1.0%. The increase in the mass concentration of nanoparticles improves the nanofluid thermal conductivity, on the one hand, due to a larger surface-to-volume ratio of the particles with nano-size and, on the other hand, due to the high thermal conductivity of solid nanoparticles. Another reason for the increase in thermal conductivity caused by the increase in mass concentration could be the formation of chains of nanoparticles in the base fluid. The experimental results from current study are in according to those more studies reported in literature. For estimation of the experimental trend, linear regressions were computed for all studied temperatures. The proposed correlations for the variation of thermal conductivity with the mass fraction for studied temperatures are described by Eqs. 1–5:

Fig. 4. The thermal conductivity ratio variation versus volume concentration for hybrid nanofluids based on water+ethylene glycol mixture, a) t = 25 °C , b) t = 50 °C.

nanoparticle sizes observed in TEM analysis. The HR-TEM image from Fig. 7 shows the presence in the central nanoparticle (having ~ 16 nm diameter) of crystalline planes that can be assigned to Fe3C (211) phase interplanar distances of 0.21 nm. The smaller nanoparticle (around 4–5 nm) attached to the bigger one in the lower part can the tentatively attributed to cubic silicon phase where the 0.13 nm (111) interplanar distance was indicated.

T ¼ 293 K : khnf ¼ 5:76∙ϕm þ 0:5778 R2 ¼ 0:8833

ð1Þ

T ¼ 296 K : khnf ¼ 6:4114∙ϕm þ 0:5952; R2 ¼ 0:8772

ð2Þ

T ¼ 303 K : khnf ¼ 6:5371∙ϕm þ 0:6174; R2 ¼ 0:8927

ð3Þ

T ¼ 313 K : khnf ¼ 6:9943∙ϕm þ 0:6314; R2 ¼ 0:9194

ð4Þ

T ¼ 323 K : khnf ¼ 8:1943∙ϕm þ 0:6504; R2 ¼ 0:8933

ð5Þ

Fig. 9 depicts the variation of thermal conductivity with the temperature at different mass concentration of nanoparticles. One can notice that for a constant mass concentration, the thermal conductivity increases with increasing temperature, the maximum increase in the thermal conductivity coefficient occurred at 50 °C. This increase in thermal conductivity could be attributed to the increase in the thermal energy of the dispersed nanoparticles. Thus, it is known that the temperature is a measure of the kinetic energies of the particles of a substance. When two particles possessing different kinetic energies collide, part of the kinetic energy of the more energetic (higher temperature) particle is transferred to the less energetic (lower temperature) particle [35]. With the increase of temperature, the molecules move faster, the number of collisions increases and the heat transfer is improved. For the description of the variation of thermal conductivity with temperature new correlations were developed: - Water +3 g/l CMCNa:

kbf ¼ 0:0024∙T−0:1203; R2 ¼ 0:9636

ð6Þ

- 0.25wt% Fe-Si/water hybrid nanofluid:

khnf ¼ 0:0023∙T−0:0827; R2 ¼ 0:9295

ð7Þ

4.3. Thermal conductivity of Fe\\Si hybrid nanofluids In this section the effects of mass concentration and temperature on thermal conductivity of Fe-Si/water hybrid nanofluids are presented and discussed. The thermal conductivity was measured for three mass concentrations (0.25%, 0.5% and 1.0%) of Fe\\Si nanoparticles within the range of temperature 20 °C–50 °C. Fig. 8 illustrates the experimental data as a function of mass concentration of nanoparticles for different temperatures. One can notice that with increasing mass concentration of nanoparticles the thermal conductivity increased. The increase in thermal conductivity is linear with the increases of both the mass concentration and temperature. The maximum increase in the thermal

- 0.5 wt% Fe-Si/water hybrid nanofluid:

Table 4 Main process parameters for laser pyrolysis synthesis of Fe\ \Si nanoparticles. Sample DC2H4NFe(CO)5 [sccm]

DSiH4 + DAr [sccm]

Laser power under Ar//after reaction zone [W]

Flame temperature [°C]

Fe-Si

20+ 80

200/185

650

100

Ar confinement flow = 3800 sccm; Ar windows flow = 500 sccm.

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Fig. 5. X-ray diffractogram of raw Fe\ \Si based nanopowder.

Fig. 10 displays the variation of thermal conductivity ratio with temperature, defined as khnf/kbf, at studied mass concentrations of nanoparticles. As can be seen, at higher mass concentrations of nanoparticles, the increase in thermal conductivity ratio with the temperature is

much higher. This figure indicates an increase in thermal conductivity ratio of 1.126that corresponds to a temperature of 50 °C and a mass concentration of 1.0%. As mentioned above, in addition to the collision between nanoparticles and the formation of the chains of nanoparticles in the base fluid, the increase in the mass concentration of nanoparticles leads to an increase in the surface area to the volume ratio resulting in improved thermal conductivity. The maximum relative thermal conductivity computed as 100(khnf − kbf)/kbf was 12.597% for a concentration of 1.0% and a temperature of 323 K. From experimental data and reviewed papers, it can be concluded that there are no generally accepted mechanisms that described the behavior of hybrid nanofluids concerning the rise in the thermal conductivity with increasing both nanoparticles concentration and temperature. Nevertheless, there are some factors that could lead to the rise in the increase in thermal conductivity and which were

Fig. 6. Transmission electron microscopy (TEM) image of nanoparticle aggregates from raw Fe-Si-based nanopowder.

Fig. 7. High-resolution Transmission Electron Microscopy (HR-TEM) of nanoparticles from the Fe\ \Si nanopowder.

khnf ¼ 0:0029∙T−0:2156; R2 ¼ 0:9754

ð8Þ

- 1.0 wt% Fe-Si/water hybrid nanofluid

khnf ¼ 0:003∙T−0:2491; R2 ¼ 0:9716

ð9Þ

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Fig. 10. The variation of thermal conductivity ratio with temperature at different mass concentrations.

Fig. 8. Thermal conductivity variation with mass concentration at various temperatures.

mentioned by many researchers: increasing the nanoparticles concentration, increasing temperature which reduces the surface energy of the nanoparticles for agglomeration and it improves the Brownian motion, the aggregation, pH, ultrasonic time and the nanoparticles size and shape. Consequently, in thermal applications, it is desirable to use a nanofluid with relatively low concentration because a large concentration of nanoparticles would lead to agglomerate and their sedimentation, would leading thus to a decrease in the relative thermal conductivity. 4.4. Thermal conductivity correlation In the order to predict the thermal conductivity of the Fe-Si/water hybrid nanofluid, a new correlation based on experimental data is presented by the curve fitting method: kðT; ϕm Þ ¼ −0:1989 þ 0:002661∙T þ 7:243∙ϕm

Fig. 11. 3D –Thermal conductivity variation with both the temperature and nanoparticles concentration.

ð10Þ

where k is the thermal conductivity, T the temperature in K, and ϕm is the mass fraction. This correlation is valid for 293 ≤ T ≤ 323 and 0 ≤ ϕm

Fig. 9. Thermal conductivity variation with temperature at various mass fractions of nanoparticles.

Fig. 12. The margin of deviation of predicted values compared to the experimental values.

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[33]. Comparison of the results was performed at three temperatures, 298, 303 and 323 K and was shown in Fig. 13. As can be seen, thermal conductivities values of hybrid nanofluid were lower than the values of the two nanofluids. The reasons could be the presence of the carbon in the conventional nanofluids that lead to increased conductivity, the method of preparation and ultrasonic time which is different for the three nanofluids studied. In next stage, the experimental data from current study were compared to results reported in literature in terms of mass concentrations [37–39]. Fig. 14 shows the comparison of thermal conductivity of FeSi/water nanofluid as a function of mass concentration of nanoparticles with experimental data available in literature. It is clear from the figure that the thermal conductivity in all studies always improved the heat transfer of base fluid, the different values between the results being due firstly to the type of particles used and the mixing ratio. 5. Conclusions

Fig. 13. Comparison of experimental results with FeC/water and SiC/water nanofluids.

≤ 0.01. The degree of accuracy (R-square) of proposed correlation was 0.9386. Additional, the data for water+3gl/ CMCNa and Fe\\Si hybrid nanofluids was plotted in 3D as one can see in Fig. 11. In order to evaluate the accuracy of the results computed with the proposed equation for the thermal conductivity (Eq. 10) relative to the experimental data, the maximum margin of deviation was computed using the following equation: Margin of deviation ¼

kexp −kpred ∙100 ½% kexp

ð11Þ

The results of the deviation margin of the calculated values are depicted in Fig. 12. The maximum margin of deviation from the experimental results is 2.66%and the minimum margin of deflection is 3.85%. These values are acceptable values for an empirical equation. 4.5. Comparison of experimental results with experimental results of similar studies In first stage, the thermal conductivity of Fe-Si/water hybrid nanofluids was compared to FeC/water [36] and SiC/water nanofluids

In this study, the preparation, the characterization and the thermal conductivity of Fe-Si/water hybrid nanofluid were experimentally investigated at a temperature range of 20–50 °C and a mass concentration of 0.25%–1.0%. The results in current study are presented below: ➢ The increase in thermal conductivity is influence by increasing mass concentration of nanoparticles and temperature; ➢ The maximum increase in thermal conductivity was noticed at a mass concentration of 1.0%. ➢ Correlations for estimating thermal conductivity of Fe\\Si nanofluids based on mass fraction and temperature variation were developed; ➢ A correlation to estimate the thermal conductivity of the hybrid nanofluid by the curve fitting method was proposed. The deviation, R2 of the proposed correlation is 0.9386. This correlation has a good accuracy for experimental data of the studied hybrid nanofluid. Nomenclature k Thermal conductivity (W/m K) R2 Accuracy of the fitted equation t Temperature (°C) T Temperature (K) Abbreviations TEM Transmission Electron Microscopy HR-TEM High-Resolution Transmission Electron Microscopy XRD X-Ray Diffraction Fe-Si Iron-Silicon CMCNa Carboxymethyl cellulose sodium salt AD Average deviation MD Maximum margin of deviation MSE Mean square error SD Standard deviation Greek symbol ϕm Mass fraction Subscript bf Base fluid hnf Hybrid nanofluid CRediT author statement

Fig. 14. Comparison of current results with experimental data from literature.

Gabriela HUMINIC and Angel HUMINIC: Theoretical studies on thermal conductivity of hybrid nanofluids, thermal conductivity of Fe-Si/ water hybrid nanofluids. Florian DUMITRACHE, Claudiu FLEACA, Ion MORJAN: Synthesis, characterization and preparation of the Fe-Si/ water hybrid nanofluids.

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Declaration of Competing Interest None Acknowledgements This work benefited by the NUCLEU Program, developed with the support of Romanian Ministry of Research and Innovation (MCI), project no. 16N/2019 and also by the 63 PCCDI/2018 Project from the Executive Unit for Financing Higher Education, Research, Development and Innovation (UEFISCDI). The authors also greatly acknowledge Dr. Eugeniu Vasile contribution concerning TEM investigations. References [1] N.N. Esfahani, D. Toghraie, Masoud Afrand, a new correlation for predicting the thermal conductivity of ZnO–Ag (50%–50%)/water hybrid nanofluid: an experimental study, Powder Technol. 323 (2018) 367–373, https://doi.org/10.1016/j.powtec. 2017.10.025. [2] A. Akhgar, D. Toghraie, An experimental study on the stability and thermal conductivity of water-ethylene glycol/TiO2-MWCNTs hybrid nanofluid: developing a new correlation, Powder Technol. 338 (2018) 806–818, https://doi.org/10.1016/j. powtec.2018.07.086. [3] P. Sati, R.C. Shende, S. 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