In this research, the viscosity of the aqueous nanofluid of TiO 2 has been modeled by artificial neural networks using experimental data. Artificial neural networks are able to estimate the pattern of dynamic viscosity variation along with

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Designing an arti
ﬁ
cial neural network to predict dynamic viscosity of aqueous nano
ﬂ
uid of TiO
2
using experimental data
☆
Mohammad Hemmat Esfe
a,
⁎
, Mohammad Reza Hassani Ahangar
b
, Mousa Rejvani
c
,Davood Toghraie
a,
⁎
, Mohammad Hadi Hajmohammad
d
a
Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran
b
Department of computer engineering, Imam hossein university, Tehran, Iran
c
Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
d
Department of mechanical engineering, Imam hossein university, Tehran, Iran
a b s t r a c ta r t i c l e i n f o
Available online 13 April 2016
In this research, the viscosity of the aqueous nano
ﬂ
uid of TiO
2
has been modeled by arti
ﬁ
cial neural networksusingexperimentaldata.Arti
ﬁ
cialneuralnetworksareabletoestimatethepatternofdynamicviscosityvariationalongwithtemperature andnanoparticlesmassfractionwithahighprecision.Anetworkwithonehiddenlayerand4neuronshasbeenused.Theregressioncoef
ﬁ
cientwasobtained0.9998inthismodeling,whichshowsveryhighprecisionofneuralnetworkwithaverysimplestructure.Inaddition,arelationshipintermsofmassfractionand temperature was presented in order to predict the viscosity of this nano
ﬂ
uid. This correlation can estimatethe viscosity of TiO
2
–
water nano
ﬂ
uid in a wide range of nanoparticles mass fraction with a maximum error of 0.5 %.© 2016 Elsevier Ltd. All rights reserved.
Keywords:
Nano
ﬂ
uidDynamic viscosityArti
ﬁ
cial neural networkCorrelationTemperature
1. Introduction
By adding nanoparticles to the base
ﬂ
uid, an increase in viscosityis inevitable. Increase in nano
ﬂ
uids viscosity should not make increasein
ﬂ
uid thermal conductivity or heat transfer coef
ﬁ
cient ineffective.Increase in viscosity leads to a pressure drop in system, and a greateramountof power is required tocompensate for thepressure reduction.Therefore, nano
ﬂ
uids viscosity as well as thermal conductivity isconsidered a very signi
ﬁ
cant parameter for investigating nano
ﬂ
uidsef
ﬁ
cacy.Different parameters affecting nano
ﬂ
uids behavior have been men-tioned in a review paper by Nwosu et al. [1]. Also, different parametersaffecting viscosity have been investigated by researchers in separatestudies. Temperature [2
–
11], volume fraction [12
–
17], packing fraction[18], thickness of nano layers [19,20], particle shape [21,22], and
aggregation radius [23] are some of the most important parametersaffecting viscosity that have been summarized in Table 1.As is observed in Table 1, many parameters affect nano
ﬂ
uidsviscosity. Some researchers have investigated nano
ﬂ
uids numerically[24
–
27].The purpose of this article is modeling the viscosity of TiO
2
-waternano
ﬂ
uids [28] by using arti
ﬁ
cial neural networks. To do this, differentstructures of neural network have been investigated, and experimentaldataandmodelingresultshavebeencomparedindifferentgraphs.Also,a relationship in terms of temperature and nanoparticles mass fractionhas been presented to predict these nano
ﬂ
uids viscosities.
2. Arti
ﬁ
cial neural network
The new point of view on neural networks based on brain perfor-mance emerged in the 1940s. The
ﬁ
rst practical application of neuralnetworks appeared by introduction of perceptron network in the late1950s. In the last 10 years, thousands of articles have been written onneural networks and these networks are widely used in different sci-ences. What currently can be said is that in future neural network willhave an important role as a scienti
ﬁ
c tool to solve special problems. Atpresent,theinformationavailableontheperformanceofbrainislimitedandthemostsigni
ﬁ
cantadvancesinneuralnetworkwillbeobtainedinfuture when more information on performance of brain and biologicalneurons is available.The applications of neural networks in different sciences includeapplication in aerospace industries as auto-pilot, in transportation in-dustries asorientation systems, in defensive affairs aspursuingmovingtargetsandmanyotherapplications.Theapplicationofneuralnetworksin the sciences mentioned above is increasing and a new application of these networks is mentioned in articles by researchers every day.
International Communications in Heat and Mass Transfer 75 (2016) 192
–
196
☆
Communicated by W.J. Minkowycz.
⁎
Corresponding authors.
E-mail addresses:
m.hemmatesfe@gmail.com (M. Hemmat Esfe),toghraee@iaukhsh.ac.ir (D. Toghraie).http://dx.doi.org/10.1016/j.icheatmasstransfer.2016.04.0020735-1933/© 2016 Elsevier Ltd. All rights reserved.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer
journal homepage: www.elsevier.com/locate/ichmt
The structure of neural network used in this research has beenshownin Fig.1. This structure is thesimplestoneamongthe investigat-ed structures (Table 1) that has the highest regression coef
ﬁ
cient.Evaluation and optimal structure of arti
ﬁ
cial neural network takesplacethroughtrialanderror.Ascanbeseen,aonelayerwith4neuronshas been used as optimal structure for modeling nano
ﬂ
uid dynamicviscosity.Table 2 shows that increasing hidden layers and the number of neuronsdonotnecessarilyincreasethenetworkprecisioninestimatingthe data. As was mentioned previously, by considering the values of R and MSE, the best selection for arti
ﬁ
cial neural network architecturein order to model the data of viscosity has been chosen a networkwith one hidden layer and 4 neurons and tansig transfer function hasbeen used.
3. Correlation
InordertoobtaintherelativeviscosityofTiO
2
aqueousnano
ﬂ
uids,acorrelation has been presented in termsof temperature and nanoparti-cles mass fraction.
μ
nf
μ
f
¼
1
:
431
−
0
:
01864
T
þ
0
:
6073
ω
þ
0
:
01334
T
2
þ
0
:
02586
T
:
ω
þ
0
:
3092
ω
2
þ
0
:
006043
T
3
þ
0
:
005644
T
2
:
ω
þ
0
:
03323
T
:
ω
2
þ
0
:
08318
ω
3
ð
1
Þ
Where mean 313.1 and SD 20.37 are used to normalize
T
(tempera-ture). Also, mean 16.5 and SD 12.85 are used to normalize (massfraction), and coef
ﬁ
cients are 95% con
ﬁ
dence bounds. This relationship
Table 1
Summary of some researchers conducted on the parameters affecting nano
ﬂ
uid dynamic viscosity.Author(s) Range of temperatureand volume fractionResearchmethodNano
ﬂ
uid Results
Tavman et al.
[2] 20
–
60 °C0
–
4 vol.%Experimental SiO
2
/waterAl
2
O
3
/waterIncrease in relative viscosity by increase in volume fraction
Pastoriza-Gallego et al.
[3] 280
–
325 K1
–
5 wt.%Experimental CuO/water The effect of particle size cannot be ignored. The greatest amount of potential
Z
isin pH 2 and pH 13.
Mariano et al.
[5] 283.15
–
323.15 KUp to 25 wt.%Experimental Co
3
O
4
/EG Intense variations of temperature
–
nano
ﬂ
uid Newtonian behavior increase of 20
–
30% in thermal conductivity at 6 vol.%
Hemmat Esfe et al.
[7] 26
–
55 °CUp to 3 vol.%Experimental Fe/EG The smaller the particle size lead to the higher thermal conductivity and viscosity;40 nm nanoparticles have a thermal conductivity 11% higher than 100 nmnanoparticles.
Yiamsawas et al.
[8] 15
–
60 °C1
–
4 vol.%Experimental TiO
2
/water EGAl
2
O
3
/water EGThe viscosity of Al
2
O
3
nanoparticles is 130% greater than TiO
2
nanoparticles.
Abdellahoum et al.
[13] 1
–
4 vol.%10
4
b
Re
b
10
5
Numerical Al
2
O
3
/water Pak and Cho model shows the maximum value of friction.
Vajjha et al.
[15] 1
–
6 vol.%3000
b
Re
b
8000Numerical Al
2
O
3
/water EGCuO/water EGThe average heat transfer coef
ﬁ
cient over the base
ﬂ
uid for a 3% volume fraction of Al
2
O
3
nano
ﬂ
uid is 36.6% and that for a 3% volume fraction of CuO nano
ﬂ
uid is 49.7%.
Zhao et al.
[16] Present two ANN with 4and 5 inputs.Numerical Al
2
O
3
/waterCuO/waterModeling by using neural network through radial basis function
Srivastava
[21] 1
–
5 vol.% Numerical Al
2
O
3
/water Particle shape deviation from spherical leads to an increase in viscosity.
ZHAO et al.
[23] Diameter of nanoparticlesfrom 7 to 40 nm0.1
–
2 vol.%
T
= 20, 25, and 30 °CExperimental SiO
2
/DI-water The amount of viscosity relate to the size of agglomerate overdependence of viscosity of nano
ﬂ
uids or 7 nm nanoparticles to PH
Fig. 1.
Optimal structure of neural network.193
M. Hemmat Esfe et al. / International Communications in Heat and Mass Transfer 75 (2016) 192
–
196
is applied in temperatures of 280
–
350k and mass fractions of 1
–
35%.Table 3 exhibits the parameters of this nonlinear regression.Fig.2showsathree-dimensionalofrelativeviscosityversustemper-ature and concentration of nanoparticles. As is observed, variations inviscosity due to change in temperature are small and the effect of mass fraction on viscosity is very noticeable. The results indicate thatbyincreasingmass fraction,changes occur rapidly,and thesevariationsgradually become more considerable So that change of mass fractionfrom 20% to 30% is more obvious.In Fig. 3, variations in value of mean square error (MSE) are seenwith different iterations of train, validation, and test data. If value of MSE increases in a certain number of iterations for validation data,results are considered as failed ones and it stops iterations and thebest result is presented as output. As can be seen in Fig. 3, stop hasoccurred with 81 iterations with MSE value of approximately 0.0008.Fig. 4 demonstrates the histogram of data error for neural networkmodeling. The horizontal axis shows different ranges of error, and thevertical axis shows the number of data in different ranges of error. Inorder to have a clearer representation, the values of
δ
and
μ
of errorgraph have been drawn in two forms of curve and histogram since thevalue of
δ
is clearer in histogram graph and value of
μ
is more obviousin curve graph. As can be observed, the peak of the errors is locatedaround zero.Fig.5 illustrates a comparison between experimental data andoutputs of neural network modeling. As can be seen, neural networkhas been very successful in modeling viscosity data and has estimat-ed empirical data with a very high precision. Therefore, this networkcan be used with high reliability to estimate the data that are notavailable.Fig.6 shows the regression of neural network results in terms of experimental results. In this study, 70% of input data were randomlyconsidered for training, and 15% of that was randomly used for testing.Good adjustment of modeling results on bisector (that is the criterionforevaluationofdata)showstheprecisionofneuralnetworkmodeling.According to this graph, the presented neural network can have anacceptable adjustment with criterion line and thus test data canestimate nano
ﬂ
uid viscosity with a maximum error less than 2%.
Table 2
Neural network parameters at different structures.Hidden layer
R
MSE SD Mean of errors Train performance Test performance2 0.9994 9.6859e
−
4 0.0310
−
0.0066 7.4279e
−
4 0.00223 0.9996 6.3575e
−
4 0.0257
−
6.7709e
−
5 5.8021e
−
4 7.4989e
−
44 0.9998 4.4153e
−
4 0.0200 0.0075 1.4973e
−
4 0.00115 0.0996 6.7173e
−
4 0.0260 0.0045 5.4655e
−
4 9.4348e
−
4[2 1] 0.9994 0.0010 0.0315 0.0071 8.1160e
−
4 0.0030[2 2] 0.9994 9.7728e
−
4 0.0317
−
0.0023 6.2407e
−
4 0.0030[3 1] 0.9995 8.5213e
−
4 0.0294
−
0.0045 8.0067e
−
4 4.2021e
−
4[3 2] 0.9996 9.2047e
−
4 0.0293
−
0.0097 6.5645e
−
4 0.0020[3 3] 0.9996 5.9938e
−
04 0.0238
−
0.0072 4.4134e
−
04 0.0019[4 1] 0.9996 7.4806e
−
4 0.0278 0.0012 7.2177e
−
4 5.3289e
−
4[4 2] 0.9996 9.8567e
−
4 0.0319 0.0019 5.7932e
−
4 5.9585e
−
4[4 3] 0.9996 6.9321e
−
04 0.0267
−
0.0028 5.1862e
−
04 0.0012[4 4] 0.9996 5.6855e
−
04 0.0239 0.0044 5.9507e
−
04 8.5482e
−
04
Table 3
regression correlation parametersSSE
R
2
Adjusted
R
2
RMSE0.02181 0.999 0.9985 0.03481Theadjustment isobtained by makingacomparison betweenthenetworkactualvalue
t
ij
andtheestimatedvalues
a
ij
bycalculatingthetotalsumofthesquareerror(SSE)forthe
n
data of the training data set.
R
2
= coef
ﬁ
cient of determination; adjusted
R
2
= degree-of-freedom adjusted coef
ﬁ
cient of determination; RMSE = root mean squared error(standard error).
Fig. 2.
Relative viscosity versus concentration and temperature.194
M. Hemmat Esfe et al. / International Communications in Heat and Mass Transfer 75 (2016) 192
–
196
Forabetterunderstandingofdatadeviationfromrealvaluesofneu-ral network modeling outputs, the concept of margin of deviation isused. This value is obtained from the following relationship:Marginofdeviation
¼
β
ANN
−
β
Exp
β
Exp
100
ð
2
Þ
The values obtained from this relationship for all neural networkoutputs are seen in Fig. 7. The maximum value of margin of deviationforthesedatais0.06%.Ifweassumethatthisvaluehasalsobeenobtain-ed for test data, we can prove the reliability of neural networks.
4. Conclusion
The purpose of this research is to investigate modeling of relativeviscosity of TiO
2
–
water nano
ﬂ
uid by using arti
ﬁ
cial neural networks.Neural network is one of the most powerful tools of modelingfor com-plicatedengineeringproblems.Inthisstudy,withinputdataoftemper-ature and mass fraction, different structures of neural networks withone and two layers and different numbers of neurons have been inves-tigated. A structure with one hidden layer and 4 neurons and tansigactivating function has been used. The maximum value of deviationfor modeling the neural network was obtained 2%, and this value forthe presented empirical relationship was obtained 3%. The data thatare not available can be predicted with high reliability by using this
0 20 40 60 80 100 12010
-8
10
-6
10
-4
10
-2
10
0
M e a n S q u a r e d E r r o r ( m s e )
Iterate
TrainValidationTestBestGoal
Fig. 3.
Performance of arti
ﬁ
cial neural network model
-0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.080123456
µ
=0.0075,
σ
=0.02Errors
I n s t a n c e
ErrorsCurve Error
Fig. 4.
Suitable curve on histogram error.
0 5 10 15 20 250.511.522.533.5Number of Data
D y n a m i c V i s c o s i t y ( c P )
Experimental DataANN Results
Fig. 5.
Comparative graph between experimental data and ANN results.
1 1.5 2 2.5 3 3.511.522.533.5
Experimental Data
A N N R e s u l t s
Equality LineANN Results
Fig. 6.
Regression of ANN results.195
M. Hemmat Esfe et al. / International Communications in Heat and Mass Transfer 75 (2016) 192
–
196
model. Also, a relationship in terms of temperature and mass fractionhas been presented to estimate viscosity data. This relationship is ableto estimate viscosity with a very good precision.
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0 5 10 15 20 25 30-0.06-0.04-0.0200.020.040.06
Number of Data
M a r g i n o f d e v i a t i o n ( % )
Fig. 7.
Margin of deviation of ANN results.196
M. Hemmat Esfe et al. / International Communications in Heat and Mass Transfer 75 (2016) 192
–
196

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