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Estimation of thermal conductivity of Al 2 O 3 /water (40%)-ethylene glycol (60%) by artificial neural network and correlation using experimental data

In this work, the estimation of thermal conductivity of Al2O3 nanoparticles inwater (40%)–ethylene glycol (60%) has been investigated. An empirical relationship has been proposed based on experimental data and in terms of temperature and
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  EstimationofthermalconductivityofAl 2 O 3 /water(40%) – ethyleneglycol(60%) by arti fi cial neural network and correlation usingexperimental data ☆ Mohammad Hemmat Esfe a, ⁎ , Wei-Mon Yan b, ⁎ , Masoud Afrand c, ⁎ , M. Sarraf  d ,Davood Toghraie a , Mahidzal Dahari d a Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran b Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, Taipei 10608, Taiwan, ROC  c Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran d Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia a b s t r a c ta r t i c l e i n f o Available online xxxx  Inthiswork,theestimationofthermalconductivityofAl 2 O 3 nanoparticlesinwater(40%) – ethyleneglycol(60%)has beeninvestigated. An empiricalrelationship has beenproposed basedon experimentaldata and intermsof temperatureandvolumefraction.Besides,amodelhasbeenpresentedusingfeedforwardmulti-layerperceptron(MLP)arti fi cialneuralnetwork(ANN).Thepresentedcorrelationrelationshipestimatesempiricaldataverywell.However,arti fi cialneuralnetworkhasahigherregressioncoef  fi cientandlowererrorcomparedtothepresentedrelationship.Afterexaminingdifferentstructuresofneuralnetworkwithdifferenttransferfunctions,astructurewas selected with two hidden layers and 5 neurons in the  fi rst and second layers and tangent sigmoid transferfunctionforbothlayers.Theresultsindicatethatarti fi cialneuralnetworkscanpreciselyestimatetheexperimen-tal data of thermal conductivity of Al 2 O 3 /water (40%) – ethylene glycol (60%) nano fl uids.© 2016 Elsevier Ltd. All rights reserved. Keywords: Nano fl uidThermal conductivityArti fi cial neural network 1. Introduction Nano fl uids are colloidal suspensions in which particles in nano sizeare dispersed in pure  fl uid. Recently, to improve the heat transfer, oneway is increased, the thermal conductivity of base  fl uids with addingsolid particles to these  fl uids. First, Choi [1] suspended metal nanoparti-clesof copperinwaterandreportedthermalconductivityenhancement.Afterthat,agreatnumberofresearcheshavebeenconductedondifferentnano fl uids from different aspects [2 – 8]. These particles include differenttypesofoxidessuchascopperoxide[9 – 11],aluminumoxide[12 – 14],ti-tanium oxide [15,16], and so on. The other nanoparticles used innano fl uids preparation are metal particles like silver nanoparticles [17].Fromdifferentnanoparticles,CNTisconsideredagoodonefornano fl uidspreparation.Choietal.[18]reported150%increaseinthermalconductiv-ity of poly ( α  - ole fi n) by adding 1% volume of multiwall nanotube(MWCNT). Similarly, Yang et al. [19] reported 200% increase in thermalconductivity by adding 0.35% multiwall carbon nanotube (MWCNT).Hemmat Esfe et al. [20] investigated aquatic nano fl uids of carbon nano-tube and examined thermophysical properties and pressure drop intwo-tube transformers. Amiri et al. [17] have produced stable nano fl uidsbythesynthesisofcarbonnanotubesdecoratedbysilverparticlesandex-amined their thermophysical properties. The heat transfer of MWCNT oilnano fl uids inside horizontal  fl attened tubes was performed by Ashtianietal.[21].Baghbanzadehetal.[22,23]haveexaminedthethermalconduc- tivity and viscosity by preparing hybrid MWCNT/SiO 2  nano fl uids and dif-ferentcombinations.Also,ChenandXie[24]examinedtheeffectofPHonzeta potential of one- and two-wall nano fl uids and measured their ther-mal conductivity.While using nano fl uids, we should remember that the effective vis-cosityofnano fl uidcanbefourtimesasmuchasthatforbase fl uid.There-fore,increaseinviscositywouldenhancepump powerandthusincreaseenergy consumption [25]. De fi nitely, several different aspects of nano fl uidshavenotbeenrevealeduptonow,andusingthese fl uidsinin-dustrialapplicationsrequiresmoreextensiveresearches.Oneof thenewsubjects used in transformers heat analysis in recent years is arti fi cialneural network [26]. Hojjat et al. [27] in an article have used MLP neural networks for modeling their empirical data. Hemmat Esfe et al. [28,29]have modeled different empirical data by using neural networks. Karimiand Youse fi  [30] have modeled the results of nano fl uids density byusingacombinationofneuralnetworkandgeneticalgorithm.Neuralnet-worksareabletomodelthecomplexpatternswellbyusingsimplecom-putations and a parallel processing similar to what takes place in humanbrain. International Communications in Heat and Mass Transfer 74 (2016) 125 – 128 ☆  Communicated by: W. J. Minkowycz ⁎  Corresponding authors. E-mailaddresses:, Yan), (M. Afrand).© 2016 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer  journal homepage:  In this work, thermal conductivity of Al 2 O 3  in water – EG (40 – 60%)base fl uidhas been studied by usingempirical data [31], correlation re-lationship,andneuralnetwork.Theeffectofdifferentparametersonre-gression coef  fi cient of correlation has been investigated and the bestrelationship with the least error would be presented. Also, differentstructuresofneuralnetworkhavebeenexaminedandanoptimalstruc-ture has been used for modeling empirical data. 1.1. Arti  fi cial neural network Arti fi cial neural network is a new subject in which computer scien-tists have become interested and on which they have spent a greatdeal of time and money to make more advances in computer sciences.Thestudyofarti fi cialneuralnetworkswasgreatlyinspiredfromnaturallearningsystemsinwhichacomplexseriesofconnectedneuronsarein-volved in learning. Fig. 1 shows the neural network structure in whichhas two hidden layers, each of which has 5 neurons. For each of theselayers, transfer function of tansig has been considered that bringsabout the best results. In the output layer, transfer function of purelinhas been used. Tansig function that has been used for the data isshown as follows:  f z  ð Þ¼  11 þ e   z   ð 1 Þ 2. Results and discussion Tounderstandtheiterationsonmeansquarederror,theimprovementin network's performance for each training, validation, and test set isshown in Fig. 2. The best response of validation set is selected to be theoutput in this work. Fig. 3 shows the results of the thermal conductivityofnano fl uidsundervariousvolumefractionsandtemperaturesforexper-imental data and the obtained model for neural network. This graph hasbeen plotted for 5 different temperatures ranging from 20 to 60 °C. It isclearly found that the neural network can estimate experimental datawith an acceptable precision.Another method that can be used to measure the agreement be-tween the neural network and the data is the regression plot. The re-gression plot for all samples is presented in Fig. 4. It is noted in Fig. 4 thattheactualoutputsofthenetworkintermsoftheassociatedvalues.The linear  fi t to the relationship precisely divides the plot's top-rightand bottom-left corners and shows that the network agrees with thedata well. Otherwise, additional training, or training a network includ-ingmorehiddenneurons,isrecommended.Tableofparametersofneu-ralnetworkmodelingfor training,validation,andtestdataandalsothegeneral performance of network is disclosed in Table 1. In Table 1,  μ   isthe mean of error and  σ   is the standard deviation of neural networkoutputs. Fig 1.  ANN structure with 2 hidden layers. 0 10 20 30 40 50 60 70 80 90 10010 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2    M  e  a  n   S  q  u  a  r  e   d   E  r  r  o  r   (  m  s  e   ) Iterate TrainValidationTestBestGoal Fig 2.  Validation performance. 60  o C20  o C50  o C40  o C30  o C Volume Concentraion (%)     T    h   e   r   m   a    l    C   o   n    d   u   c   t    i   v    i   t   y    (    W .   m   -    1  .    K   -    1     ) 0 0.5 1 1.50.320.340.360.380.40.420.440.46 Experimental DataNeural network model Fig. 3.  Comparison between experimental data and ANN at different volumeconcentrations.126  M. Hemmat Esfe et al. / International Communications in Heat and Mass Transfer 74 (2016) 125 – 128  Toobtainrelative thermalconductivityvalueof Al 2 O 3 /water(40%) – ethylene glycol (60%) nano fl uids for temperature  T   ranging from 20 to60 °C and volume fraction  φ  from 0.3 to 1.5% without requiring thetable of experimental data, a corrected relationship has been proposedto obtain these values in the mentioned conditions. k nf  k  f  ¼ − 1587 − 1 : 05  10 6 φ  − 0 : 489 T  þ 281 ln  T  ð Þþ 1 : 06  10 6 sin  φ  ð Þþ 3 : 98  10 4  1 T  − 1 : 03  10 2 φ  2 − 9 : 1 φ  T  − 1 : 02  10 3 φ   ln  T  ð Þþ 703 φ  2 T  þ 0 : 02 φ  T  2 − 1 : 151 φ  2 T  2 ð 2 Þ The comparison between experimental data [31] and correlation re-sultswaspresentedinFig.5.ItisclearlyrevealedinFig.5thatthethermal conductivity of Al 2 O 3  (with average crystallite size of 36 nm)/water – ethylene glycol nano fl uids has increased from 4% to nearly 35%. In thisplot, 45 data concerning relative thermal conductivity of Al 2 O 3 /water – ethylene glycol nano fl uids have been compared with estimated values.A brief look at this plot reveals that the presented correction in thiswork has a good precision and can well estimate the experimental data.TheseresultsarepresentedinFig.6inadifferentway.Inthis fi gure,correlation data have been plotted in terms of experimental data. Themore precise the estimated data are, the more agreement the relation-ship results have with bisector. In this plot, the results of the presentedrelationshipareveryclosetothebisectorandregressionofresultsfromexperimental data is less than 2%. A comparison between modeling byneural network and the presented correction indicates that neural net-workmodelingismoreprecise.Theregressioncoef  fi cientofneuralnet-work is 0.9993 and that of the presented relationship is 0.9955. Thestandard deviations of neural network and the presented relationshipare 0.001033 and 0.005783, respectively, and it shows the superiorityof neural network. 3. Conclusions In this work, modelings of thermal conductivity of nano fl uid usingneural network and correlation relationship have been presented basedonexperimentaldata.Correlationregressioncoef  fi cientis99.55%andre-gression coef  fi cient of neural network modeling is 99.93%. 15% of exper-imental data have been used to test neural network. In regression plot,the results of these data have been predicted with an MSE of approxi-mately 3.5 ×10 -6 . It shows that the trained network has provided agood agreement between the predicted values and experimental data.The presented relationship in this work can also estimate thermal con-ductivity of Al 2 O 3  (with average crystallite size of 36 nm)/water – EG(40 – 60)nano fl uidsintermsoftemperatureandvolumefractionwithac-ceptable precision. 0.34 0.36 0.38 0.4 0.42 0.440.340.360.380.40.420.44 Experimental Data    A   N   N   R  e  s  u   l   t  s Equality LineTrain DataValidation DataTest Data Fig 4.  ANN regression diagram.  Table 1 General performance of network.R MSE  μ σ  Train data 0.99965 6.293e − 7 8.9446e − 7 8.0432e − 4Validation data 0.99894 5.7282e − 7 2.4337e − 4 7.6614e − 4Test data 0.99709 3.4719e − 6 1.1626e − 4 1.9881e − 3All data 0.9993 1.0498e − 6 5.4909e − 5 1.0329e − 3 Number of Data    R  e   l  a   t   i  v  e   T   h  e  r  m  a   l   C  o  n   d  u  c   t   i  v   i   t  y 0 10 20 30 4011. DataCorrelation Results Fig 5.  Comparison between experimental data and correlation results. Experimental Data    C  o  r  r  e   l  a   t   i  o  n   R  e  s  u   l   t  s 1.05 1.1 1.15 1.2 1.25 1.3 1.351. ResultsEquality Line -2 %+2 % Fig 6.  Regression plot of correlation results.127 M. Hemmat Esfe et al. / International Communications in Heat and Mass Transfer 74 (2016) 125 – 128   Acknowledgment The  fi nancial support by the Ministry of Science and Technology,R.O.C., through the contract MOST 103-2221-E-027-107-MY2 is alsohighly appreciated. The authors gratefully acknowledge High ImpactResearch Grant UM.C/HIR/MOHE/ENG/23 and Faculty of Engineering,University of Malaya, Malaysia for their support in conducting thisresearch work. References [1] S.U.S. Choi, Enhancing thermal conductivity of   fl uids with nanoparticle, ASME FED231 (1995) 99 – 105.[2] D.Ciloglu,A.Bolukbasi,Acomprehensivereviewonpoolboilingofnano fl uids,Appl.Therm. Eng. 84 (2015) 45 – 63.[3] D. Wen, G. Lin, S. 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