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Improve the thermal conductivity of 10w40-engine oil at various temperature by addition of Al 2 O 3 /Fe 2 O 3 nanoparticles Mohsen Tahmasebi Sulgani, Arash Karimipour Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran abstract article info Article history: Received 24 November 2018 Received in revised form 3 February 2019 Accepted 24 March 2019 Available online 27 March 2019 Oils are used as coolants and lubricants in different industrial systems with the aim of reducing friction between parts and their abrasion. The objective of the present study was to investigate the effect of addition of Al 2 O 3 -Fe 2 O 3 Nano powder hybrid on the thermal properties of 10w40 engine oil. In this study, the effect of nanoparticle con- centration at different mass fractions (0, 0.25, 0.5, 1, 2, and 4) was examined. Experiments were conducted within a temperature range of 2565 °C. The nano-lubricant was prepared using the two-stage method. An ultrasonic probe was used for 45 min to uniformly distribute the nanoparticles in the base uid. The thermal conductivity coefcient of the hybrid nanouid was measured using the KD2-Pro thermal analyzer, the results of which indi- cated that even the smallest mass concentration improved the thermal properties of the nano-lubricant. Accord- ingly, the largest improvement occurred at a mass fraction of 4%, i.e. 33% of the base oil. In order to calculate the thermal conductivity of the nano-lubricant using the temperature and mass fractions of the particles, the curve tting method was applied to the experimental data to nd a highly accurate experimental relation in SigmaPlot V12. © 2019 Published by Elsevier B.V. Keywords: Thermal properties 10w40-oil Various temperature Experimental study Al 2 O 3 /Fe 2 O 3 nanoparticles 1. Introduction Today, storage of energies and increasing their efciency are among the most fundamental requirements of the industry. All internal com- bustion engines and industrial machines take advantage of engine oil to prevent corrosion of parts and reduce their abrasion caused by con- stant contact. In addition to reducing corrosion and friction, oils are used for ltering, cooling, dissipation of heat from the engine, and sealing of parts [13]. Hence, it can be assumed that appropriate use of engine oils improves engine efciency and durability and reduces fuel consumption. Numerous studies have been conducted to improve the thermal properties of lubricants. For instance, addition of materials with high thermal conductivity to the base uid is a well-known method to improve the heat transfer process in systems [46]. Solid par- ticles offer a higher level of conductivity compared to the conventional uids used in heat transfer applications. In 1873, Maxwell succeeded in improving the heat transfer rate of liquids by addition of solid particles to them [7]. However, the drawbacks of this method involved pressure drop, precipitation, corrosion, and impurities. Masuda et al. were able to partly deal with these problems by using particles of tinier sizes [8]. Nanouids are a new category of uids with a high heat transfer poten- tial. They are prepared by dispersion and suspension of metal and non- metal nanoparticles of smaller than 100 nm in a base uid such as water, oil, and ethylene glycol [9]. Experimental studies show that the increase or decrease in coef- cient of conductivity of nanouids is affected by parameters such as concentration of nanoparticles, type of suspended particles and the base uid, shape of particles and their size, temperature, surfactants, type and duration of applied ultrasonic, and accumulation of particles [1012]. Moreover, studies also indicate that addition of nanoparticles signicantly increases thermal conductivity of the uid. In addition, since the nanoparticles can remain suspended for a longer period in the uid, the possibility of abrasion and obstruction of pipes due to quick deposition of particles is decreased [1315]. In their study, Wu et al. investigated the lubrication properties of two types of engine oils as well as the effect of copper oxide (CuO), tita- nium oxide (TiO 2 ), and diamond nanoparticles (Nano diamonds). To this end, the reciprocating sliding friction and wear test was used. The results showed that addition of nanoparticles to oil signicantly contrib- utes to reduction of abrasion and friction and improvement of oil prop- erties. They reported that the friction coefcients of the API-SF and the base uid containing CuO nanoparticles were reduced by 18.4% and 5.8%, respectively, and the wear depths were reduced by 16.7% and 78.8%, respectively [16]. Ku et al. assessed the lubrication characteristics of fullerene nanoparticles added to mineral oils with respect to their volumetric fraction. They used a disk-on-disk device at different volu- metric fractions and vertical loads and experimentally investigated the temperature of friction surfaces and the friction coefcient of the Journal of Molecular Liquids 283 (2019) 660666 Corresponding author. E-mail address: [email protected] (A. Karimipour). https://doi.org/10.1016/j.molliq.2019.03.140 0167-7322/© 2019 Published by Elsevier B.V. Contents lists available at ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq

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Page 1: Journal of Molecular Liquids - research.iaun.ac.irresearch.iaun.ac.ir/pd/karimipour/pdfs/PaperM_2634.pdf · Improve the thermal conductivity of 10w40-engine oil at various temperature

Journal of Molecular Liquids 283 (2019) 660–666

Contents lists available at ScienceDirect

Journal of Molecular Liquids

j ourna l homepage: www.e lsev ie r .com/ locate /mol l iq

Improve the thermal conductivity of 10w40-engine oil at varioustemperature by addition of Al2O3/Fe2O3 nanoparticles

Mohsen Tahmasebi Sulgani, Arash Karimipour ⁎Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

⁎ Corresponding author.E-mail address: [email protected] (A. K

https://doi.org/10.1016/j.molliq.2019.03.1400167-7322/© 2019 Published by Elsevier B.V.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 24 November 2018Received in revised form 3 February 2019Accepted 24 March 2019Available online 27 March 2019

Oils are used as coolants and lubricants in different industrial systems with the aim of reducing friction betweenparts and their abrasion. The objective of the present studywas to investigate the effect of addition of Al2O3-Fe2O3

Nano powder hybrid on the thermal properties of 10w40 engine oil. In this study, the effect of nanoparticle con-centration at differentmass fractions (0, 0.25, 0.5, 1, 2, and 4)was examined. Experimentswere conductedwithina temperature range of 25–65 °C. The nano-lubricant was prepared using the two-stage method. An ultrasonicprobe was used for 45 min to uniformly distribute the nanoparticles in the base fluid. The thermal conductivitycoefficient of the hybrid nanofluid was measured using the KD2-Pro thermal analyzer, the results of which indi-cated that even the smallest mass concentration improved the thermal properties of the nano-lubricant. Accord-ingly, the largest improvement occurred at a mass fraction of 4%, i.e. 33% of the base oil. In order to calculate thethermal conductivity of the nano-lubricant using the temperature and mass fractions of the particles, the curvefittingmethod was applied to the experimental data to find a highly accurate experimental relation in SigmaPlotV12.

© 2019 Published by Elsevier B.V.

Keywords:Thermal properties10w40-oilVarious temperatureExperimental studyAl2O3/Fe2O3 nanoparticles

1. Introduction

Today, storage of energies and increasing their efficiency are amongthe most fundamental requirements of the industry. All internal com-bustion engines and industrial machines take advantage of engine oilto prevent corrosion of parts and reduce their abrasion caused by con-stant contact. In addition to reducing corrosion and friction, oils areused for filtering, cooling, dissipation of heat from the engine, andsealing of parts [1–3]. Hence, it can be assumed that appropriate useof engine oils improves engine efficiency and durability and reducesfuel consumption. Numerous studies have been conducted to improvethe thermal properties of lubricants. For instance, addition of materialswith high thermal conductivity to the base fluid is a well-knownmethod to improve the heat transfer process in systems [4–6]. Solid par-ticles offer a higher level of conductivity compared to the conventionalfluids used in heat transfer applications. In 1873, Maxwell succeeded inimproving the heat transfer rate of liquids by addition of solid particlesto them [7]. However, the drawbacks of this method involved pressuredrop, precipitation, corrosion, and impurities.Masuda et al. were able topartly deal with these problems by using particles of tinier sizes [8].Nanofluids are a new category of fluids with a high heat transfer poten-tial. They are prepared by dispersion and suspension of metal and non-

arimipour).

metal nanoparticles of smaller than 100nm in a basefluid such aswater,oil, and ethylene glycol [9].

Experimental studies show that the increase or decrease in coeffi-cient of conductivity of nanofluids is affected by parameters such asconcentration of nanoparticles, type of suspended particles and thebase fluid, shape of particles and their size, temperature, surfactants,type and duration of applied ultrasonic, and accumulation of particles[10–12]. Moreover, studies also indicate that addition of nanoparticlessignificantly increases thermal conductivity of the fluid. In addition,since the nanoparticles can remain suspended for a longer period inthe fluid, the possibility of abrasion and obstruction of pipes due toquick deposition of particles is decreased [13–15].

In their study, Wu et al. investigated the lubrication properties oftwo types of engine oils as well as the effect of copper oxide (CuO), tita-nium oxide (TiO2), and diamond nanoparticles (Nano diamonds). Tothis end, the reciprocating sliding friction and wear test was used. Theresults showed that addition of nanoparticles to oil significantly contrib-utes to reduction of abrasion and friction and improvement of oil prop-erties. They reported that the friction coefficients of the API-SF and thebase fluid containing CuO nanoparticles were reduced by 18.4% and5.8%, respectively, and the wear depths were reduced by 16.7% and78.8%, respectively [16]. Ku et al. assessed the lubrication characteristicsof fullerene nanoparticles added to mineral oils with respect to theirvolumetric fraction. They used a disk-on-disk device at different volu-metric fractions and vertical loads and experimentally investigated thetemperature of friction surfaces and the friction coefficient of the

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Table 2Properties and characteristics of nanoparticles.

Properties Fe2O3 Al2O3

Color Red brown WhitePurity 98 99+ %Specific heat (J/kg·K) 104 880Density (gr/m3) 5.24 3.89Structure Spherical Nearly sphericalDimensions (nm) 20–40 20Specific surface area (m2/g) 20–60 N138

661M. Tahmasebi Sulgani, A. Karimipour / Journal of Molecular Liquids 283 (2019) 660–666

nano-lubricants. They reported that at high volumetric fractions, thefriction and wear coefficients were reduced, indicating improvementin the lubricating characteristics of mineral water due to addition of ful-lerene (C60) nanoparticles [17]. Eastman et al. assessed the thermalconductivity coefficient of Al2O3, CuO, and Cu nanoparticles using twobase fluids of water and HE-200 oil. They reported that this coefficientwas increased by 60% at a volumetric fraction of 5% compared to thebase fluid [18]. Beck et al. studied the effect of size of nanoparticles fortwo nanofluids of water-alumina and ethylene glycol-alumina. Theyvaried the size of nanoparticles within the range of 8–282 nm and,based on their final results, reported that the thermal conductivity ofalumina nanofluid was reduced for average nanoparticle sizes smallerthan 50 nm [19]. Das et al. studied the behavior of water-CuO andwater-Al2O3 nanofluids with respect to changes in temperature. Theirresults suggested that thermal conductivity coefficient was increasedwith temperature increasing. This effect was also reported to be moreevident at higher volumetric fractions [20]. Harandi et al. examinedthe effect of increasing temperature and volumetric fraction on hybridnanofluids composed of iron oxide (Fe2O3) nanoparticles, multi-walled carbon nanotubes, and ethylene glycol as the base fluid withintemperature and volumetric fraction ranges of 25–50 °C and 0–2.3%, re-spectively. Their results suggested a 30% increase in the conductivity co-efficient at a temperature of 50 °C and volumetric fraction of 2.3% [21]. Asummary of fundamental information from literature studies is pre-sented in Table 1.

The coefficient of thermal conductivity of Fe2O3-Al2O3/Engine oil hy-brid nano-lubricant was investigated for the first time in this study[44–51]. The engine oil employed was of 10w40 type, which is widelyused in lightweight vehicles. Effort was made to improve the thermalproperties of this oil by adding a mixture of circular-shaped iron oxide(Fe2O3) and aluminum oxide (Al2O3) nanoparticles with differentsizes. The considered temperature and mass concentration rangeswere 25–65 °C and 0.25–4wt%, respectively. The different nanoparticleswere used in equal amounts (50–50), and the nano-lubricant was pre-pared through the two-stage method.

2. Preparation of nanofluids

Engine oil 10W40 was used as the base fluid for the nano-lubricantconsidered in this study. The nanoparticles included Al2O3with an aver-age diameter of 20 nm and Fe2O3 with an average diameter of 2–40 nm.The thermophysical properties of the nanoparticles are given in Table 2.

Moreover, the 10w40 engine oil properties are presented in Table 3.The employed nanoparticles were manufactured by US Research

Nanomaterials, Inc. SEM and XRD tests were conducted to ensure theappropriate surface and atomic structures of the nanoparticles. The re-sults are demonstrated in Fig. 1.

The roughly circular structure of Al2O3 particles and the circularstructure of the Fe2O3 particles are shown in Fig. 1.

The results of XRD test for the nanoparticle samples are presented inFig. 2. As indicated, the XRD test provides comprehensive informationon the chemical compound and crystal structure of the substances.

Table 1A summary of the researches conducted on improvement of thermal conductivity of nano-lubricants.

Nanoparticle Base fluid Temperature(°C)

Concentration(%)

Enhancement(%)

Ref.

TiO2 Oil 20–50 0.1–1 7.08 [22]Mg/MWCNT Engine oil 25–60 0.25–2 50 [23]Cu Oil 40–100 0.2–1 wt% 49 [24]Mg/MWCNT 10 W40 25–50 0.25–2 wt% 65 [25]WO3-Ag Transformer oil 40–100 1–4 wt% 41 [26]MWCNT 20 W50 20 0.1–0.5 wt% 22.7 [27]Ag Engine oil 40–100 0.36–0.72 wt% 37.1 [28]CuO 20 W50 25 0.2–6 wt% 8.3 [29]

Oil was used as the base fluid in this study due to its wide range ofapplications as coolant and lubricant in industrial systems and engines.The weights of nanoparticles and the base fluid were calculated fromEq. (1) and using the material properties given in Tables 1 and 2. Theweights of oil and nanoparticles were measured with an accuracy of0.001 g using the A&D GF-300 Precision Balance. These weights are pre-sented in Table 4 for different concentrations. A volume of 50 ml foreach nano-lubricantwas prepared as suggested by the standardmanualof KD2-Pro device.

wt %ð Þ ¼ mð ÞAl203 þ mð ÞFe2O3

mð ÞAl203 þ mð ÞFe2O3

� 100 ð1Þ

After measuring the weight of the nanofluid and nanoparticles, thesurface temperature of the magnetic stirrer was increased up to 80°C.During this heating process, the oil viscosity drastically decreased,which was when the nanoparticles were gradually added to the fluid.Themagnetic stirrer was then used for 45min tomix the nanoparticles.After preparing the oil and nanoparticles mixture, the lubricant samplewas exposed to ultrasonic waves for 45 min using an ultrasonic probedevice (UP400ST model manufactured by German-based Hesher com-pany with a power of 400 W and frequency of 24 kHz) to create long-term stability for nanoparticles and eliminate their agglomerates. Theemployed nanoparticles, base fluid, and nano-lubricant are demon-strated in Fig. 3.

3. Thermal conductivity measurement

Various methods are available to measure the thermal conductivityof nanofluids including transient hot-wire method, steady-statemethod, temperature oscillation method, and 3-omega method. In thisstudy, the transient hot-wire method along with the KD2-Pro device(Decagon devices, Inc., USA) was used to measure the thermal conduc-tivity of the nanofluid. The KS-1 sensor was also employed for measure-ment. The Memmert WNB7 water bath was used for temperaturecontrol and to create uniform temperature during the experiment.

4. Results and discussion

4.1. Validation

In order to assess the performance of the measurement system andthe equipment used in this system, the results were verified prior tomeasuring the thermal conductivity of nano-lubricant. To validate theresults, the thermal conductivity of pure water was measured and

Table 3Properties and characteristics of 10w40 engine oil.

Engine oil properties (10w40) Value

Kinematic viscosity (at 100 °C) 14.81 cStViscosity index (VI) 160Lowest flammability 232 °CLowest current temperature −240 °CDensity at °15 °C 873 kg/m3

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Fig. 1. SEM image of the nanoparticles used in this study. A: Fe2O3. B: Al2O3.

662 M. Tahmasebi Sulgani, A. Karimipour / Journal of Molecular Liquids 283 (2019) 660–666

compared to the results reported in ASHRAE handbook [30]. The mea-surement was conducted at the considered temperature range for theexperiment, the results of which are shown in Fig. 4. As indicated, theperformance of the system is acceptable.

4.2. Effect of mass fraction on thermal conductivity

Fig. 5 demonstrates the results of measurement of thermal conduc-tivity of nanofluid with respect to mass fraction within a temperaturerange of 25–65 °C. As shown, the thermal conductivity increases by in-creasing mass concentration of nanoparticles. Moreover, the thermalconductivity increases with a greater slope at higher concentrations.Considering the governing physics of the problem, which states thatthermal conductivity of the nanomaterials is considerably higher thanthat of the base fluid, the positive changes in thermal conductivity ofthe nanofluid can be attributed to the higher thermal conductivity ofthe nanomaterials present in the nano-lubricant. Thermal conductivityis improved by increasing concentration of the nanomaterials, whichmeans increasing the number of these particles in the base fluid.

As depicted in Fig. 5, thermal conductivity of the nano-lubricantwith a mass fraction of 0% (base fluid) decreases with temperature

Fig. 2. Results of XRD test applied to th

increasing. Considering the experimental results in this study andbased on the previous studies, these variations are due to the governingphysics of oil properties.

4.3. Effect of mass fraction on thermal conductivity

Variation of thermal conductivity of the nanofluid with respect totemperature at different volumetric fractions is shown in Fig. 6. As indi-cated by the results, thermal conductivity is increasedwith temperatureincreasing. Thermal conductivity of the added materials, as their intrin-sic characteristic, is among the factors affecting the improvement ofthermal conductivity of nanofluids as temperature increases. In fact, athigh temperatures, the molecular movement of the fluid as well asthat of the nanoparticles in the base fluid are increased by increasingtemperature. These changes are accompanied by transfer of energy be-tween nanofluid layers, which accordingly increase the thermal con-ductivity of nanofluids. Addition of nanoparticles to oil also alters thebehavior of thermal conductivity of the base oil, which inevitablyleads to the increasing trend of thermal conductivity at all concentra-tions under any temperature conditions.

e nanoparticles. A: Fe2O3. B: Al2O3.

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Table 4Weight ofmaterials based onmass fraction of different samples of hybrid nano-lubricants.

Mass fraction Mass (±0.001) (gr)

Oil 10w40 Fe2O3 Al2O3

0 50 0 00.25 49.875 0.0625 0.06250.5 49.75 0.125 0.1251 49.5 0.25 0.252 49 0.5 0.54 48 1 1

Temperature (°C)

Ther

mal

cond

uct

ivit

y(W

/m.K

)

20 25 30 35 40 45 50 55 60 65 700.57

0.6

0.63

0.66

0.69

0.72

0.75

ASHRAE Handbook-Water

Experimental data- Water

Fig. 4. Comparison between the experimental results of thermal conductivity of purewater with those presented in ASHREA handbook.

663M. Tahmasebi Sulgani, A. Karimipour / Journal of Molecular Liquids 283 (2019) 660–666

4.4. Thermal conductivity ratio

In this section, the ratio of thermal conductivity of nanofluid to thatof base fluid is obtained using Eq. (2).

Thermal conductivity ratio %ð Þ ¼ knfkbf

ð2Þ

Thermal conductivity ratio of the nano-lubricant is presented inFig. 7. As shown, the changes in this ratio are increased with tempera-ture increasing. At low volumetric fractions, no significant increasescan be observed in thermal conductivity due to low concentration ofnanoparticles present. At higher concentrations, the number of colli-sions and, consequently, the heat transfer between fluid layers is in-creased due to presence of more nanoparticles. In this case, thethermal conductivity of the nano-lubricant experiences a larger increasecompared to that of the base fluid. The thermal conductivity was in-creased by 33% in the best case scenario in our study.

Fig. 3. A: base fluid(Oil-10W40). B: Nano lubricant. C: Fe2O3 nanoparticles. D: Al2O3

nanoparticles.

4.5. Thermal conductivity correlation

A review of the literature suggests that thermophysical properties ofthe nanofluid are directly affected by physical and chemical structuresof the nanofluid, which themselves are affected by different parameterssuch as temperature, volumetric fraction, particles size, surface, atomic,and chemical structure of the nanoparticles, and even the nanofluidpreparation method [31–43]. Since no accurate, appropriate relationis available for prediction of thermal conductivity of 10w40/Al2O3-Fe2O4 nano-lubricant, an experimental relation was presented inthis section obtained through the curve fitting method using SigmaPlot V12. This relation is a function of mass fraction of nanoparticlesand temperature.

Mass fraction (%)

Ther

mal

cond

uct

ivit

y(W

/m.K

)

0 0.5 1 1.5 2 2.5 3 3.5 40.13

0.14

0.15

0.16

0.17

0.18

T=25oC

T=35oC

T=45oC

T=55oC

T=65oC

Fig. 5. Effect of mass fraction on thermal conductivity of 10w40/Al2O3-Fe2O4 nano-lubricant.

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Temperature (°C)

Ther

mal

condu

ctiv

ity

(W/m

.K)

20 25 30 35 40 45 50 55 60 65 700.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19wt=0%

wt=0.25%

wt=0.5%

wt=1%

wt=2%

wt=4%

Fig. 6. Effect of temperature on thermal conductivity of 10w40/Al2O3-Fe2O4 nano-lubricant.

664 M. Tahmasebi Sulgani, A. Karimipour / Journal of Molecular Liquids 283 (2019) 660–666

The proposed experimental relation for prediction of thermal con-ductivity of the considered nanofluid is expressed in Eq. 3.

knfkbf

¼ 0:113 � 1:011T �wt0:376 þ 0:921 ð3Þ

where k represents thermal conductivity coefficient, T is the nanofluidtemperature in Celsius, andwt is theweight percentage of the nanopar-ticles. Moreover, indices nf and bf denote nanofluid and base fluid,respectively.

In order to accurately examine the proposed experimental relation,Eq. 4 is used to calculate the deviation of the results obtained from the

Temperature (°C)

Ther

mal

cond

uct

ivit

yra

tio

20 25 30 35 40 45 50 55 60 65 701

1.05

1.1

1.15

1.2

1.25

1.3

1.35

wt=0.25%

wt=0.5%

wt=1%

wt=2%

wt=4%

Fig. 7. Ratio of thermal conductivity of 10w40/Al2O3-Fe2O4 nano-lubricant to that of baseoil.

proposed relation from the experimental results at all temperaturesand mass fractions.

Deviation margin %ð Þ ¼ kexp−kpredkexp

� 100 ð4Þ

In this relation, exp. and pred denote experimental values and valuespredicted by the proposed relation.

The deviation between the two values is demonstrated in Fig. 8. Asshown, most points are located on or near the bisector, which indicatesthe appropriate accuracy of the proposed relation.

Moreover, the largest deviation margin for the thermal conductivityratio was 0.68%, which is acceptable for an experimental relation.

The measured results and the output of the proposed model at alltemperatures are presented in the comparison chart in Fig. 9 for furthercomparison. These charts present the thermal conductivity ratio of thenano-lubricant with respect to mass fraction at different temperatures.

5. Conclusion

In this study, the preparation procedure of nano-lubricant Fe2O3-Al2O3/10w40 was described and its thermal conductivity was investi-gated subject to a temperature range of 25–65 °C and mass concentra-tion of 0.25–4%. The results obtained based on the research variablesare as follows:

This nanofluid achieved an acceptable stability given the preparationprocedure which included use of heating processes, magnetic stirring,and ultrasonic waves.

Thermal conductivity of the nanofluid was significantly increaseddue to the effect of addedmass fraction. The highest increase in thermalconductivity (33%) was achieved at a mass fraction of 4% and a temper-ature of 65 °C.

Thermal conductivity increased with temperature increasing. Theslope of this increase was greater at higher temperatures, allowing thisnanofluid perform more efficiently in high-temperature applications.

The experimental relation for thermal conductivity was obtainedusing curve fitting method. Given its acceptable accuracy, this relationcan be used within the temperature range of the experiment.

Experimental data

Corr

elat

ion

outp

uts

1 1.05 1.1 1.15 1.2 1.25 1.3 1.351

1.05

1.1

1.15

1.2

1.25

1.3

1.35

Maximum positive error= 0.68%

Maximum negative error= 0.5%

Fig. 8. Deviation margin of the calculated results compared to the experimental results.

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T=35 °C

Mass fraction (%)

The

rmal

cond

ucti

vity

rati

o

0 0.5 1 1.5 2 2.5 3 3.5 41

1.05

1.1

1.15

1.2

1.25

1.3

1.35Experimental dataCorrelation

T=25 °C

Mass fraction (%)

The

rmal

cond

ucti

vity

rati

o

0 0.5 1 1.5 2 2.5 3 3.5 41

1.05

1.1

1.15

1.2

1.25

1.3

1.35Experimental dataCorrelation

T=55 °C

Mass fraction (%)

The

rmal

cond

ucti

vity

rati

o

0 0.5 1 1.5 2 2.5 3 3.5 41

1.05

1.1

1.15

1.2

1.25

1.3

1.35Experimental dataCorrelation

T=45 °C

Mass fraction (%)

The

rmal

cond

ucti

vity

rati

o

0 0.5 1 1.5 2 2.5 3 3.5 41

1.05

1.1

1.15

1.2

1.25

1.3

1.35Experimental dataCorrelation

T=65 °C

Mass fraction (%)

The

rmal

cond

ucti

vity

rati

o

0 0.5 1 1.5 2 2.5 3 3.5 41

1.05

1.1

1.15

1.2

1.25

1.3

1.35Experimental dataCorrelation

Fig. 9. Comparison between the experimental results and the results of the proposed method at different temperatures.

665M. Tahmasebi Sulgani, A. Karimipour / Journal of Molecular Liquids 283 (2019) 660–666

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666 M. Tahmasebi Sulgani, A. Karimipour / Journal of Molecular Liquids 283 (2019) 660–666

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