International Communications in Heat and Mass Transfer

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Contents lists available atScienceDirect

International Communications in Heat and Mass Transfer

journal homepage:www.elsevier.com/locate/ichmt

Experimental investigation toward obtaining nanoparticles' sur fi cial interaction with base fl uid components based on measuring thermal conductivity of nano fl uids

Reza Naghdi Sedeh, Ali Abdollahi

^⁎

, Arash Karimipour

Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

A R T I C L E I N F O

Keywords:

Nanoﬂuid Thermal conductivity Baseﬂuid types CuO nanoparticles TiO2nanoparticles

A B S T R A C T

In this study the effect of temperatures, the CuO and TiO₂nanoparticles' mass fraction, and basefluid types were studied on thermal conductivity of nanofluid. CuO and TiO2nanoparticles were dispersed in ethanol and liquid paraffin model 107,160 separately by using ultrasonic waves. The stability of nanoparticles in basefluids was estimated by exploiting DLS and Zeta Potential analysis. The results showed that the thermal conductivity enhances with the increase in temperature; conversely, with the increase in temperature the thermal conductivity of the basefluid decreases. The results of this study showed that by increasing the mass fractions of metal oxides nanoparticles the thermal conductivity of nanofluid increases. Also, by increasing the concentration of oxides nanoparticles in liquid paraffin, the changes in the thermal conductivity of nanofluid at concentrations of < 1%

are insignificant, but by increasing the concentration of nanoparticles from 1% mass to 5%, the changes in the thermal conductivity of nanofluid are remarkable. The results of the calculation for the interaction parameter showed that in the low concentrations of metal oxides nanoparticles, the interaction effect between surfaces of metal oxide nanoparticles and ethanol molecules is greater than the liquid paraffin. The results also showed that the thermal conductivity of ethanol/CuO is greater than the other nanofluids (ethanol/TiO₂, liquid paraffin/

TiO2, and liquid paraffin/CuO) at various temperatures and nanoparticles' mass fraction. Finally an empirical equation including temperature, nanoparticles mass fraction, and physical properties of nanoparticles and basefluids was predicted by using hybrid GMDH-type neural network to estimate the interaction parameter between nanoparticles surface and basefluids molecules.

1. Introduction

Because of the positive impacts of nanostructured materials on various engineeringfield including preparation of highly-efficient nanoparticles-loaded materials such as nanocomposites, the application of these nano-sized materials has been highlighted by many researchers [1–9]. The implementation of nanoparticles, nanofibers and nanosheets in variousfields of science have been developed due to their unique and significant physical and chemical properties in different applications including reinforced nanostructure-loaded composites, catalysts used in chemical processes, highly-efficient drugs delivery system in medical application, as well as their thermal utilization which makes it afford- able to use them as new heat transferfluids within the industries [9].

Addition of solid nano-sized materials to heat transfer working liquids leads to achieve new ﬂuids, (which are known as nanoﬂuids), with appreciable thermal and hydrodynamic properties.

The term of nanofluid wasfirst proposed by Choi [10,11] and he expressed that by adding few amount of nanoparticles to different basefluids such as ethylene glycol, glycerine, water and oil, a homo- genized mixture with considerable thermal conductivity is obtained.

The viscosity and thermal conductivity of nanofluid are influenced by both nanoparticles mass fraction and temperature [12,13]. These two thermophysical properties also directly affect the energy for pumping nanofluid as well as heat transferring through a hot and cold source, respectively. It has been reported in many cases that the thermophysical properties of nanofluids is higher than that of basefluids [12,13]. Fur- thermore, these properties depends on other factors such as nanoparticle size and basefluid and nanoparticles type [12]. The implementation of these novelfluids as new heat transferfluids as well as their various hydrodynamic and thermal properties have been studied by many numbers of researchers [12]. Following is a summary of the results obtained regarding the effect of various parameters on

https://doi.org/10.1016/j.icheatmasstransfer.2019.02.016

⁎Corresponding author.

E-mail address:[email protected](A. Abdollahi).

T

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nanoﬂuids' thermal conductivity.

Chopkar et al. studied the effects of nanoparticles type on thermal conductivity of water/Al2Cu and water/Ag2Al nanofluids. They investigated the impacts of nanoparticles volume fraction, size and temperature on the relative thermal conductivity of nanofluid. They exhibited that the relative thermal conductivity of nanofluid declines with nanoparticles diameter and they claims that temperature significantly influence thermal conductivity of nanofluids [13]. Masuda et al. studied the effect of temperature on the thermal conductivity and viscosity of nanofluids containing Al2O3, SiO2, and TiO2nanoparticles in deionized water as basefluid [14]. They showed that the relative thermal conductivity of nanofluid, in contrary to the results obtained by many other scholars, declined with the temperature enhancement. Besides, Munkhbayar et al. investigated the impacts of hybrid nanoparticles mass fraction and temperature on thermal conductivity of water based nanofluid. Their results showed that by adding Ag–MWCNT nanoparticles, a significant enhancement on thermal conductivity of Ag–MWCNT/water nanofluid is achieved. In addition, their results revealed that the maximum value of the thermal conductivity of nanofluid was obtained at the conditione were temperature was set on 40 °C and 0.05 wt% MWCNTs and 3 wt% Ag nanoparticles were added to basefluid [15].

Warrier et al. did a research and found a new correlation in order to estimate the thermal conductivity of nanofluids containing Ag nanoparticles in water as basefluid. They measured the thermal conductivity at various nanoparticles size and loads. Their results revealed that the nanoparticles size has direct impact on thermal conductivity of the mentioned nanofluids and with declination in nanoparticles size the thermal conductivity of nanofluid declined significantly. The results obtained from the experimentation were in accordance with those obtained by their proposed model at various nanoparticles volume fractions [16]. Xie et al. investigated the effect of Al2O3nanoparticles on thermal conductivity nanofluids with water and pump oil as basefluids [17]. They studied the effect of nanoparticles mean diameter and temperature on thermal conductivity of nanofluids. Theirfindings revealed that with the increase of nanoparticles size the thermal conductivity of nanofluid declined and with the increase of temperature a significant enhancement in thermal conductivity is obtained. Beck et al.

performed a research in order to measure the thermal conductivity of nanofluids containing Al2O3nanoparticles with various mead diameters dispersed in water and ethylene glycol as basefluids. Their results revealed that the thermal conductivity of nanofluids decreases with declination of nanoparticles size below 50 nm [18]. In addition, Chen et al. [19] studied the effect of nanoparticles mean diameter on thermal conductivity of SiO2/water nanofluids. They revealed that with the increase in nanoparticles mean diameter the relative thermal conductivity of nanofluid enhances. Furthermore, they exhibited that the interaction between nanoparticles surface and basefluid components has remarkable effect on thermal conductivity of nanofluid; and consequently, with the increase of nanoparticles size the interface thermal resistance declines for SiO2/water nanofluid due to the higher attrac- tion forces between nanoparticles surface and basefluids molecules [20].

The aim of this study is to investigate the effect of nanoparticles and basefluids types on thermal conductivity of oil-based and ethanol-based nanofluid containing CuO and TiO2 nanoparticles as well as find a comprehensive correlation for prediction of interaction parameter at various nanoparticles mass fraction and temperature. For this purpose, in this research the thermal conductivity of liquid paraffin based nanofluids containing CuO and TiO2 nanoparticles were measured at different mass fractions and various temperatures. Finally, a correlation including temperature, mass fraction, and nanoparticles and basefluids physical properties was proposed based on hybrid GMDH-type neural network method to predict interaction parameter between the nanoparticles surface and basefluid molecules at various conditions.

2. Experimentation

2.1. Materials

In this research TiO2nanoparticles were purchased from U.S. Nano Company with purity higher than 99.91% and CuO nanoparticles were prepared by using precipitation method which was presented in our previous research [21–24], the physical properties of nanoparticles are presented inTables 1 and 2, respectively. Moreover, for preparation of nanoﬂuids, ethanol and liquid paraﬃn model 107,160 was purchased from Merck Company, Germany with detailed physical properties presented inTables 3 and 4. In addition, deionized water was used for washing the laboratory glasswares [23].

2.2. Instruments

For measuring the thermal conductivity of nanofluid, a thermal properties analyzer, (KD2 Pro Deacagon, USA) was employed similar to our previous research [25]. For imaging and estimating the size and morphology of nanoparticles, Transmission Electron Microscopy analysis, (TEM), (Hitachi, 9000 NA, Japan), was used on dry nanoparticles [25]. Also for estimation of CuO and TiO2nanoparticles stability within ethanol and paraffin model 107,160 Zeta Potential analysis was performed on nanofluids samples containing 0.005 wt% nanoparticles (ZetaSizer, Malvern, ZetaSizer Nano ZS, United Kingdom). During applying each measurement the temperature was set on constant value by using an isothermal circulator bath, (−40, 7 l Ref. Circulator, Poly- Science Co., U.S.A) and for preparation of stock nanofluid certain amount of nanoparticles was measured by using a precise electric balance, (HT series, Che Scientific Co., Hong Kong). Finally, for measuring the sizes of nanoparticles within the aqueous and non-aqueous basefluids and observe the distribution size of nanoparticles, Dynamic Light Scattering, (DLS), (Malvern, ZetaSizer Nano ZS, United Kingdom), was performed on diluted samples [25].

2.3. Nanoﬂuid preparation

In this study, for preparation of nanofluids with different nanoparticles mass fractions 1 g of CuO or TiO2 nanoparticles was first weighed and then dispersed in 19 g of ethanol or liquid paraffin separately under stirring condition of 500 rpm for 30 min [25]. Afterwards,

Table 1

Physical properties of CuO nanoparticles.

Molecular weight 79.54 g/mol

Density 6.315 g/ml

Melting point 1326 °C

Boiling point 2000 °C

Table 2

Physical properties of TiO₂nanoparticles.

Molecular weight 79.86 g/mol

Density 4.23 g/ml

Melting point 1843 °C

Boiling point 2972 °C

Table 3

Physical properties of liquid paraﬃn model 107,160.

EC no. and CAS-no 232-384-2 and 8012-95-1

Vapor pressure at 20 °C < 0.01 Pa

Density at 20 °C 0.86 g/ml

Kinematic viscosity at 40 °C 42.5 mm²/s

Boiling point 300–500 °C

Ignition point 300 °C

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for separation of the agglomerates of nanoparticles within the base- ﬂuids, the solutions were placed under sonication waves with a time period of 0.5 s and amplitude of 60% for three steps of 20 min [25].

After preparation of stock nanofluid, other concentrations of nanofluids were made by diluting the main nanofluid according toTable 5[25].

In order to prepare diluted nanofluids, (for example 1 wt%), 4 g of stock nanofluid with a concentration of 5% was taken in accordance with the values presented inTable 5and then the desired basefluid, (ethanol or liquid paraffin), was added to nanofluid until the total mass of nanofluid reach to 20 g. Accordingly, for preparation of nanofluids with other various nanoparticles loads a certain amount of stock col- loidal suspension was diluted by adding pure basefluids [25].

2.4. Measuring thermal condcutivity of nanoﬂuids

In this research for measuring the thermal conductivity of nanofluid with various mass fractions of the mentioned nanoparticles in the basefluids, 10 ml of each sample was introduced to a cylindrical glass vessel with 1 cm diameter, 12.74 cm height, and 0.5 mm wall thickness which was used also in our previous research [25]. The vessel, (containing 10 ml nanofluid), was placed in the isothermal circulator bath vertically atfixed temperature and the probe of KD2 Pro was put inside the nanofluid vertically for measuring thermal conductivity of nanofluid. The mechanism of thermal conductivity measurement was based on Transient Hot Wire method, (THW), in which heat is conducted through the probe of thermal analyzer and then by cooling the probe, the thermal conductivity is measured. Therefore, by applying THW the temperature of nanofluid enhances slightly leading to deviation on the experimental results [5]. Thus for eliminating any further experimental errors and avoid effect of every unstable temperature during applying KD2 Pro, the measurements were repeated 12 times at constant condition with interval time of 5 min similar to those obtained in our previous research [25]. To show the experimental errors the standard deviation for thermal conductivity measurement atfixed temperature and CuO and TiO2nanoparticles mass fraction was obtained by using the following equation [25]:

= ∑ −

S. D. (R R )

n

i k,i k2

2 (1)

where Rk, iis the ratio of thermal conductivity of nanoﬂiuds to those measured for pure baseﬂuid, (Rk= knf/kbf) for each measurement,Rkis average thermal conductivity ratio and m is numbers of measurements which is equal to 12.

2.5. Uncertainty analysis

In this research the uncertainty analysis was deﬁned by applying thermal conductivity measurement accuracy, the accuracy of precise electric balance, and isothermal circulator bath accuracy. For this purpose, the uncertainty of experimentations was calculated by means of the accuracy of thermal circulator bath, ( ± 0.0 05 °C), the accuracy of the precise electric balance, ( ± 0.0003 g), and the accuracy of KD2 Pro, ( ± 1%) [25]. For calculating the uncertainty of experimentation in thermal conductivity measurement, Eq.(2)was used [26]:

=± ⎛

⎝

∆ ⎞

⎠ + ⎛

⎝

∆ ⎞

⎠ + ⎛

⎝

∆ ⎞ U M. . k ⎠

k

w w

T T

2 2 2

(2) In this research the maximum value of uncertainty for thermal conductivity measurement of nanoﬂuids was found to be 6.2%.

3. Results and discussion

3.1. Nanoﬂuid characterization 3.1.1. TEM analysis

In this study TEM analysis was applied on de-moisturized CuO and TiO2 nanoparticles to determine the size and and shapes of nanoparticles. To do so, a small amount of each nanoparticle was dispersed in pure ethanol and inserted on the clean surface of graphite, by the evaporation of ethanol the samples were then introduced to TEM.Fig. 1 a reveals the images of TEM analysis for CuO nanoparticles. Thefind- ings presented in this figure exhibit that CuO nanoparticles possess mean diameter < 100 nm and the nanoparticles mean diameter ranged from 10 to 50 nm. Furthermore, it is obvious that the nanoparticles morphology was spherical.Fig. 1 b also presents the images of TEM analysis for TiO2nanoparticles. The results of thisfigure also exhibits that the mean diameter of these nanoparticles was < 60 nm ranging from 10 to 50 nm and the shapes of nanoparticles were semi-spherical.

3.1.2. DLS analysis

In this research Dynamic Light Scattering, (DLS), also was employed to determine the mean diameter of CuO nanoparticles and distribution size of nanoparticles within ethanol and liquid paraﬃn model 107,160.

Fig. 2represents the results of DLS analysis for the nanofluids with different basefluids and nanoparticles. These results clearly indicates that for CuO-loaded nanofluids with basefluids of ethanol and liquid paraffin the average diameter of the nanoparticles is about 20–60 nm, (Fig. 2a, b), and for TiO2dispersed in ethanol and liquid paraffin the average diameter of the nanoparticles is about 10–40 nm, (Fig. 2c, d).

3.1.3. Zeta potential analysis

Zeta potential analysis reveals the repulsive forces between dispersed particles within aﬂuid [5]. The maximum value of zeta potential represents the maximum intensity of distributed electrostatic charges covering nanoparticles' surface. For the zeta potential higher than +40 mV or less than−40 mV, stable nanoparticles are found within the baseﬂuids. Large magnitude of the zeta potential represents the higher repulsive electrostatic forces between nanoparticles preventing to form the agglomerates [4,5,23,27,28].

The results of zeta potential test for CuO-loaded nanoﬂuids dispersed in ethanol and liquid paraﬃn are presented inFig. 3a and b.

This results exhibits that the most of CuO nanoparticles has maximum zeta potential at electrical potential less than−40 mV declaring high stability of CuO nanoparticles in ethanol and liquid paraﬃn [4,29].

Furthermore, the results of zeta potential test for TiO2-loaded nanofluids dispersed in ethanol and liquid paraffin are presented inFig. 3c and d. This results also reveal that the most of these nanoparticles has maximum zeta potential at electrical potential less than−40 mV pre- senting high stability of TiO2nanoparticles in basefluids [4,29].

Table 4

Physical properties of ethanol.

Chemical formula CH3-CH2-OH

Molecular weight (g/mol) 46.06

Melting point (C°) −114.1

Boiling point (°C) 78.37

Density @ 25 °C (g/ml) 0.789

Viscosity @ 25 °C (cp) 1.074

Table 5

Mass of stock nanoﬂuid needed for preparation of diluted nanoﬂuids, (obtained from our previous research) [25].

Nanoﬂuid mass fraction

in baseﬂuid Mass of nanoﬂuid taken from stock solution (g)

Final mass of nanoﬂuid after dilution (g)

5 wt% – 20

1 wt% 4 20

0.5 wt% 2 20

0.1 wt% 0.4 20

0.05 wt% 0.2 20

0.01 wt% 0.04 20

0.005 wt% 0.02 20

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3.2. Thermal conductivity

The results of relative thermal conductivity, (Rk= knf/kbf), for CuO- loaded nanofluids dispersed in ethanol is presented inFig. 4a, (these results were obtained at various temperatures and nanoparticles mass fractions). It is obvious from thesefindings that with the temperature enhancement from 25 to 70 °C the value of relative thermal conductivity of nanofluid increases from 1.12 to 1.71 at nanoparticle mass fraction of 5 wt%. Moreover, these results exhibit that with the increase of CuO mass fraction from 0.005 to 0.5 wt% the value of relative thermal conductivity of nanofluids enhances insignificantly at lower temperature while for temperature above 40 °C the value of relative thermal conductivity enhances remarkably with nanoparticles loads.

Accordingly, it is obvious that with the increase in CuO nanoparticles mass fraction from 0.005 to 5 wt% the relative thermal conductivity of nanoﬂuid enhances about 11% for temperature of 25 °C, and with the increase of mass fraction from 0.005 to 5 wt% the ratio of thermal conductivity enhances about 70% for the temperature of 70 °C,

declaring high impact of mass fraction on relative thermal conductivity at higher temperature.

Fig. 4b represents the results of the relative thermal conductivity for CuO/liquid paraffin nanofluids at various temperatures and mass fractions. It is also concluded from these results that with the increase of temperature from 25 to 70 °C the value of relative thermal conductivity increases from 1.21 to 1.61 at the condition where CuO nanoparticles was chosen to be 5 wt%. Furthermore, thesefindings exhibits that with nanoparticles mass fraction enhancement from 0.005 to 0.5 wt% the value of relative thermal conductivity of nanofluid increases insignificantly while for the mass fraction above 0.5 wt% the value of thermal conductivity ratio increases more tangibly. Further- more, it is obvious from the results of thisfigure that with the increase in CuO nanoparticles mass fraction from 0.005 to 5 wt% the value of enhanced thermal conductivity increases from 3% to 23% for temperature of 25 °C, and with the increase of mass fraction from 0.005 to 5 wt% the valued of enhanced thermal conductivity increases from 8%

and 63% for the temperature of 70 °C.

The results of relative thermal conductivity for TiO2/ethanol are shown inFig. 4c at various temperatures and nanoparticles mass fractions. It is evidence from the results presented in thisﬁgure that with the increase of temperature from 25 to 70 °C the value of relative thermal conductivity increases from 1.08 to 1.63 at the condition where 5 wt% TiO2nanoparticles used. Also theseﬁndings exhibits that with the increase of TiO2nanoparticles mass fraction from 0.005 to 5 wt%

the ratio of thermal conductivity of nanofluid increases insignificantly for lower temperature declaring lower effect of mass fraction on thermal conductivity of nanofluid at lower temperature, while for higher temperature the value of thermal conductivity ratio change significantly with nanoparticles mass fraction. For this nanofluid it is also resulted that with the increase in TiO2nanoparticles mass fraction from 0.005 to 5 wt% the value of enhanced thermal conductivity increases from 1% to 7% for temperature of 25 °C respectively; on the other hand, with the increase of mass fraction from 0.005 to 5 wt% the value of the enhanced thermal conductivity raises from 3% to 64% for the temperature of 70 °C.

The results of relative thermal conductivity for TiO2-loaded nanofluids dispersed in liquid paraffin is presented inFig. 4d, (these results were obtained at various temperatures and nanoparticles mass fractions). It is obvious from thesefindings that with the temperature enhancement from 25 to 70 °C the value of relative thermal conductivity of nanofluid increases from 1.19 to 1.58 at nanoparticle mass fraction of 5 wt%. Moreover, these results exhibit that with the enhancement in nanoparticles mass fraction from 0.005 to 0.5 wt% the value of relative thermal conductivity of nanofluids enhances insignificantly at lower temperature while for temperature above 40 °C the value of relative thermal conductivity enhances remarkably with nanoparticles mass fractions. Accordingly, it is obvious that with the increase in TiO2na- noparticles mass fraction from 0.005 to 5 wt% the relative thermal conductivity of nanofluid enhances about 9% for temperature of 25 °C, and with the increase of mass fraction from 0.005 to 5 wt% the ratio of thermal conductivity enhances about 52% for the temperature of 70 °C.

3.3. Temperature eﬀect

It is obvious from the results obtained from measurement of nanofluid thermal conductivity that with the temperature enhancement the value of relative thermal conductivity of CuO/ethanol, CuO/liquid paraffin, TiO2/ethanol, and TiO2/liquid paraffin increases asfixed nanoparticles mass fraction (Fig. 4a to d). Furthermore, for the nanofluids contain nanoparticles above 0.5 wt% with the temperature enhancement from 25 to 70 °C the ratio of thermal conductivity raises significantly, while for those contain nanoparticles lower than 0.5 wt% the change in thermal conductivity of nanofluid is more insignificant. Based on the results achieved in previous researches, the Brownian velocity of nanoparticles or random motion of nanoparticles in basefluids, which Fig. 1.TEM image of, a, CuO [21–24] and, b, TiO2nanoparticles.

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Fig. 2.The results of DLS test for low concentration a, CuO/ethanol, b, CuO/liquid paraffin, c, TiO₂/ethanol, d, TiO₂/liquid paraffin nanofluids.

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leads to extreme micro-convection, is responsible for nanofluid thermal conductivity enhancement by temperature increase [5]. According to this theory, increasing the numbers of micro-convection by means of nanoparticles leads to more basefluid molecules transfer. By transferring these basefluids components from the region with higher temperature to the region with lower temperature more equal-temperature

region is resulted and higher thermal conductivity achieved [5]. Koo et al. reported that the temperature enhancement causes more strong Brownian motion and leads to high random velocity of nanoparticles [5,30]. Accordingly, theﬁndings presented in this research also reveal that the random motion of nanoparticles and the inﬂuence of temperature on these motions is responsible for the thermal conductivity Fig. 2. (continued)

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Fig. 3.The results of Zeta-potential test for a, CuO/ethanol, b, CuO/liquid paraffin, c, TiO2/ethanol, d, TiO2/liquid paraffin nanofluids.

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Fig. 3. (continued)

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enhancement by means of the increase in temperature, (higher thermal conductivity of nanofluids at higher temperature is attributed to effects of temperature on magnitude of nanoparticles random motions). The results of this research also exhibit that with the increase of temperature from 25 to 70 °C at the condition where nanoparticles mass fraction was set on 5 wt% the relative thermal conductivity increases 70.0, 55.0, 61.0, and 52.0% for CuO/ethanol, CuO/liquid paraffin, TiO2/ethanol, and TiO2/liquid paraffin, respectively. These results show that temperature has higher effect on the thermal conductivity of CuO/ethanol nanofluid in comparison to other nanofluids at higher nanoparticles mass fractions.

3.4. Mass fraction eﬀect

The results of experimentation also declared that from with the increase in nanoparticles mass fraction the ratio of nanofluids thermal conductivity to pure basefluids enhances significantly, (Fig. 4a to d).

This impact is due to the solid content within the aforementioned basefluids and with the increase in nanoparticles mass fraction the numbers of Brownian motion of nanoparticles which is leading to produce more micro-convection raises significantly; consequently, higher nanofluid thermal conductivity would be resulted [24].

3.5. Eﬀect of baseﬂuids and nanoparticles type

In order to measure the interaction of nanoparticles surface and baseﬂuids molecules the following equation was obtained based on Brownian motion of nanoparticles as well as micro convection in baseﬂuid by Koo et al. [30]:

=

× ⁺

f k R

β φ C ρ .

5 10 . . . .

bf k Brownian p bf bf

κ T ρ D ,

4 , ( 273)

p. (3)

In this equationCp,bf,κ,D,φare heat capacity of basefluid, Stephan Boltzmann constant, nanoparticles diameter, and volume fraction of nanoparticles within basefluid. In this study in order to determine the volume fraction of CuO or TiO2 nanoparticles in basefluids the following equation was implemented:

=

+ −

φ w

w ^ρ (1 w)

ρ p

bf (4)

where,wis mass fraction of dispersed nanoparticlesin aforementioned nanofluids. In addition, the value ofβ, in Eq.(3), is the fraction of liquid that travels with nanoparticles by means of random motion. They Fig. 4.The ratio of thermal conductivity of nanofluid to basefluid at various

temperature and nanoparticles mass fractions for CuO/ethanol, CuO/liquid paraffin, TiO2/ethanol, and TiO2/liquid paraffin nanofluids.

Fig. 4. (continued)

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reported that for nanoparticles volume fraction < 1 vol% this parameter can be obtained independently from nanoparticles and baseﬂuids type. The following equation can be used for nanoﬂuids with nanoparticle volume load < 1 vol% [30]:

= φ⁻

β 0.0137(100 ) ^0.8229 (5)

Furthermore, the value of relative thermal conductivity of nanoﬂuid caused by nanoparticles Brrownian motion, (Rk,Brownian), can be calculated by using the following equation:

= −

Rk Brownian, Rk exp, Rk Maxwell, (6)

whereRk,expis the relative thermal conductivity of nanoﬂuid that can be obtained experimentally and the value ofRk,Maxwellcan be calculated by using the following equation:

= + −

+ − −

R k k φ

k k k k φ

1 3( / 1)

( / 2) ( / 1)

k Maxwell

p bf

p bf p bf

, (7)

For estimating the surficial interaction of nanoparticles with basefluid molecules, the value of interaction parameter, (f), was obtained for CuO/ethanol, CuO/liquid paraffin, TiO2/ethanol, and TiO2/liquid paraffin nanofluids by using Eq.(3). The results of calculated interaction parameter for aforementioned nanofluids are shown inFig. 5as function of temperature and nanoparticles mass fraction. It is obvious from the results of thisfigure that with the enhancement in CuO and TiO2nanoparticles mass fraction and temperature the value of interaction parameter raises and with the temperature enhancement the impact of nanoparticles mass fraction is remarkable. These results also declare that for nanofluids in which ethanol is used as basefluids, the value of fis higher than other liquid paraffin-based nanofluids. The value of interaction parameter of CuO/ethanol, CuO/liquid paraffin, TiO2/ethanol, and TiO2/liquid paraffin nanofluids was correlated by means of GMDH-based neural network method. The following equation can be used in order to estimate interaction parameter (R²= 0.976):

= + +

f A1 A α2 1 A α3 2 (8)

In this relation the constant values are:

= − = =

A1 0.0137049,A2 0.826877,A3 0.193426

= + + + ⎛

⎝

⎞

⎠ =

α B B T B T w B λ T

λ ρ

. exp . ρ

50 , ^np

bf

1 1 2 3 0.5

4 (9)

= + + ⎛

⎝

⎞

⎠+ ⎛

⎝

⎞

⎠+ ⎛

⎝

⎞

⎠

α C C w C w λ T

C λ T

. exp .

100 exp .

2 1 2 0.5 50

3 0.5

4 5

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= − = = =

B1 0.0836032,B2 0.00913595,B3 0.0120681,B4 0.0592591

= = = = −

=

C 0.649908, C 0.603035, C 1.73851, C 5.4837, C 13.7828,

1 2 3 4 5

It is obvious that interfacial nanolayers of basefluid molecules which surround the nanoparticles' surface have a remarkable impact on nanofluid thermal conductivity; and consequently, with the enhancement of basefluid nanolyer thickness higher thermal conductivity is achieved [31–34]. On the other hands, with the enhancement in nanolyer thickness the velocity of Brownian random walk of nanoparticles decreases due to the larger nanoparticles mean diameter. This leads to result lower micro-convection and consequently lower nanofluid thermal conductivity [30]. In this research it is obvious that the nanolayers of basefluids molecules overcome to the random motion of nanoparticles and leads to the higher thermal conductivity of nanofluids. Thus, it can be resulted that with the enhancement in the surficial interaction between nanoparticles' surface and basefluid compo- nent the value of relative thermal conductivity enhances; therefore, higher magnitude of interaction parameter between nanoparticles surface and basefluids molecules is responsible for producing larger relative thermal conductivity.

Fig. 5.The value offobtained at various temperatures at nanoparticles mass fractions for a, CuO/ethanol, b, CuO/liquid paraﬃn, c, TiO₂/ethanol, and d, TiO2/liquid paraﬃn.

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4. Conclusion

In this study the effect of temperatures, the CuO and TiO2nano- particles' mass fraction, and basefluid types were studied on thermal conductivity of nanofluid. CuO and TiO2nanoparticles were dispersed in ethanol and liquid paraffin separately by using ultrasonic waves. The stability of nanoparticles in basefluids was estimated by using DLS and Zeta Potential analysis. The results showed that the thermal conductivity changes with the increase in temperature; consequently, with the increase in temperature the thermal conductivity of the nanofluid increases. The results of this study showed that by increasing the mass fractions of oxides nanoparticles, the thermal conductivity of nanofluid increased.

Also, by increasing the concentration of oxides nanoparticles in nanofluids with liquid paraffin, the changes in the thermal conductivity of nanofluid at low concentrations of < 0.5% are insignificant, but by increasing the concentration of nanoparticles from 0.5% mass to 5%, the changes in the thermal conductivity of nanofluid are much higher and more tangible. The results of the calculation for the interaction parameter showed that the inter-surficial interaction effect between oxide nanoparticles and ethanol molecules is greater than the liquid paraffin.

The relationship presented in this study shows that for the interaction parameter of nanoﬂuids as a function of mass fraction, temperature and density of nanoparticles, the amount of deviation of calculated data from the relationship provided by the neural network method is very limited and the relationship was used to estimate nanoparticles-baseﬂuid interaction parameter with high precision.

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Fig. 5. (continued)