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International Journal of Thermal Sciences 90 (2015) 150e172

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International Journal of Thermal Sciences

journal homepage: www.elsevier .com/locate/ i j ts

Review

Applications of artificial neural networks for thermal analysis of heatexchangers e A review

M. Mohanraj a, *, S. Jayaraj b, C. Muraleedharan b

a Department of Mechanical Engineering, Hindusthan College of Engineering and Technology, Coimbatore 641032, Indiab Department of Mechanical Engineering, National Institute of Technology Calicut, Calicut 673601, India

a r t i c l e i n f o

Article history:Received 5 May 2014Received in revised form22 October 2014Accepted 20 November 2014Available online 7 January 2015

Keywords:Artificial neural networksModelingHeat exchangersThermal analysis

* Corresponding author. Tel.: þ91 9486411896.E-mail address: [email protected] (M. Mo

http://dx.doi.org/10.1016/j.ijthermalsci.2014.11.0301290-0729/© 2014 Elsevier Masson SAS. All rights re

a b s t r a c t

Artificial neural networks (ANN) have been widely used for thermal analysis of heat exchangers duringthe last two decades. In this paper, the applications of ANN for thermal analysis of heat exchangers arereviewed. The reported investigations on thermal analysis of heat exchangers are categorized into fourmajor groups, namely (i) modeling of heat exchangers, (ii) estimation of heat exchanger parameters, (iii)estimation of phase change characteristics in heat exchangers and (iv) control of heat exchangers. Mostof the papers related to the applications of ANN for thermal analysis of heat exchangers are discussed.The limitations of ANN for thermal analysis of heat exchangers and its further research needs in this fieldare highlighted. ANN is gaining popularity as a tool, which can be successfully used for the thermalanalysis of heat exchangers with acceptable accuracy.

© 2014 Elsevier Masson SAS. All rights reserved.

1. Introduction

Heat exchangers are widely used in engineering applicationssuch as refrigeration and air conditioning systems, automobiles,thermal power plants, chemical and textile processing industries,etc. Heat exchangers are the devices facilitating effective heattransfer between the two fluids by virtue of their temperaturedifferences. The complexity in the analysis of heat exchangers shallbe due to its geometry and the physical phenomena involvedduring the heat exchange between the fluids. In general, the heatexchangers are studied both analytically and experimentally usingfirst and second laws of thermodynamics [1]. The theoretical heatexchanger analysis involves more assumptions and complicatedequations, whereas the experimental methods are more expensivedue to its initial investment required in developing an experimentalsetup [2]. To overcome these difficulties, ANN models were devel-oped for simulation, optimization and performance prediction ofthermal systems involving heat exchangers [3e5]. ANN establishesthe correlations based on some training data, which does notrequire any specific analytical equations and system descriptions.Non-linear parameters involved in the heat transfer processes of

hanraj).

served.

heat exchangers can be correlated using ANN with minimumerrors.

Some of the studies on heat exchangers reviewed earlier arereporting the design and development of plate type heat ex-changers [6], ceramic based heat exchangers [7], applications ofcompact heat exchangers [8], fouling of heat exchangers in aircraftair conditioning systems [9], the application of nanofluids in heatexchanger [10] and computational fluid dynamics (CFD) applica-tions in heat exchanger design [11]. Similarly, many researchers hadreviewed the applications of ANN for refrigeration, air conditioningand heat pump systems [12], heat transfer problems in nuclearengineering [13], sizing of solar photovoltaic systems [14],modeling and control of combustion processes [15], modeling ofenergy systems [16], modeling of renewable energy systems [17]and for chemical process control [18]. The previously cited re-views of heat exchangers and engineering applications of ANNconfirmed that, there is no specific review reported on the usage ofANN for heat exchanger applications.

The three main objectives of the present review are as follows: (i)to summarize the studies related to thermal analysis of heat ex-changers accomplished by ANN, (ii) to make a comparison amongthe network architectures for heat exchanger analysis and (iii) toidentify the limitations and further research needs of ANN for thethermal analysis of heat exchanger. The remaining part of this papercontains following six sections: An overview of thermal analysis ofheat exchangers is described in Section 2. The Section 3 provides an

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M. Mohanraj et al. / International Journal of Thermal Sciences 90 (2015) 150e172 151

overview of ANNmodeling of heat exchangers. The articles reviewedare consolidated in Section 4. The limitations of ANN modeling forheat exchanger analysis and further research needs in this area arehighlighted in Section 5 and Section 6, respectively. Section 7 pro-vides the conclusion arrived by this study.

2. Thermal analysis of heat exchangers e an overview

An overview of thermal analysis of heat exchangers by theo-retical and experimental methods is presented in this section. Alsothe CFD and ANN analysis of heat exchangers are discussed.

2.1. Theoretical and experimental analysis of heat exchangers

The logarithmic mean temperature difference (LMTD) andeffectiveness-number of transfer units (ε-NTU) methods are thecommonly usedmethods of heat exchanger analysis [19]. The LMTDmethod requires mass flow rates, inlet and outlet temperatures ofboth hot and cold fluids, whereas, ε-NTU method requires the heatcapacity rate of hot and cold fluids for the heat exchanger analysis.The assumptions made in the conventional methods of heatexchanger analysis include the following: (i) constant overall heattransfer coefficient (U) and specific heat capacity, (ii) no heat lossbetween the heat exchanger and its surroundings, (iii) negligiblekinetic and potential effects and (iv) steady state conditions exists.However, in many heat exchanger applications, the properties andcomposition of the fluids (in case of using zeotropic mixed fluids)may vary with time and the value of U is continuously varying [20].Hence, the assumptions are not strictly valid for the analysis of heatexchangers operating with mixed fluids. As a result, the evaluationof heat exchanger performances using LMTD and NTU methodswould require correction factors. Whereas the experimental anal-ysis of heat exchanger analysis requires major investments indeveloping an experimental facility and its instrumentation.

2.2. Heat exchanger analysis using computational fluid dynamics(CFD)

CFD is another methodology used for investigating the flow,heat transfer, pressure drop, design, optimization, troubleshootingand fouling of heat exchangers. CFD methodology involves solvingof mathematical equations with the help of a selected numericalprocedure [10]. CFD modeling employs the conventional fluid dy-namics equations by resolving the entire domain in small grids orelements and applying the governing equations on these discrete

0

2

4

6

8

10

12

14

16

18

20

2000 2001 2002 2003 2004 2005 2006 2

Y

detroperseidutsforeb

muN

Fig. 1. Applications of ANN for heat excha

elements for finding the solutions. However, the CFD analysis in-volves often multiple number of equations and assumptions. TheCFD method of heat exchanger performance predictions is found tobe closer to the experimental values, yielding good agreement,usually in the range between 2% and 10%. But in some cases, it maydeviate even up to 36%, which is not really acceptable [10].

2.3. Heat exchanger analysis using ANN

The heat exchanger analysis using ANN overcomes the limita-tions associated with LMTD, ε-NTU, CFD and the experimentalapproach [21]. The ANN can establish the nonlinear relationshipbetween input and output based on a set of available training data.The time distribution of the number of studies reported using theANN methodology of heat exchanger analysis is illustrated in Fig. 1.From Fig. 1, it is clear that the number of investigations reported inthis area is gradually increasing during last two decades. Thermalanalysis of heat exchanger using ANN is becoming popular withresearchers working in this area.

3. Modeling of heat exchangers using artificial neuralnetworks

The commonly used ANN architectures for thermal analysis ofheat exchangers are multilayer feed forward network (MLFFN),radial biased function network (RBFN), generalized regressionneural network (GRNN) and adaptive neuro fuzzy interface systems(ANFIS). The basic information on ANN architectures is not dis-cussed in this paper, since it is very much available and dealt indetail in the open literature [14e17].

3.1. Selection of the ANN parameters

The ANN parameters such as, the number of neurons in theinput, hidden and output layers, network architecture, transferfunction, learning algorithm, momentum factor and learning rateare to be selected for developing an ANN model. Proper data se-lection also plays a major role in the success of ANN architectureused. The number of neurons in the input layer is usually equal tothe number of parameters that affect the performance of heat ex-changers. The input layer distributes the values to each neuron inthe hidden layer. A layer(s) of processing neurons between theinput and the output layers is called as the hidden layer(s). Thenumber of hidden layers and the number of hidden neurons mayvary depending on the accuracy required. The number of neurons

007 2008 2009 2010 2011 2012 2013 2014

ear

nger analysis reported in this review.

M. Mohanraj et al. / International Journal of Thermal Sciences 90 (2015) 150e172152

in the hidden layer, number of hidden layers, momentum factorand learning rate values are to be optimized to attain the resultswith required accuracy. The number of neurons in output layer isusually equal to the number of parameters selected for predictingthe heat exchanger performance.

3.2. Training of the ANN

ANN is trained with a set of known inputeoutput data andsuitable learning method to perform a function by adjusting thevalues of weight coefficient between the processing neurons. The

Fig. 2. Flow chart of ANN tra

training process continues until the network output matches withthe desired output. Changing the weights and biases shall reducethe error between the network output and the desired output. Thetraining process is terminated automatically when the error fallsbelow a determined value or the maximum epochs is exceeded.Fig. 2 depicts the steps involved in training of ANN used for thethermal analysis of heat exchanger [14e17]. The steps involved inthis are listed as follows:

(i). Before collecting the training data, a good representation forthe input and output parameters has to be found.

ining processes [14e17].

Table 1Modeling of condensers.

Authors[references]

Networkarchitectures

Type ofheat exchanger

Parameterspredicted

Islamoglu [22] MLFFN Wire on tubecondenser

Q�

Hayati et al. [23] ANFIS Wire on tubecondenser

Q�

Ertunc andHosoz [24]

ANFIS Evaporativecondenser

Condenser heatrejection rate, Trefleaving the condenser,DBT and WBT of airleaving the condenser.

Mohanrajet al. [25,26]

MLFFN Fin and tubecondenser

Exergy destructionand efficiency

Zhao andZhang [27]

MLFFN Fin and tubecondenser

Heating capacity,Dps in refrigerantand air sides.

Tian et al. [28] MLFFN Parallel flowcondenser

Capacity of heatexchanger, air andrefrigerant side Dps, Tref

Yang et al. [29] MLFFN Fin and tubecondenser

Heating capacity,air side and refrigerantside Dps,


Identification of parameters that influence the performanceof heat exchangers (neurons in the input layer) and theperformance parameters of a heat exchanger to be investi-gated (neurons in the output layer) are to be selected fornetwork training. Constant parameters are neglected.

(ii) For the second law analysis of heat exchangers, the influenceof the dead state (ambient conditions) should be considered.

(iii) Since the networks are trained under supervision, theinputeoutput data are collected from experiments or fromnumerical simulation. The collected data were divided intothree data sets (training data set, validation data set, testingdata set). The data for training, validation and testing are tobe selected in the entire experimental range.

(iv) Normalization of inputs and outputs is done either in therange between 0 and 1 or between �1 and 1 (depending onthe type of training data). Normalization of inputs and out-puts enhances the learning speed of the network.

(v) Development of an ANN model and the definition of theinputs and outputs.

(vi) Selection of network architecture according to the applica-tion involved.

(vii) Training of the network with normalized input and outputvalues using neural network toolbox of MATLAB.

(viii) The network parameters (such as training data requirement,number of hidden layers, number of hidden neurons,learning rate and momentum factor) are to be optimized toattain results with good accuracy.

(ix) Extraction of results from the trained network.

The training data set is used to train the weights in the neuralnetwork to produce the desired output. The validation data set isused to find the best configuration and training parameters. Thetest data set is used to evaluate the parameters of the trained neuralnetworks. About 70% of the randomly selected data sets areassigned as training data sets and remaining data can be used fortesting and validating the network.

3.3. Testing of network

The performance of the network is evaluated using statisticalparameters, such as the absolute fraction of variance (R2), correla-tion coefficient (R), root mean square values (RMS), mean absoluteerror (MAE), mean absolute relative error (MARE) and coefficient ofvariance (COV) by changing the network parameters. The networkparameters were optimized either trial and error method or bynovel optimization techniques to achieve better results.

4. Reviewing applications of ANN for the analysis of heatexchangers

The reported studies for thermal analysis of heat exchangers arecategorized into four subsections based on the applications of ANNas follows: (i) modeling of heat exchangers [22e91], (ii) estimationof heat exchanger parameters [92e118], (iii) estimation of phasechange characteristics in heat exchangers [119e159], and (iv)control of heat exchangers [160e172]. Additionally, the comparisonamong the network architectures is discussed in this section[173e197].

4.1. ANN modeling of heat exchangers

The successful applications of the ANN approach for modeling ofheat exchangers are reviewed in this subsection. The reviewed in-vestigations are categorized into twelve subsections based on itsapplications. A summary of investigations on modeling of heat

exchangers are also consolidated and presented in the form ofTables (Tables 1e10).

4.1.1. Modeling of condensersThe applications of ANN for modeling of condensers used in

refrigeration, air conditioning and heat pump systems are reviewedand presented in Table 1. In related work, Islamoglu [22] predicted

the Q�of a natural convection wire on tube heat exchanger using

MLFFN. The Q�was obtained with reference to twelve parameters

(At, Aw, dt, dw, Lt, Lw,m�ref , Tref at the inlet, volumetric flow rate of air,

Ta at condenser inlet, total area of tube and wire, and Tcond of

refrigerant). The network with a 12-5-1 configuration predicts Q�

with MaRE of 5.56% and 7.94% for training and testing, respectively

with MRE of 4%. In a similar application, Q�of a wire on tube heat

exchanger was predicted using ANFIS and compared with MLFFN[23]. The MaRE and MREs using ANFIS were 8.98% and 2.54%,respectively. On the other hand, MLFFN hasMaRE of 7.94% and MREof 4%. In another work, Ertunc and Hosoz [24] compared the per-formance predictions of an evaporative condenser using MLFFNand ANFIS techniques. They predicted the condenser heat rejectionrate, the refrigerant temperature leaving the condenser, DBT andWBTof the leaving air with reference to seven parameters (DBT and

WBT of air at the inlet to the condenser,m�a,m

�ref , m

�w, absolute pref

and Tref at the inlet to the condenser). Their results showed that,both MLFFN with a 7-5-4 configuration and ANFIS predictions arewithin 5% deviation of the experimental values. The accuracy ofANFIS predictions was higher when compared to MLFFN pre-dictions for the performance prediction of condensers.

In similar work, two MLFFN models were developed for pre-dicting the exergy destruction and exergy efficiency of a directexpansion solar assisted heat pump with reference to solar in-tensity and ambient temperature [25,26]. In this paper, the exergyperformance of a condenser alone is discussed. The MLFFN pre-dictions of exergy destruction are closer to the experimental resultswith good R values of 0.9898 and COV values of 1.043. Similarly, theexergy efficiency of the condenser is closer to experimental valueswith R values of 0.9957 and COV values of 0.7996. In another work,Zhao and Zhang [27] predicted the performance of an air cooledcondenser using two ANN configurations and compared with each

Table 2Modeling of cooling coils and liquid line suction heat exchangers.

Authors [references] Networkarchitectures


Parameterspredicted

Islamoglu et al. [31] MLFFN Liquid line suctionheat exchangers

Tref and mref�

Heimel et al. [32] MLFFN Liquid line suctionheat exchangers

Q�, mref

�

Kumlutas et al. [33] MLFFN Evaporator Tsur and Q�

Yigit and Ertunc [34] MLFFN Wire on tubecooling coil

Ta and RH

Tahavvor andYaghoubi [35]

MLFFN Evaporator Frost thicknessand density

Table 4Modeling of plate type heat exchangers.

Authors[references]



Parameters predicted

Selbas et al. [41] MLFFN Plate type Q�, 3

Peng and Ling [42] MLFFN Plate type Dp on cold and hot side,total weight and total cost.

Peng and Ling [43] MLFFN Plate type j and f factors


other. One is a multi-input single output (MISO) configuration andthe other is a multi-input multi-output (MIMO) configuration. InMISO configuration, the MIMO configuration is divided into threeMISO configurations for ANN training and afterward the trainedMISO configurations are combined into a single MIMO configura-tion. Another network is MIMO approach, which is modeleddirectly. The network inputs arem

�ref , m

�a, refrigerant Ti, Tsat and

entering DBT of air. The outputs of the network consist of heatingcapacity and pressure drop (Dp) on both refrigerant and air sides.Their results showed that the MISO approach requires less trainingdata than that of MIMO, which becomes more valuable when thetraining data are extracted from experimentations. The deviationsof the heating capacity, the refrigerant-side and air-side Dp pre-dicted by both MISO and MIMO are within 5% deviation whencompared to the experimental values.

Tian et al. [28] predicted the thermal performance of a parallelflow condenser working with R134a as refrigerant using theMLFFN. In their work, DBT, WBT, inlet va, m

�ref , Tref and pref of the

refrigerant entering the condenser were considered as input pa-rameters. It was reported that a MLFFN with 6-9-5 configurationpredicts the condenser capacity, Tref leaving the condenser and Dpfor both air side and the refrigerant side with RMS errors between0.0015 and 0.0060, R values of 0.9999 and MREs in the range of0.2414e1.3194%. In another work, the heating capacity, refrigerantside and air side Dp of a condenser were predicted using MLFFN[29]. In their work, seven dimensionless p-terms have been usedfor predicting the h values. Similarly, four dimensional p-termshave been used for predicting refrigerant side Dp and two dimen-sionless p-terms have been used for predicting the air side Dp. TheMLFFN was optimized to 7-5-1, 4-3-1 and 2-3-1 configurations forpredicting the heating capacity, refrigerant side Dp and air side Dp,respectively. The standard deviations of trained dimensionlessneural networks are 0.66%, 4.83% and 0.11% for heating capacity,refrigerant side Dp and air side Dp, respectively.

4.1.2. Modeling of liquid line suction heat exchangers andevaporators

The applications of ANN for modeling of liquid line suction heatexchangers and evaporators are reviewed and the details are listedin Table 2. Liquid line suction heat exchangers are widely used in

Table 3Modeling of run-around heat exchangers.


Type of heatexchanger


Akbari et al. [37,38] MLFFN Run-aroundmembraneheat exchanger

Sensible and latentheat effectiveness.

Tan et al. [39] MLFFN Compact Over all Q�

Ermis [40] MLFFN Compact Dp, h and Nu

compression based refrigeration and air conditioning systems toimprove its performance [30]. In a related work, Islamoglu et al.[31] successfully used MLFFN for predicting the Tref at suction lineoutlet and m

�ref of a non-adiabatic capillary tube suction line heat

exchanger used in refrigeration systems. A MLFFN with sevenneurons in the input layer (representing the degree of sub cooling,suction line inlet temperature, internal diameter of a capillary tube,internal diameter of the suction line, length of the capillary tube,length of the heat exchanger and adiabatic inlet length) and twoneurons in the output layer (representing refrigerant suction lineoutlet temperature andm

�ref ) was developed. It was reported that, a

7-7-2 network configuration predicts the Tref suction line outlet andm�ref with MRE of 1.94% and 2.26%, respectively when compared to

the experimental results. Similarly, MLFFN was used for predictingthe performance of suction line heat exchangers [32]. The networkhas ten neurons in input layers representing inlet p, pressure dif-ference, length, diameter and inlet enthalpy from the capillary tubeside, p,m

�ref , inlet enthalpy, length and inner diameter of the coaxial

heat exchanger side. The outputs are m�ref through the capillary

tube and enthalpy of the suction line outlet. TheMLFFNwith 10-30-15-2 predicts the m

�ref through capillary tube and enthalpy of suc-

tion line outlet within 15% deviations.Kumlutas et al. [33] developed aMLFFNmodel for predicting the

temperatures of evaporator surface at three locations, averagetemperature and amount of heat absorbed by the evaporator sur-face with reference to three parameters such as the gap betweenevaporator surface and glass shelf, evaporator height and Tsur of adomestic refrigerator. The network was optimized for 3-15-5configuration. It was reported that, the optimized network predictsthe temperatures at points 1, 2 and 3, and Tavg with MREs of 2.62%,2.99%, 2.81% and 2.96%, respectively. The MRE of evaporator heatabsorption rate is 1.42%. Similarly, the MLFFN technique was usedto predict the temperature and RH of air at the outlet of a wire-on-tube type cooling coil [34]. They developed a MLFFN with nineneurons in the input layer (representing Tair enters the cooling coil,RH, vair, frost weight, coil Tsur,m

�ref and its temperatures at inlet and

outlet and Tab) and two neurons in the output layer (representing Taand RH at the outlet). The input and output values were normalizedin the interval between �1 and 1. The network with a 9-9-20-2configuration was identified as the optimal topology. The MLFFNpredictions yield a maximum R value of 0.999 and 0.982 for tem-perature and RH, respectively, with their errors less than 1% and 2%.Similarly, Tahavvor and Yaghoubi [35] predicted the frost

Table 5Modeling of fin and tube condensers.

Authors[references]




Pacheco-Vegaet al. [45]

MLFFN Fin and tube Q�

Pacheco-Vegaet al. [46]

MLFFN Fin and tube Q�

Ding et al. [47] MLFFN Fin and tube heat Tref and TaWu et al. [48] MLFFN Fin and tube cooler TCO2

, pressure raise,Tair, Q

�

Table 6Modeling of shell and tube heat exchangers.

Authors[references]




Xie et al. [50] MLFFN Shell and tube Q�, DT between oil and water.

Mandavganeet al. [51]

MLFFN Shell and tube T of cold and hot water outlet

Pandharipandeet al. [52]

MLFFN Shell and tube T of cold and hot water outlet

Kashani et al. [53] MLFFN Shell and tube RfoDuran et al. [54] MLFFN Shell and tube Cost estimation

Table 8Modeling of mixtures.

Authors[references]


Heat exchangerconfiguration


Hosoz et al. [70] MLFFN Cooling tower Heat rejection rate, m�

of makeup water, Tw attower outlet, DBT and RHof air leaving the stream

Gao et al. [71] MLFFN Cooling tower Outlet Tw, DTw, hCTGao et al. [72] MLFFN Cooling tower Air gravity, cooling DT,

cooling efficiency, h,mass transfer coefficientand evaporation loss

Islamogluet al. [73]

MLFFN Cooling tower COP

Qi et al. [74] MLFFN Cooling tower Outlet TwWu et al. [75] MLFFN Cooling tower Heat absorption capacity,

heating efficiency, rationof sensible and latentheat transfer, outlet airDBT, outlet aqueoussolution temperature,ratio of sensible to total


deposition on a horizontal circular tube under natural convectionusing MLFFN. In their work, the network consists of five neurons ininput layer representing Tab, cold surface temperature, RH, dt andtime of operation and two neurons in the output layer representingfrost thickness and frost density. It was reported that MLFFN with5-10-20-20-20-2 configuration predicts both frost thickness andfrost density with R2 values of 0.9999.

heat transfer, humiditydifference betweeninlet and outlet.

Hosoz et al. [76] MLFFN Evaporative cooler DBT and RH, mass ofwater evaporated,sensible cooling rateand effectiveness

Kiran andRajput [77]

MLFFN ANFIS,FIS

Evaporative cooler Outlet Ta and 3.

4.1.3. Modeling of run-around heat exchangersA run around heat exchanger is a heat recovery system which

combines two recuperators heat exchangers by a third fluidexchanging the heat with each fluid in turn [36]. The applications ofANN modeling of run-around heat exchangers are reviewed in thissubsection. Table 3 summarizes the ANN applications of run-around and compact heat exchangers. Akbari et al. [37] predictedthe sensible and latent effectiveness of a run-around membraneenergy exchanger using two separate MLFFN models. Training datasets of about 140,000 points were predicted using a finite differencemodel. The sensible and latent effectiveness was predicted withreference to five input parameters, such as, number of heat transferunits, heat capacity rate ratio, difference between the inlet andoutlet Ta, humidity ratio of indoor and humidity ratio of outdoor air.In their work, a MLFFN with 5-10-10-1 configuration predicts bothsensible and latent energy transfers in the run-around membraneenergy exchangerwith RMSE values of 0.05 �C and 2�10�5 kgv/kga,respectively and their corresponding average absolute errors are0.03 �C and 1.4 � 10�5 kgv/kga. In further work, the transient heatand mass transfer performance of a run-around heat membraneheat exchanger was predicted using MLFFN [38]. Two separatemodels were developed for predicting the sensible and latent

Table 7Modeling of solar energy collectors.


Application Parameters predicted

Kalogirou et al. [57] MLFFN SWH (Flat plate) Q�, DTw

Kalogirou [58] MLFFN SWH (Flat plate) Solar energy output,Quantity of hot waterper month

Kalogirou et al. [59] MLFFN SWH (Flat plate) TwKalogirou et al. [60] MLFFN SWH (Flat plate) Energy performance

and Maximum TwFacao et al. [61] MLFFN,

RBFNSWH (Flat plate) Q

�

Sozen et al. [62] MLFFN SWH (Flat plate) htheCetiner et al. [63] MLFFN SWH (Flat plate) Q

�mw�

Dikmen et al. [64] MLFFN,ANFIS

SWH(Evacuated tube)

hthe

Farkas andGecy-Vig [65]

MLFFN SWH (Flat plate) Tw at eight locations.

Caner et al. [66] MLFFN SAH htheEsen et al. [67] MLFFN SAH hthe and TaBenli et al. [68] MLFFN SAH hthe

effectiveness. The sensible and latent effectiveness were predictedwith reference to twelve parameters such as NTU, heat capacityratio, outdoor temperature and humidity ratio at the current timeand its difference with the outdoor temperature and humidity ratioduring last 4 h of the system operation. The MLFFN was optimizedto 12-16-16-1 structure. It has been reported that MAE betweentransient numerical model and MLFFN are 0.5 �C for sensibleeffectiveness and 0.2 gv/kga for the latent effectiveness.

4.1.4. Modeling of compact heat exchangersThe heat exchangers with large surface area per unit volume are

known as compact heat exchangers. Tan et al. [39] have applied theMLFFN model for predicting the overall Q

�of a compact fin-tube

heat exchanger using air and water/ethylene glycol anti-freezemixtures as the working fluids. The network was trained withinlet temperature of the liquid, inlet Ta, ml

�, ma

�, inlet obstructions,

and ethylene glycol anti-freeze mass concentrations were consid-ered as inputs to the MLFFN. The overall Q

�between the two test

fluids was considered as an output parameter. It was reported that6-6-1 network configuration predicts the overall Q

�of a heat

exchanger with a high degree of accuracy compared to conven-tional non-linear regression models. The MAE of the MLFFN pre-dictions reported in their work was 0.6%, 0.9% and 0.9%,

Table 9Modeling of earth to air heat exchangers.




Kumar et al. [79] MLFFN Earth to airheat exchangers

Heating andcooling performance

Zhang andHaghighat [80,81]

MLFFN Earth to airheat exchangers

Nu at three locations

Gang and Wang [82] MLFFN Geothermalheat exchangers

Exit temperature ofgeothermal heatexchanger

Table 10Modeling of power plant heat exchangers.




Krzywanski andNowak [83]

MLFFN Super heaters h

Hakeem et al. [84] MLFFN Thermosiphonreboiler

To of the boiler

Prieto et al. [85] MLFFN Condenser Q�


respectively, for the training, test and validation data sets. Similarly,Ermis [40] developed a MLFFN for predicting the Nu, h and Dp of acompact heat exchanger. In their work, the input layer consists ofseven neurons representing the ratio of rib spacing to height, Re, va,inlet Ta, outlet Ta, heat transfer area and dh. The network with 7-11-3 configuration was identified as an optimum topology. It was re-ported that MLFFN predicted Dp, h and Nu were closer to theexperimental results with R values of 0.9952, 0.9995 and 0.9993,respectively. The MREs of all predicted values are less than 6%.

4.1.5. Modeling of plate type heat exchangersA summary of ANN applications for modeling of plate type heat

exchangers are listed in Table 4. Selbas et al. [41] usedMLFFNmodelfor heat transfer analysis of plate heat exchangers. In their work, Q

�

and 3 values of the plate heat exchanger were predicted withreference to inlet hot and cold water temperatures and its m

�.

Experimentally observed data were used for training and testingthe network. Their results indicate that ANN predicted results arecloser to experimental results with good R values of 0.9994 and0.9976 for Q

�and 3, respectively. Peng and Ling [42] used hybrid AI

technique (GA and MLFFN) for optimal design of plate-fin heatexchanger and compared with the conventional approach. It wasreported that GA assist with back propagation algorithms providessignificant improvement in the optimization when compared toother traditional design procedures. The convergence iterationswere reduced from 33 to 15 and its processing time was alsoreduced by 40.6% (from 412.325 to 293.324 s) using the new hybridtechnique. Further, they have developed a MLFFN to predict the jand f factors of plate-fin heat exchangers [43]. In their work, j and ffactors were predicted with reference to fin height, fin pitch, finthickness, fin length and Re at the air side. TheMLFFNwith a 5-6-4-2 configuration predicts the j and f factor values with MSEs lessthan 1.5% and 1%, respectively.

4.1.6. Modeling of fin and tube heat exchangersFin and tube heat exchangers are widely used in refrigeration,

air conditioning and heat pump applications [44]. A summary ofANN applications for modeling of fin and tube heat exchangers arediscussed in this subsection and also listed in Table 5. Pacheco-

Vega et al. [45] predicted the Q�

in humid airewater heat ex-changers using conventional correlations and MLFFN. The inputsto the network are Re, inlet air DBT, inlet air WBT, inlet Tw and fin

spacing. The outputs are sensible heat, total heat and Q�. The

MLFFN with 5-5-3-3 configuration predicts the outputs within10% deviation, whereas the correlation predictions have morethan 10% deviation. In another work, a MLFFN was successfully

applied to predict the Q�

of a fin and tube refrigerant heat

exchanger [46]. In their study, Q�was predicted with reference to

eleven parameters, namely, ma�

, DBT, humidity ratio, inlet Tref, finspacing, width, number of rows, number of columns, number ofcircuits and tube spacing in longitudinal and transverse directions

and diameter. The network configuration was optimized by a 11-11-7-1 configuration. Three sets of test data were considered forcomparison, in small, medium and large error range. The resultreported for the first test was 0.761%, while the actual error was0.112%. The second test gave estimated and actual errors as 23.3%and 6.19%, respectively, while 48.78% and 14.21% were the valuesfor the third test. Similarly, outlet Tref and Tair of a fin and tube heatexchanger were predicted using ANN [47]. It was reported thatANN model predicts both outlet Tref and Tair with average errorvalues less than 0.2 �C.

Wu et al. [48] used MLFFN for the performance prediction of agas cooler (3-row staggered wavy-fin heat exchanger) in a carbondioxide (CO2) based trans-critical heat pump. They developed anetwork with five neurons in the input layer (representing thetemperature of CO2 at the gas cooler inlet, pressure of CO2 at the gascooler inlet,m

�of CO2 through the gas cooler, Ta passing through the

cooler and va) and four neurons in the output layer (representingthe temperature of the CO2 at the cooler outlet, pressure raise in thecooler, Ta at the cooler outlet and Q

�). Their results indicate that 5-5-

4-4 network configuration predicted the performance withmaximum deviations of 1.81%, 5.4%, 8.5% and 7.03% for temperatureof CO2 at the cooler outlet, pressure raise in the cooler, Tair at thecooler outlet and Q

�, respectively.

4.1.7. Modeling of shell and tube heat exchangersANN modeling was successfully used for performance predic-

tion of shell and tube heat exchangers [49]. Table 6 summarizes theapplication of ANN for modeling of shell and tube heat exchangers.Xie et al. [50] predicted the performance of a shell and tube heatexchanger (using oil and water as working fluids) using MLFFN andcompared with experimental results and correlation results. Intheir study, Q

�, DT in oil and water were predicted with reference to

the respective Re values, inlet temperatures of oil and water, totalnumber of tubes, diameter of center tube, total number of bafflesand its pitch. The network was optimized with a 8-6-5-3 configu-ration. It was reported that ANN predicted results are closer to theexperimental results within 2% deviation, whereas correlationspredictions can have about 8% deviation. Similarly, a MLFFN wasdeveloped for modeling a shell and tube heat exchangers [51,52]. AMLFFN with four neurons in the input layer (representing coldwater inlet and outlet temperatures and m

�of cold and hot water)

and two neurons in the output layer (representing cold and hotoutlet water temperatures) was developed. The network wasoptimized to a 4-15-15-15-2 configuration. Their network pre-dictions are reported to be 98e99.5% closer to the experimentalvalues.

Kashani et al. [53] developed a MLFFN model for onlinemonitoring and prediction of crude oil fouling behavior for in-dustrial shell and tube heat exchangers. In their study, threevariables such as tube side crude oil flow rate, tube side inlettemperature of oil and shell side inlet temperature of oil wereconsidered as the network input variables, while the only outputvariable is Rfo. The network was optimized to a 3-5-1 configura-tion. This network is capable of estimating the Rfo two days inadvance with the MRE of about 8%. Moreover, the predictionability of the network can be extended to about 10 days with theMRE of about 11%. In another work, a MLFFN was developed forcost estimation of shell and tube heat exchangers [54]. Thisnetwork configuration consists of an input layer with five neuronsrepresenting tube pitch, dt, ds, rear head factor and stationaryhead factor. The output layer consists of one neuron representingthe cost per exchange area. The LM learning algorithm and logsigmoid transfer functionwere used in their work. It was reportedthat network configuration with 5-10-10-1 has good predictioncapability with an R value of 0.97. In a similar work, Fadare and


Fatona [55] predicted the Nu of a staggered cross flow tube-typeheat exchanger using MLFFN with reference to Re and row num-ber. It has been reported that the MLFFN with a 2-5-5-1 config-uration predicts the Nu with MARE less than 1% and 4%,respectively for training and testing data sets.

4.1.8. Modeling of solar energy collectorsSolar energy collectors are special kind of heat exchangers,

which transfers the thermal energy obtained from solar radiation tothe transport fluid medium as the internal heat energy [56]. Asummary of investigations reported on solar collectors is consoli-dated in Table 7. Kalogirou et al. [57] predicted the performance of athermosiphon SWH using MLFFN. In their work, the performanceparameters such as, the amount of energy extracted and themaximum temperature raise were predicted with reference tostorage tank heat transfer coefficient, storage capacity (in terms ofliters), system type (open or closed), total radiation, diffuse radia-tion, Tab and initial temperature. It was reported that the networkhaving 7-24-2 configuration predicted the amount of energyextracted and maximum temperature raise with maximum de-viations of about 1 MJ and 2.2 �C, respectively. In a further workKalogirou [58] developed two MLFFN models for predicting thelong term energy performance of a solar water heating system. Thefirst network predicts the solar energy output and the secondnetwork predicts the solar energy output and the average quantityof hot water output per month. The first network consists of thir-teen neurons in the input layer (representing, month, daily solarradiation, mean ambient temperature during day time and nighttime, three coefficients of the system, normalized temperatureprofile as a function of volume during low and high radiationconditions, mixing draw off normalized temperature, heat losscoefficients, temperature of the cold water from mains, specificvolume of the system and maximum draw off temperature) forpredicting the solar energy output of the system. The secondnetwork consists of fourteen neurons representing similar to thefirst network, additionally, the water demand temperature wasconsidered. The first MLFFN with a 13-5-1 configuration predictsthe solar energy output with R2value of 0.9972. The second MLFFNwith a 14-7-2 configuration predicts the solar energy output andaverage quantity of hot water output per month with R2 values of0.9878 and 0.9973, respectively.

Further, Kalogirou et al. [59] have developed eight MLFFNmodels for predicting the temperatures at four typical locations in asolar water heating system for two different meteorological con-ditions corresponding to Cyprus and France. The authors predictedthe temperatures for fault diagnosis. The inputs to the network areglobal solar radiation, beam radiation, Tab, incidence angle, windspeed, ambient RH, flow availability and inlet temperature. AMLFFN with 8-19-1 architecture predicts the temperatures withgood R2 in the range of 0.92e0.999 and 0.8823e0.9996 for trainingand validation, respectively. Recently, the energy output of a largescale solar systems were predicted using a MLFFN [60]. The threeinputs to the network are day time average Ta, daily total radiationfalling on solar collector and storage Tw at the start of the day. Thetwo outputs are daily energy output and maximum Tw in the tank.It was reported that MLFFN predicts the daily energy performanceand maximum Tw with good R2 values of around 0.95.

Facao et al. [61] predicted the heat output of a hybrid SWH usingtwo ANN models (MLFFN and RBFN) with reference to nine pa-rameters such as solar radiation, Tab, Tgi, Twi, evaporator length,condenser length, m

�g , m

�w and U. It has been reported that, MLFFN

with 9-6-1 configuration predicts the collector heat output with avery good R value of 0.998. The prediction accuracy of MLFFN wasfound to be better, when compared with RBFN. Similarly, the hth ofa SWH was predicted using MLFFN with reference to seven input

parameters such as date, time, Tsur, solar radiation, declinationangle, azimuth angle and tilt angle [62]. The network was opti-mized by a 7-20-20-1 configuration. It was reported that, thisMLFFN predicted hth are closer to the experimental results with amaximum and minimum deviations of 2.558 and 0.0019, respec-tively. In another work, Cetiner et al. [63] predicted the perfor-mance of the solar hot water generator using a MLFFN. Theirnetwork consists of four neurons in input layer representing Tab,inlet Tw entering the absorber, wind velocity and direct radiationwith two neurons in the output layer representing flow rate andheat quantity. It was reported that a MLFFN having 4-7-2 configu-ration predicts m

�and Q

�with MRE ratio of about 1.2% and 9.1%,

respectively. In another work, Dikmen et al. [64] predicted the hth ofan evacuated tube solar collector using MLFFN and compared withANFIS. In their work, the network inputs are Tab, solar radiation,collector tilt-angle and mean storage tank temperature and theoutput of the network is hth of the system. It was reported that thenetwork with a 4-12-1 configuration predicts hth of the SWH withR2 values of 0.8119, whereas ANFIS predicts hth with R2 values of0.6817. Their results confirmed that MLFFN predictions are betterthan that of ANFIS predictions. Similarly, Farkas and Geczy-Vig [65]developed a MLFFN for predicting the thermal performance of asolar water heater. In their work, the temperature distribution inthe storage tankwas predicted at eight locations along the height ofthe storage tank. The input layer consists of twelve neurons rep-resenting solar radiation, Tab, m

�w, load and the temperature of

layers at eight time intervals. The output layer consists of eightneurons representing the temperatures at eight different locationsinside the storage. The network with 12-19-8 configuration usingtan-sigmoid transfer function predicts the temperature distributionwith average deviations of 0.22 �C during the training and 0.24 �Cduring the validation.

Caner et al. [66] predicted the hth of a SAH with a zig-zagabsorber surface using MLFFN. The network developed in theirwork consists of eight neurons in input layer representing Ti and Toof air passing through the collector, solar intensity, quantity ofstored water, Tab and Tsur of collector, model number and date withone neuron in the output layer represents hth of the collector. TheRMS errors of the ANN predicted hth are 1.67% and 1.78%, respec-tively, for model-I and model-II and solar collectors with corre-sponding statistical R2 values of 0.9984 and 0.9994. Similarly, Esenet al. [67] predicted the performance of a SAH using MLFFN andWNNs. In their work, six neurons in input layer represent the Taentering the collector, the temperatures at four different points atthe absorbing plate and solar radiation with two neurons in theoutput layer representing hth and Ta leaving the collector unit. Itwas reported that, a 6-4-2 network configuration predicts theperformance with RMS errors of 0.004 and 0.0099 for Ta and hth,respectively. They also concluded thatWNNs have better predictioncapability compared to MLFFN. Benli [68] predicted hth of a SAHusing MLFFN. The hth was predicted with reference to six param-eters, such as inlet and outlet Ta, solar radiation intensity,m

�a, Ta and

Tsur of collector. It was reported that the network with 6-3-1structure predicts hth of a SAH with R2 values of 0.9971.

4.1.9. Modeling of direct contact type heat exchangersIn direct contact type heat exchangers (otherwise known as

mixtures), both hot and cold fluids get mixed together and transferthe heat by direct contact [69]. Heat exchangers like cooling towers,evaporative coolers and jet condensers are categorized under thisclassification. Many investigators have applied ANN approach forpredicting the performance of direct contact type heat exchangers,as listed in Table 8.

Hosoz et al. [70] predicted the performance of a cooling towerusing MLFFN. In their network, five input neurons represent the


DBT and RH of the air stream entering the tower, Tw entering thetower, air volume flow rate and m

�w. The output neurons represent

the heat rejection rate in the cooling tower, m�of makeup water, Tw

at tower outlet, DBT and RH of air stream leaving the tower. Thenetwork was optimized to a classic 5-5-5 configuration. It was re-ported that network predictions were closer to the experimentaldata with R values of 0.992, 0.981, 0.994, 0.994 and 0.975, respec-tively, for heat rejection rate in the cooling tower, m

�of makeup

water, Tw at cooling tower outlet, DBT and RH of the air streamleaving the tower, corresponding RMS errors of 43.83 W, 0.09 kg/h,0.31 �C, 0.31 �C and 0.78%. The MREs were reported in the rangebetween 0.89% and 4.64%.

Gao et al. [71] predicted the thermal performance of a naturaldraft counter flow cooling tower under crosswind conditions usingMLFFN. The parameters such as circulating outlet Tw, DT and effi-ciency of the cooling towerwere predictedwith reference to DBTandWBT of inlet air, inlet Tw, m

�w, and va. The network with a 5-6-3

configuration predicts the performance of the cooling tower with Rvalues of 0.999, 0.998 and 0.995 for temperature at the outlet,DT andefficiency of the cooling tower, respectively with corresponding RMSerrors of 0.044, 0.066 and 0.53. Further, Gao et al. [72] have alsodeveloped a MLFFN with four neurons in input layer representingRH, circulating inlet water temperature, water spraying density andFr for predicting air gravity, cooling temperature difference, coolingefficiency, h, mass transfer coefficient and evaporation loss propor-tion. The MLFFN was optimized for a 4-8-6 configuration. The MREsof the MLFFN predicted outputs are in the range of 0.48e3.92% withR values varying between 0.992 and 0.999.

The COP of a cooling tower was predicted with reference to fourparameters such as m

�w=m

�a ratio, the inlet Tw, the outlet Tw and the

inlet WBT of air using MLFFN [73]. The output layer has one neuronrepresenting the COP. The network was optimized with a 4-15-1configuration. It was reported that MRE of MLFFN predicted COPwas less than 0.2% compared to the experimental values. It was alsoconcluded that, MLFFN method of COP predictions provides fast,accurate and consistent results when compared to conventionalmethods. In another work by Qi et al. [74], the performance of thecooling tower was predicted using MLFFN. In their work, a MLFFNwas developed with eight inputs, namely nozzle height, equivalentdiameter of water droplets, initial velocity of water droplets, va,ratio of air to water, DBT of inlet air, RH of inlet air and inlet Tw. Theonly output variable was outlet Tw. The results predicted by theMLFFN model were compared with the experimental data. It wasreported that, the ANN model with 8-17-1 configuration predictsthe Tw values with a MAE of 1.31%, when compared to the experi-mental results. In similar work, the performance characteristics of acooling tower (using aqueous solution) were predicted usingMLFFN [75]. In their work, a MLFFNwith five neurons in input layer(representing inlet DBT and WBT of air, inlet temperature of anaqueous solution, m

�of an aqueous solution and m

�a) and nine

neurons in output layer (representing heat absorption capacity,heating coefficient of efficiency, ratio of sensible heat transfer to thelatent heat transfer, outlet air DBT, outlet aqueous solution tem-perature, ratio of sensible to total heat transfer and humidity ratioof moist air difference between inlet and outlet) was developed.The MLFFN using 5-11-9 configuration predicts the performancecharacteristics closer to experimental results with R values in therange of 0.9249e0.9988 and MREs between 0.0008% and 0.54%.

The performance of an evaporative cooler was predicted usingMLFFN by Hosoz et al. [76]. The performance parameters (such asDBTand RH of the leaving air, mass of thewater evaporated into theair stream, sensible cooling rate, and effectiveness) of an evapora-tive cooler were predicted with reference to four parameters suchas DBT, RH of the air stream entering the cooler, water m

�w and air

volume flow rate. A MLFFN with 4-4-5 configuration predicts the

performance of an evaporative cooler with R values in the range of0.969e0.993, MREs in the range from 0.66% to 4.04%. Kiran andRajput [77] compared the performance prediction capability of anindirect evaporative cooling system using three AI techniques suchas MLFFN, ANFIS and fuzzy interface systems (FIS). The inputs tonetwork are primary and secondary m

�a, ambient DBT and WBT,

while the outputs are outlet Ta and effectiveness. It was reportedthat MLFFN predicts the performance of an indirect evaporativecooling system with better accuracy when compared to other AItechniques such as ANFIS and FIS.

4.1.10. Modeling of earth to air heat exchangersEarth to air heat exchangers are widely used for space heating

and cooling applications in buildings as elaborated by Bisoniya et al.[78]. Table 9 gives the consolidated details of the studies reportedwith earth to air heat exchangers. A summary of reported in-vestigations are discussed in this subsection. Kumar et al. [79]predicted the heating and cooling performance of earth to airheat exchangers using ANN. Two ANN models, namely determin-istic and intelligent have been developed in their work. Six vari-ables (length, humidity, Tab, ground surface temperature, groundtemperature at burial depth and air m

�a) affecting the thermal

performance of the earth-to-air heat exchangers were consideredin their work for predicting the outlet air temperature of a heatexchanger. It was reported that the intelligent model predicts theoutlet air temperature with an accuracy of ±2.6%, whereas, thedeterministic model predicts with an accuracy of ±5.3%. In a similarwork, Zhang and Haghighat [80,81] predicted the Nu in largerectangular cross-sectional area earth-to-air heat exchangers usingMLFFN. In their work, the input layer consists of six neuronsnamely, length, height, width, inlet size, DT between the surfaceand inlet air and bulk air speed, whereas the output layer consists ofthree neurons namely average Nu over the duct ceiling, wall andfloor. The network was trained with thirty CFD simulation cases.The network with 6-15-3 configuration was identified as an opti-mum topology for predicting the Nu. It was reported that MLFFNpredicted results are more accurate when compared to that ob-tained using CFD simulations. Similarly, the static and dynamicmodels based onMLFFNwere developed by Gang andWang [82] topredict the temperature of the water at the outlet of the groundheat exchanger. In their work, two MLFFN models were developedfor predicting the temperature under static and dynamic modes. Itwas reported that the dynamic model performs better than thestatic model. The dynamic ANN model was capable of predictingthe exit temperature of the ground source heat exchanger with anabsolute error less than 0.2 �C.

4.1.11. Modeling of heat exchangers used in power plantsThe studies reported with power plant heat exchangers are

summarized and presented in Table 10. Krzywanski and Nowak[83] successfully predicted the h of two super heaters used in acirculating fluidized bed boiler using ANN. The ranges of inputs tothe network for predicting the h include the load of the boiler(40e100%), distance from the gas distributor (6.2e41.7 m), velocityof the fluid (2.1e6.0 m/s), average bed voidage (0.97e0.99) and bedtemperature (930e1298 K). It was reported that the h predictedusing the MLFFN with 5-1-5-1 configuration for the first superheater yields R2 values of 0.9968 with MAE of 0.48. The networkwith 5-2-5-1 configuration was reported as an optimum topologyfor predicting the h of the second super heater. The R2 and MAEvalues are 0.9981 and 0.75, respectively, for predicting the h values.In similar application, Hakeem et al. [84] predicted the temperatureprofiles as well as temperatures at various operating conditions in avertical thermosiphon reboiler. The network consists of three inputparameters, namely heat flux, distance and submergence with one

Table 12Estimation of heat transfer coefficients.

Authors[references]


Tube configuration Parameterspredicted


output parameter representing the outlet temperature. Theexperimental data obtained from the literature were used fortraining the MLFFN with the error back propagation algorithm. TheMLFFN with 3-10-10-1 configuration predicts the outlet tempera-ture with MARE less than 4.3% when compared with the experi-mental results.

Two similar MLFFN models were developed for forecasting theperformance of a condenser used in a thermal power plant [85]. Intheir work, the performance parameters such asQ

�, h and cleanli-

ness factor were predicted. The Q�was predicted with reference to

nine parameters such as temperature of water at the inlet andoutlet, level of sea water load chamber, differential pressure loss inthe circulating water, temperature of drainage, hot well tempera-ture, m

�of the condensate, condenser pressure and Tsat of the tur-

bine exhaust. In the case of h and cleanliness factor, the Tsat of waterwas included. The average test errors of ANN predicted Q

�, h and

cleanliness factor are within a deviation of 1%, 17% and 8%,respectively.

4.1.12. Modeling of special purpose heat exchangersApplications of ANN used in the special purpose heat ex-

changers are listed in Table 11. Vortex heat exchangers are the de-vices where a gas is fed with positive pressure undergoes mass andtemperature division, forming two separate flows [86]. While oneflow becomes cooled and dried, the other gets heated and moist. Ina related work, a MLFFN model was developed for predicting theperformance of counter flow vortex tube [87]. The network withfour neurons in the input layer (representing the inlet pressure,mass flow rate, cold mass fraction and nozzle number) and oneneuron in the output layer (representing the DT between hot andcold outlets) was developed for predicting the cooling and heatingperformance of the vortex tube. It was reported that network with4-7-1 configuration yields good statistical performance such as R2,RMSE and RAE values of 0.9989, 0.5016 and 0.0540, respectively. Ina similar work, the effect of nozzle number, inlet pressure and coldmass fraction of heating and cooling performance (temperaturegradient between the cold and hot outlets) of a counter flow typevortex tube was predicted using MLFFN [88]. The back-propagationlearning algorithmwith LM variant and Fermi transfer functionwasused in this study. It was reported that network predictions of thetemperature gradient between hot and cold junctions are closer toexperimental values with R2 of 0.9947, RMS error of 0.1882% andthe MAE percentage of 0.0460. The performance of a counter flowRanqueeHilsch vortex tubes was predicted using MLFFN withlimited experimental data [89]. In their work, the DTwas predictedwith reference to four parameters such as, inlet pressure, ratio oflength of vortex tube to internal diameter of vortex tube, number ofnozzles and fraction for cold flow. It has been reported that MLFFNwith a 4-50-1 configuration predicts the DT between the outputstreams are closer to that of the experimental results.

The Nu and Dp of micro-channel heat exchangers are predictedusing GMDH neural networks by Amanifard et al. [90]. The Nu waspredicted with reference to geometrical parameters such as Ht/Dh,

Table 11Modeling of special purpose heat exchangers.



Parameterspredicted

Kocabas et al. [87] MLFFN Vortex tube DTUluer et al. [88] MLFFN Vortex tube DTDincer et al. [89] MLFFN Vortex tube DTAmanifard et al. [90] GMDH Micro-channel Nu and DpWijayasekara et al. [91] Hybrid Printed circuit

heat exchangerQ�and Dp

Hc/Dh,, flow parameter (Re) and heat transfer parameter (q). The Dpwas predicted with reference to Ht/Dh, Hc/Dh and Re. Their resultsindicate that, network predictions of Nu and Dp are closer to thecorresponding experimental results with acceptable accuracy.Similarly, Wijayasekara et al. [91] predicted the heat transfer rate,pressure drops in on the cold and hot side of the printed circuit heatexchangers. In their work, the over-training problem of ANNmodelwas alleviated by introducing an error back propagation and LMalgorithms for over training resilience (EBaLM-OTR) technique. Theinput layer consists of five neurons namely, cold side inlet pressure,cold side inlet temperature, hot side inlet pressure, hot side inlettemperature andmass flow rate. The network predicts the pressuredrops in hot and cold side and Q

�with acceptable error limits be-

tween 10�5 and 10�3.

4.2. Estimation of heat exchangers parameters

Heat transfer coefficient (h), fouling factor (Rfo) and frictionfactor (f) are the three important parameters pertaining to any heatexchanger in operations. Many investigators using ANN have aimedat the estimation of these heat exchangers parameters in betteraccuracies. A review of the studies in this area is elaborated here.

4.2.1. Estimation of heat transfer coefficientThe applications of ANN for predicting the heat transfer co-

efficients are summarized in Table 12. Jambunathan et al. [92]evaluated the convective h using a MLFFN with reference to non-dimensional temperature distribution, a and time. It was reportedthat MLFFN with a 3-6-3-1 configuration predicts the convective hwith about ±2.7% deviations. In the worst-case, average error of±6.5% was obtained from a 3-4-3-l configuration, which confirmsthat network converged faster with increasing number of nodes inthe first hidden layer. In another work by Ghajar et al. [93], animproved correlation was developed for predicting the h of a hor-izontal heat exchanger tube (with three inlet configurations such asreentrant, square-edged and bell-mouth inlets under uniform wallheat flux boundary condition) using MLFFN. In their work, the hvalues were predictedwith reference to Re, Pr, Gr, X/d and mbl/mwa. Atotal of 1290 data points (441 for reentrant, 416 for square-edged,and 433 for bell-mouth) were used as training data for thenetwork. It was reported that 5-11-1 MLFFN configuration predictsthe h values within 5% deviation.

Islamoglu and Kurt [94] estimated the Nu using a MLFFNmodel.The heat transfer analysis was made in a heat exchanger havingcorrugated channels. Four inputs of the network representing,corrugation angle, axial length of cycle, dh and Re. The output of thenetwork was Nu. The network with 4-5-1 configuration predicts

Jambunathanet al. [92]

MLFFN Flow over tubes (air) hcon

Ghajar et al. [93] MLFFN Horizontal tube withthree inlet configurations

h

Islamogluand Kurt [94]

MLFFN Corrugated channels Nu

Colorado et al. [95] MLFFN Helical coil NuMehrabi et al. [96] ANFIS Double pipe

heat exchangersh, inside andoutside Dps

Kamble et al. [97] MLFFN, Horizontal tube h and NuThaseen et al. [98] ANFIS Flat bundle tubes Nu and DpsKarami et al. [99] ANFIS Air cooled condenser with

twisted tube insertsNu

Akdag et al. [102] MLFFN Oscillating induced tubes Nu


the Nu with maximum and minimum relative errors of 10% and0.25% and MREs less than 3.36%. Similarly, a MLFFN based physical-

empirical model was developed for predicting the Q�in a helical coil

using oil and glycerol/water solution as working fluids [95]. AMLFFN model with four neurons in input layer representing Pr, Ra,helical diameter and number of coils turns was developed forpredicting Nu of oil and glycerol/water solution. The network with4-4-1 configuration predicts the Nu with R value of 0.98 whencompared to the experimental results.

Mehrabi et al. [96] used ANFIS for predicting U and Dp charac-teristics of helicoidal double-pipe heat exchangers with referenceto five input variables such as inner and annular dean number,inner and annular Pr and pitch of the coil. Their results showed thatANFIS predicts the U, inner Dp and annular Dp with R values of0.994, 0.995 and 0.951, respectively, and the corresponding RMSerrors of 13.61%, 5.08% and 13.81%. Similarly, Kamble et al. [97]predicted the h and Nu using MLFFN with reference to particlesize, DT between bed and immersed surface and fluidizing velocity.Their results reported that MLFFN with a 3-5-2 configuration pre-dicts both h and Nu with R values of 0.9999. ANFIS was also used topredict the Nu and Dp characteristics in a flat bundle tubes withreference to Re, longitudinal pitch-to-small diameter ratio, and thetransverse pitch-to-small diameter ratio [98]. The accuracy be-tween numerical values and ANFIS model results were obtainedwith a MRE for average Nu and Dp less than 1.9% and 2.97%,respectively. Karami et al. [99] predicted the Nu with reference toRe and the twist ratio in an air cooled condenser heat exchangerequipped with twisted tape inserts using ANFIS. It was reportedthat, the maximum errors of training and testing data were foundto be 0.111% and 2.378%, respectively. The MRE of the training andtest data are correspondingly 0.011% and 1.316%.

The oscillation induced heat transfer enhancements have beenwidely used in compact heat exchangers [100] and wire on tubeheat exchangers [101]. In a related work, the Nu was predicted foran oscillating annular flow with reference to four parameters,namely, kinetic Re, dimensionless amplitude, filling heights, andheat flux [102]. The network structure was optimized for 4-5-1configuration. The network predictions of Nu by ANN are closer tothe experimental values within a deviation of about 5%.

Table 14Estimation of friction factor.

Authors [references] Network Heat exchanger Parameters

4.2.2. Estimation of fouling factorMaterial deposits on the surfaces of heat exchanger tubes will

influence its thermal performance [103]. The factor considered formaterial deposits are called as the fouling factor (Rfo). ANN has beensuccessfully used for predicting the Rfo in heat exchangers[104,105]. Table 13 consolidates the applications of ANN for pre-dicting the Rfo. The thermal efficiency of a heat exchanger obtainedusing the conventional analytical approach is higher than that ofthe experimental values due to the effect of fouling [106]. The ANNbased estimation of Rfo provides a flexible approach by simulatingthe actual experimental operating conditions. Aminian and Shah-hosseini [107] used MLFFNmodel for predicting the Rfo of crude oil.

Table 13Estimation of fouling factor.



Parametersinvestigations

Aminian andShahhosseini [107]

MLFFN Pre heat exchangers Rfo

Aminian andShahhosseini [108]

MLFFN Pre heat exchangers Rfo

Lalot and Palsson [109] MLFFN Cross flow RfoGarcia [110] MLFFN Coil type Control of RfoRomeo and Gareta [111] Hybrid Boiler heat exchanger Control of Rfo

Training data sets were extracted from the experimental resultsreported in literature. The network consists of three input neuronsrepresenting dt, crude velocity and tube surface temperature. It wasreported that the network configuration with a 3-5-6-1 structurepredicts the Rfo having a MRE of 26.23% when compared to theexperimental results. In a further work on this topic, Rfo in crude oilpre-heaters were predicted using MLFFN with reference to Re, Pr,and Tsur [108]. It was reported that, MLFFNwith 3-8-1 configurationpredicts the Rfo with less absolute MRE of 14.05%, 22.47% and15.83% for training, testing and overall database, respectively.

Lalot and Palsson [109] predicted the Rfo of a cross-flow heatexchanger using ANN. A numerical model was used to generate thetraining data for the network under clean and fouling conditions.The five inputs to the network are Ti and To of the cold fluids, Ti ofhot fluid, m

�of cold and hot fluids. The output layer has only one

neuron representing the Rfo. It was concluded that, ANN modelingis quite sensitive for predicting the Rfo with less computationaltime, when compared to the conventional method of estimation. Toovercome the drawback of heat exchanger fouling, a novel super-vision strategy using ANN was proposed by Garcia [110]. The pro-posed supervision strategy can detect, isolate and accommodatethe faults in a closed loop temperature control of a heat exchangeron the basis of static and dynamic ANN techniques. The developedstrategy was divided into three modules. The first module checksthe consistency of the supervision system. The second modulemonitors the heat exchanger for fouling condition with the abilityto diagnose the probable causes of fouling. A third module predictsthe remaining operating time under acceptable conditions, asso-ciated to a decision making task to schedule the supervision flowchart. The developed supervision strategy is a novel application ofANN for detecting, isolating and predicting heat exchanger foulingwith good accuracy. In another work, Romeo and Gareta [111] usedANN and fuzzy logic hybrid approach for controlling the Rfo inbiomass boiler heat exchangers. It was reported that, the powerproduction can be improved by about 3.5% using a hybrid ANNapproach to control the fouling rate in boilers.

4.2.3. Estimation of friction factorsThe summary of ANN studies reported for the estimation of

friction factor (f) is listed in Table 14. Beigzadeh and Rahimi [112]predicted the Nu and f in helical coiled tubes. The experimentswere carried out with hot fluid flowing through coiled tubes whichis immersed in a cold bath. Two ANN models were developed forpredicting Nu and f. The MLFFN model for estimating Nu had fourinput parameters, namely Re, Pr, curvature ratio, and coil pitch. Inanother MLFFN model for predicting f has three input parameterssuch as Re, curvature ratio and coil pitch. The predicted Nu and ffrom MLFFN models were compared with the experimental results

architectures configuration investigations

Beigzadeh andRahimi [112]

MLFFN Helical tubes Nu and f

Beigzadeh andRahimi [113]

ANFIS Helical tubes Nu and f

Zdaniuk et al. [114] MLFFN Straight tubewith internal fins

j factor andf factor

Xie et al. [115] MLFFN Vortex generators Nu and fNasr et al. [116] MLFFN Wire coil inserts Nu and fNasr and Khalaj [117] MLFFN Corrugated tubes

with twistedtape inserts

Khalaj et al. [118] MLFFN ANFIS Wire coil inserts Nu and f

Table 15Prediction of boiling heat transfer coefficients.


Parameterspredicted

Balcilar et al. [121] MLFFN, GRNN,RBFN

hb and qb

Wang et al. [122] MLFFN hb of pure andmixed fluids

Scalabrin et al. [123] MLFFN hbScalabrin et al. [124] MLFFN hbScalabrin et al. [125] MLFFN hbLiu et al. [126] MLFFN hbAlizadehdakhel et al. [127] MLFFN DpPorto et al. [128] Hybrid hbWei et al. [129] Hybrid qbWen et al. [130] RBFN hb


as well as the theoretical predictions reported in literature. TheMLFFN model with 9 hidden neurons was selected for predicting ofNu with R2 of 0.9993, MSE of 2.46, andMRE of 12.95%. Similarly, theMLFFNmodelwith 12hiddenneurons predicts f in the tubeswithR2,MRE and MSE of 0.9997, 1.26% and 4.36 � 10�7, respectively. Infurther work, two ANFIS models were developed for predicting Nuand f in coiled tubes [113]. Thefirst network had four inputs, namely,Re, Pr, curvature ration and coil pitch for predicting the Nu values.Whereas, second network had three inputs representing Re, cur-vature ratio, and coil pitch for predicting the f values. TheMRE of thetwo ANFIS models for predicting Nu and f are 6.24% and 3.54%,respectively.

Zdaniuk et al. [114] used the feed forward network approach forpredicting the j and f for water flow in straight tubes with internalhelical fins. The four inputs considered in their work are helix an-gles (between 25� and 48�), number of fins (between 10 and 45), finheight-to-diameter ratios (between 0.0199 and 0.0327), and Re(between 12,000 and 60,000). The networks were trained withexperimental results obtained from literature. It was reported thatnetwork with log-sigmoid functions in the first layer and a linearnode function in the output layer are the most advantageous ar-chitecture for prediction of j and f within acceptable error limits.Similarly, Xie et al. [115] used a MLFFN to correlate Nu and f forthree types of heat exchangers using plain, slit and fins with lon-gitudinal delta-winglet vortex generators. The MLFFN configura-tion used in their work consists of twelve inputs representing thegeometrical parameters (Re, N, dt, fin pitch, tube pitches longitu-dinal and transverse tube pitches, height, width and length of theslit, length and height of the vortex generator and angle of attack)with two output neurons representing Nu and f. The network isoptimized to a 12-9-5-2 configuration. The maximum MRE andRMS errors between ANN predicted and experimental data arewithin 5% and 1.44% deviations, respectively.

Nasr et al. [116] enhanced the performance of heat exchangersusing wire coil inserts. In their work, Nu and f were obtained usingtwo MLFFN models. The MLFFN with four input parameters in theinput layer representing Re, Pr, e/dh and p/dh were used for pre-dicting Nu. The structure of ANN for predicting f consists of threeinput parameters in the input layer (Re; p/dh; e/dh) and f is the onlyoutput term in the output layer. The MLFFN with a 4-4-1 configu-rationpredicts the heat transfer coefficientwith an excellent R valueof 1 and MRE of 1.78%. The network with a 3-4-2-1 architecturepredicts the f with MRE of 3.26 and R2 of 0.9936. In a further work,the h and f in corrugated tubes combined with twisted tape insertswere predicted using two MLFFN models [117]. Two MLFFNs weredeveloped with five neurons in the input layer (representing Re,height of the corrugation/tube diameter, pitch of the corrugation/heightof corrugation,b andpitchof the twisted tape/diameter of the tube) andone neuron in the output layer (representing h and f). The MLFFNwas optimized to 5-13-5-1 and 5-9-8-1 configurations for predict-ing h and f, respectively. The MLFFN predictions are closer to theexperimental results with good MRE and R2 values (2.80% and0.9966) and (0.36% and 1) for h and f, respectively. In a similar work,the Nu and fwere predicted usingMLFFN and ANFIS of wire coil andtwisted tape inserts [118]. It was reported that the MRE betweenpredicted results and experimental data were found to be less than3% for MLFFN and 1.5% for ANFIS.

4.3. Phase change characteristics in heat exchangers

The accurate predictions of boiling and condensation heattransfer coefficient values are highly essential for optimal design ofheat exchangers such as evaporators and condensers [119,120]. Theconventional method of predicting the phase change characteris-tics involves complicated analytical equations and assumptions. To

overcome this difficulty, ANN models were introduced by manyresearchers for predicting the hb and hcond. A survey of ANN used inpredicting the phase change characteristics are consolidated andpresented in Tables 15e19.

4.3.1. Boiling characteristicsThe ANN applications for predicting the boiling heat transfer

characteristics (hb) are reviewed and summarized in Table 15.Balcilar et al. [121] investigated the pool boiling characteristics ofTiO2 nano-fluids using MLFFN, GRNN and RBFN models. Thenetwork consists of seven dimensional input parameters, namely k,r, m, cp, particle size, surface roughness of heating surface and wallsuperheat and concentration of the nano-particle. The output layerconsists of hb and qb. The R2 of the predicted heat flux for MLFFN,GRNN and RBFN models are 0.916, 0.8846 and 0.8989, respectively.The corresponding values for hb are 0.8638, 0.8795 and 0.8472. Theresults confirmed that, MLFFN has more prediction accuracy whencompared to RBFN and GRNN models. Similarly, a generalizedcorrelation for predicting the hb of two pure fluids (R22 and R134a)and two mixed refrigerants (R407C and R410A) was developed[122]. Four dimensionless parameters from existing generalizedcorrelations are selected as inputs, while Nu is the output to thenetwork. A MLFFN with 4-8-1 configuration and log-sigmoidtransfer function in hidden and output layer predicts the Nu withan average, mean and RMS deviations of 2.5%, 13.0% and 20.3%,respectively. About 74% of the deviations are within 20%, which ismuch better than that of the existing generalized correlations.

Scalabrin et al. [123] proposed a new correlation for predictinghb of pure fluids using MLFFN. Boiling heat transfer coefficients ofeight pure fluids and a ternary refrigerant mixture were predictedin their work. The hb of the refrigerants is predicted using MLFFNwith reference to five parameters such as Tr,m

�, qb, vapor quality (x)

and tube di. For eight pure fluids (R11, R12, R22, R32, R134a, R290,R600a and argon) and a mixture (R407C), altogether 5236 datapoints have been considered for training and validation. Out of5236 data points, 4803 data points were used for training with anoverall absolute average deviation of 7.72% and a bias of �1.62%,while the remaining data points were used for the purpose ofvalidation. By excluding the two pure fluids (R12 and argon), theremaining 3791 data points with six pure fluids and the mixture(R407C) were used for training with MAE of 4.45% and a biasof �0.44%. The accuracy of the results predicted from the ANNmodel was reported with acceptable error limits.

In further work, Scalabrin et al. [124] developed two MLFFNmodels for predicting the hb of mixed refrigerants. In the firstmodel, the controlling of physical quantities is considered as inputsfor predicting the hb values of pure fluids. While in the second ANNmodel, the values of hb of two individual pure fluid and mixturecomposition were considered as inputs for predicting hb of the

Table 16Prediction of critical heat flux.

Authors [references] Network architectures Working fluid

Mazzola et al. [132] MLFFN WaterVaziri et al. [133] MLFFN, RBFN WaterNafey [134] MLFFN Steamewater mixtureCong et al. [135] MLFFN Water, R113, R12Zaferanlouei et al. [136] ANFIS WaterChen et al. [137] Hybrid WaterWei et al. [138,139] GNN Distilled waterMoon et al. [140,141] MLFFN WaterGuanghui et al. [142] MLFFN Water

Table 18Flow regime identifications.


Regions identified

Mi et al. [150,151] MLFFN Bubbly, slug, churnand annular

Tambouratzis andPazsit [152,153]

MLFFN Bubbly, slug, churnand annular

Timung, and Mandal [154] PNN Bubbly, slug, churnand annular

Roshani et al. [155] MLFFN Bubbly, slug, churnand annular

Table 19Prediction of condensation heat transfer coefficients.


mixed refrigerants. The hb values predicted by ANN were reportedwith satisfactory accuracies for the R290/R600a and R32/R134amixtures. The authors also used ANN for modeling of flow boilingcharacteristics of pure fluids [125]. In their work, the input layerconsists of five neurons representing Tr,m

�ref , q, x and dt. One neuron

is used in the output layer representing hb. They also proposed anew modeling technique for the fluid dynamics conditions alongthe tube. The actual flow conditions observed in the experimentswere directly linked with a conventional real number called SFfactor (form of flow), ranging in a standardized interval. It was re-ported that the ANN has been successfully used for predicting theflow boiling characteristics and also the flow pattern in two phaseboiling conditions. Liu et al. [126] also have evaluated qb using ANN.In their experimental work, the qb was enhanced using additives.The effects of thirty additives tested by other researchers wereanalyzed in their model. The input layer consists of four neuronsrepresenting the number of carbon atoms inside the straight car-bon chain in the non polar group, ratio between the atomic weightof the non-polar and polar groups, type of additive used and thekind of polar group with one neuron in the output layer repre-senting qb. The network with a 4-6-3-1 configuration predicts theqb with 90% accuracy when compared to the experimental results.

Alizadehdakhel et al. [127] predicted the Dp using CFD andMLFFN during two phase flow inside the tube. In their work, the Dpwas calculated using MLFFN with reference to the gas velocitynumber, liquid velocity number and tube slope. The network with a3-20-1 configuration predicts the Dpwith good R2 values of 0.9985.Their results also indicate that, CFD predictions are better thanMLFFN predictions. Porto et al. [128] predicted the two phase heattransfer coefficients using a hybrid AI approach (GA and MLFFN) inevaporators. In their work, the network was trained with 690 datapoints covering a wide range of saturated two phase flow regimesfor R-22, R-134a and R-404A refrigerants. In their work, GA wasused to optimize the network parameters. It was concluded that GAintegrated MLFFN predicts the two phase heat transfer coefficientwith acceptable accuracy when compared to the experimental re-sults. Wei et al. [129] predicted the boiling heat flux (qb) using GAbased MLFFN. In their work, the qb was predicted with reference toheated length, system pressure, wall superheat and G. Their resultsreported that GA based MLFFN, which predicts the qb within 15%deviation. Similarly, Wen et al. [130] predicted the hb of R407Cmixture inside horizontal tubes using RBFN with reference to fiveinputs such as G, q, x, Tsat and d. It was reported that, this networkpredicts hb within 10% deviation.

Table 17Prediction of void fraction.

Authors [references] Network architectures Heat exchanger configuration

Castillo et al. [143] MLFFN Geothermal heat exchangersZhang et al. [144] MLFFN Mini channelMalayeri et al. [145] RBFN Experimental test rig

4.3.2. Critical heat fluxCHF is an important parameter considered in the design of heat

exchangers in which evaporation or boiling phase change occurs[131]. Many investigators used the ANN approach for predicting theCHF. Table 16 gives consolidated details of the applications of ANNfor predicting CHF.

Mazzola [132] integrated ANN modeling with mathematicalcorrelation for predicting water cooled q of a heat exchanger. Thedatum-dependent parameter (z) was predicted with reference to G,dt, Lt, vl, vg and the x using MLFFN. Based on the predicted constantvalue z, the CHFwas predicted using the correlations. The predictedCHF was found to be closer to the experimental results with a MAEof 8.9% and RMSE of 12.1%. Vaziri et al. [133] predicted the CHFusing RBFN and compared the result with MLFFN. The CHF waspredicted at fixed inlet conditions, local conditions and fixed outletconditions. It has been reported that RBFN structure has superiorperformance in prediction of CHF when compared to the MLFFN.RBFN predicts CHF with RMS errors of 0.24%, 7.9%, 0.16% andMLFFNpredicts CHF with RMS errors of 1.29%, 8.31% and 2.71%, in fixedinlet conditions, local conditions and fixed outlet conditions,respectively.

Nafey [134] used MLFFN for predicting the CHF of steamewatermixture flowing through the heat exchanger pipes. The neurons ininput layer represent Lt, inside diameter, wall thickness, p, T, massvelocity and quality of steam. The MLFFN configuration was opti-mized to 7-9-1 for predicting CHF. The learning rate and mo-mentum coefficients were optimized as 0.75 and 0.85, respectively.Experimental results of CHF are comparedwith the results obtainedby the developed MLFFN based correlation. The comparison is alsomade with the results obtained by a best-fit correlation. The de-viations betweenMLFFN results and experimental results are foundto be less than 5.5% with correlation coefficients of 0.998. Inanother work, Cong et al. [135] predicted CHF of water, R113 andR12 using ANN. The network consists of four input neurons rep-resenting rl=rv, the ratio of the characteristic dimension of theheated surface to the diameter of the impinging jet, reciprocal ofthe We, and the number of impinging jets. The MLFFN was opti-mized to 4-9-1 configuration. The network predicts CHF with RMSerror of 17.39% and MRE of 11.89%.



Demir et al. [156] MLFFN hcBalcilar et al. [157] MLFFN, RBFN,

GRNN, ANFIShc and Dp

Balcilar et al. [158] MLFFN Dps during evaporationand condensation

Ermis et al. [159] MLFFN Heat storage capacity


Zaferanlouei et al. [136] predicted the CHF using ANFIS. In theirwork, the CHF was predicted at fixed inlet, local and fixed outletconditions. It was reported that ANFIS model predicts the CHF withRMS test errors of 4.79%, 5.04% and 11.39%, for the fixed inletconditions, local conditions and fixed outlet conditions, respec-tively. The predicted results indicate that ANFIS has superior per-formance in predicting CHF when compared to MLFFN. In similarattempt, Chen et al. [137] predicted a non dimensional number(Kutateladze number) of a concentric tube open thermosiphonusing a hybrid approach (MLFFN and GA). The network work wastrained with experimental data extracted from the literature. Theinput layer consists of four dimensionless parameters, namelydensity ratio, the ratio of heated tube length to the inner diameterof the outer tube, frictional area ratio and the ratio of equivalentheated diameter to characteristic bubble size. The output layerconsists of one neuron representing the Kutateladze number. It wasreported that MLFFN-GA hybrid approach predicts the CHF withMRE of 8.46%. The CHF was estimated based on Kutateladze num-ber predicted by ANN.

Wei et al. [138,139] predicted the CHF using GNN. In their work,the CHF was predicted with reference to pressure, G and criticalquality. The developed model in their work can predict the CHF(range of pressure between 1.08 and 3.11 MPa), G (between 56.5and 141.6 kg/m2 s) and critical quality (between 0.694 and 0.987).The RMS errors of the training, validation and testing data are alllower than 0.05148, 0.07263 and 0.06594, respectively. The RMSerror of the GNN predicted results were lower than 0.15. Moon andChang [140] predicted CHF using MLFFN and compared with thefuzzy theory. The CHF was predicted with reference to p, G and x. Itwas reported that MLFFN predicts the CHF with better accuracywhen compared to other conventional correlations and fuzzy the-ory. Their results reported that the RMS error of MLFFN predictedCHF was within a limit of 20%. As an extension of their work, theCHF was predicted for three conditions such as fixed inlet, fixedoutlet and local conditions [141]. It was reported that, MLFFNpredicts the CHF with RMS errors of 8.9%, 13.1% and 19.3% for fixedinlet, fixed exit and local conditions, respectively. In another work,Guanghui et al. [142] predicted the CHF under low pressure andoscillation conditions for both natural and forced circulation con-ditions using MLFFN. The input parameters of the network are p,mean m

�, relative amplitude, inlet sub-cooling, oscillation period

and the ratio of heated length to the diameter of the tube andoverall length/diameter ratio. The output layer has one neuronrepresenting CHF. It was concluded that, MLFFN with a 6-10-1configuration predicts the CHF accurately. They also reported that,the minimum number of neurons in the hidden layer is a product ofthe number of neurons in the input and output layer.

4.3.3. Estimation of void fractionVoid fraction is an important parameter used to characterize the

two-phase flow in heat exchangers. Table 17 gives a consolidatedaccount of the applications of ANN for the estimation of voidfraction in multiphase flow. Castillo et al. [143] developed a newcorrelation using MLFFN for modeling two phase flows in thegeothermal exchangers. The network consists of eight neurons ininput layer namely wall head pressure, steam quality, wellborediameter, viscosity,rf , Re, We, and Fr with one neuron in the outputlayer representing the void fraction. The MLFFN with 8-6-1configuration predicts the void fraction with good R of 0.9722 withlower values of RMS errors. Accurate prediction of frictional pres-sure drop and void fraction during two phase flow inmini-channelsis essential. Zhang et al. [144] predicted the Dp in a mini channelheat exchanger with reference to dh, G, p, and xeq and void fractionwas predicted with reference to jf, jg, dh, and p using MLFFN. Theirresults reported that MLFFN predictions of Dp and void fraction are

better than that obtained using conventional correlations. Malayeriet al. [145] predicted void fraction using RBFN with reference to themodified volumetric flow ratio, We, and Dp. It was reported thatRBFN predicts the void fraction with average relative error of 3.6%for the training data and 5.8% for the testing data.

4.3.4. Two phase flow regime identificationsTwo phase flows commonly occur in heat exchanger applica-

tions such as condensers and evaporators of refrigeration systems,boilers and condensers of thermal power plants, petrochemicalindustries, nuclear and chemical reactors [146]. The identificationof two phase flow regimes in heat exchangers is essential toinvestigate its transient behavior. The conventional methods usedfor measuring the two phase flow are by visual observation [146],or using X-rays [147] and gamma rays [148]. However, the con-ventional methods are having many drawbacks [149]. To overcomethis difficulty, ANNmethodwas proposed bymany researchers. Thereported investigations on this topic are reviewed and the consol-idated list is presented in Table 18.

Mi et al. [150,151] identified the four flow regimes such asbubbly, slug flow, churn flow and annular flow based on non-intrusive impedance void-meter input signals using supervisedMLFFN. This network identifies the flow regimes with an accuracyof 94%. In similar work, Tambouratzis and Pazsit [152,153] used theANN approach for predicting four different flow regimes (such asbubbly, slug, churn and annular flow) during the boiling phasechange phenomena. In their work, 996 KURRI images were used toinvestigate the four regions of boiling phase change characteristics.The extracted images were used as training data for the network. Itwas reported that, their network predicts the two phase charac-teristics with 98.56% accuracy.

Two phase flow patterns in a micro-channel heat exchangerwere identified using PNN and compared with the conventionalcorrelation models [154]. The parameters considered in their workfor predicting two phase characteristics are liquid and vapor phasesuperficial velocity, channel diameter, angle of inclination and fluidproperties such as density, viscosity and surface tension. In theirwork, two phase flow patterns have been divided into six categoriessuch as bubbly, slug, annular, churn, liquid ring and liquid lumpflows. The flow patters predicted by PNN are found to be in goodagreement for all flow patterns except for liquid lump flow. Themultiphase regime of oilewateregas multiphase phase flow wasidentified using MLFFN [155]. In their work, the input parametersare first and second full energy peaks of the detector output signal.The two outputs of the network represent oil and water percent-ages. It was reported that the MLFFN with a 2-7-10-2 configurationpredicts the output with MAE less than 1%.

4.3.5. Condensation characteristicsANN has been successfully applied in predicting the condensa-

tion characteristics. A review of few reported investigations isdescribed in Table 19. Demir et al. [156] predicted the hcond and Nuof R600a using MLFFN. Input layer consists of six neurons repre-sentingmref

�, mean vapor quality, input vapor quality, output vapor

quality, Tsat, DT between pipe wall and condensing fluid. The outputlayer consists of two neurons representing the hcond and Nu.Tangent sigmoid and linear transfer functions were used in hiddenand output layer, respectively. The network was optimized to a 6-5-2 configuration. The network predicts the hcond and Nu with MREsof 3.97% and 3.99%, respectively. Similarly, the hcond andDp of R134ainside the vertical smooth tubes were predicted using four ANNmodels, such as MLFFN, RBFN, GRNN and ANFIS [157]. The networkconsists of five input parameters, namely G, q, Tsat, DT betweencondensing temperature and inlet tube wall temperature andaverage vapor quality. Two output neurons representing


experimental hcond and Dp. The results showed that MLFFN andRBFN architectures were reported with good agreement for pre-dicting the experimental hcond and Dp within 5% for all testedconditions. In further work, Balcilar et al. [158] predicted the Dp ofthe refrigerants during evaporation and condensation in horizontalsmooth and micro-fin tubes using MLFFN. The refrigerantsconsidered in their study are R32, R125, R410A, R134a, R22, R502,R507A, R32/R134a (25/75 by mass), R407C and R12. In their work,two MLFFN models were developed for predicting the Dp duringevaporation and condensation. One is having a 12-10-10-1 struc-ture and another is of 12-40-1 configuration. The inputs of the firstnetwork are G, tube length, inlet and outlet vapor qualities, pc,latent heat of condensation, rl and rv, ml and mv, dh and all liquid Re.The inputs for the second network configuration are G, tube length,inlet, and outlet vapor qualities, pc, latent heat of condensation,mass fraction of liquid, and vapor phases, m of liquid and vaporphases, dh and two-phase density of (rTP). Results showed that the12-40-1 configuration has better predictability than that of the 12-10-10-1 configuration due to the use of proper input parameters inthe correlation. They also reported that MLFFN predicted Dp valuesare closer to actual Dp obtained with an error rate of about ±7%.

Thermal energy storage capacity of a heat exchanger was esti-mated using MLFFNwith four neurons in input layer representing aheat transfer area, Re, inlet temperature of heat transfer fluid andtime [159]. The MLFFN with a 4-8-1 configuration predicts thethermal energy storage capacity with average MRE, standard de-viation and R2 values of 6.63%, 7.78 and 0.9919, respectively.

4.4. Control of heat exchangers

Control of heat exchangers plays a major role in achieving bettersystem performance and energy saving. Conventional controllersare not suitable for the systems having nonlinear behavior, whichincludes uncertainties and time delays that may lead to thereduction of heat exchanger effectiveness. Nonlinear controllersbased on AI techniques like fuzzy logic and ANN can overcomethese issues [160e162]. A summary of ANN applications for controlof heat exchangers are consolidated and presented in Table 20.

Diaz et al. [163] predicted the dynamic performance of heatexchangers using ANN. The results are compared with proportionalintegral (PI) and proportional integral derivative (PID) controllers.In their work, a novel methodologywas proposed for predicting the

Table 20Control of heat exchangers.

Authors[references]



Parameterscontrolled

Diaz et al. [163] Aireliquid heat exchanger MLFFN Control of TaVarshney and

Panigrahi [164]Fin tube heat exchanger MLFFN Control of T

Abbassi andBahar [165]

Evaporative condenser MLFFN Thermal capacity

Nanayakkaraet al. [166]

Evaporator RBFN Cooling capacity

Vasickaninovaet al. [167]

Tubular heat exchanger MLFFN h and volumeflow rate

Hu et al. [168] HVAC heat exchangers MLFFN Chilled wateroutlettemperaturesand outlet Ta

Li et al. [169,170] Evaporator of airconditioning system

MLFFN DBT and WBT

Jahedi andArdehali [171]

HVAC Heat exchanger WNN-IIR Temperatureand humidity

Gang et al. [172] Ground sourceheat exchanger

MLFFN Temperature

dynamic behavior of heat exchangers. An internal model schemewas developed to control the over-tube air temperature with twoANN models (one to simulate and another to control the heatexchanger). The results are compared with that of PI and PIDcontroller. The reported results confirm that, the ANN method ofheat exchanger control performed better than the conventional PIand PID control techniques. Varshney and Panigrahi [164] experi-mentally controlled the temperature of a heat exchanger in a closedflow air circuit using ANN and PID controllers. The temperatureinside the test section has been maintained at a set point value byvariation of air flow rate over the heat exchanger tube surface andthe water flow inside the heat exchanger tubes. The performance ofthe controller has been investigated for multiple set point values.The ANN based control has higher speed of response with lesssteady state error when compared to the PID control. The controlaction based on the ANN technique has less oscillation compared tothat of PID based control. Also, it was found that the dual actuations(air flow andwater flow control) have better performance than thatwith single actuation (either air flow or water flow control).

Abbassi and Bahar [165] presented the details of a thermody-namic modeling of an evaporative condenser (under steady stateand transient state conditions) to control the thermal capacity us-ing ANN and compared the results with that of PID controllers. Theydeveloped an MLFFN architecture with five neurons in the inputlayer (representing refrigerant Tcond, m

�ref , inlet air temperature,

inlet specific humidity and m�w) and three neurons in the output

layer (representing the amount of water evaporated, condenserload and outlet specific humidity and temperature). Their resultsshowed that the ANN based controllers can minimize the processerror better than the PID controllers. They have also reported that,the ANN based controller can be a good substitute for the PIDcontrollers in heat exchanger applications. In another work, a novelRBFN architecture characterized by activation functions with dy-namic synaptic units (DSU) was adopted in controlling theammonia evaporator and compared with two other neural networkstructures such as direct mapping neural network (DMNN) andRBFN with dynamic neural units (DNN) [166]. From the three dy-namic networks reported in their study, it was concluded thatneural networks with DSU needs less input and hidden layer nodesthan conventional DMNNwith nonlinear static activation functionsand RBFNN with DNN. The RBFNN with DSU results in fasterconvergence in the training process to control the evaporator moreeffectively.

Vasickaninov�a et al. [167] controlled the thermal processes ofheat exchanger using MLFFN and compared with the PID controls.The input layer of the network consists of three neurons namely dt,r and cp. The output layer consists of two output neurons namely hand volume flow rate. The MLFFN with a 3-6-2 configuration con-trols the thermal processes of a heat exchanger with an integratedsquare error of 279.35, whereas the PID controller has an integratederror of 304.7. The reported results confirmed that the ANN pre-dicted control strategy is a good tool for successful control of thethermal processes happening in heat exchangers with significantenergy savings. Similarly, Hu et al. [168] predicted the static anddynamic performance of a HVAC heat exchanger using ANN. Theyused two MLFFN models for predicting the static and dynamicresponse of a heat exchanger used in a mechanical HVAC system. Intheir work, five input parameters (such as inlet chilled Tw, outletchilled Tw, inlet temperature of hot air, chilled waterm

�andm

�a) were

considered for predicting the Q�of a heat exchanger. The MLFFN

with a 5-10-1 configuration predicts the Q�within an accuracy of

±4.87% deviations. Another ANN model with ten neurons in theinput layer and two neurons in the output layer was developed forpredicting the dynamic performance of a heat exchanger. Thenetwork with a 10-20-2 configuration predicts the chilled water


outlet temperature and outlet air temperature with maximumrelative errors of 11.42% and 6.94%, respectively. In another work, Liet al. [169,170] developed aMLFFN to control the evaporator used inan air conditioning system. In their work, a MLFFN was developedto predict the DBT and WBT of the air at exit. The network consistsof twelve neurons in input layer representing indoor DBT and WBTof air at three different time intervals, while the six other inputs arethe compressor and fan speeds at two different speeds. The twooutputs include DBT and WBT of air. It was reported that thenetwork with a 12-30-2 configuration predicts the DBT andWBT ofthe air leaving the evaporator of the heat exchanger with anaverage relative errors and MREs of 0.30% and 1.36%, respectively.

Jahedi and Ardehali [171] controlled the temperature and hu-midity of air leaving the HVAC heat exchanger using WNN withinfinite impulse response (IIR) filer for the faster and accurateidentification of system dynamics. It was reported that, the per-formance of a HVAC heat exchanger using WNN-IIR controllershowed improved energy efficiency when compared to the pro-portional derivative (PD) controllers. In a recent investigation, anANN based control strategy was proposed by Gang et al. [172] tocompare the cooling water temperature leaving from ground heatexchanger and cooling tower. In their work, a MLFFN with LMlearning algorithm was developed with ten neurons in the inputlayer representing temperatures at different locations in a heatpump circuit and one neuron in the output layer representingtemperature of cooling water leaving the cooling tower and groundheat exchanger. It was reported that ANN based control is moreenergy efficient when compared to schedule based control systemand temperature differential based control system.

4.5. Comparison of the ANN architectures for heat exchangeranalysis

ANN architectures used for heat exchanger analysis discussed inthis paper are summarized in Table 21. From Table 21, it can beconcluded that MLFFNs were widely used for heat exchangeranalysis due to its simplicity (compared to other network models).The most common variants in MLFFN architectures for modeling ofthermal systems are LM, SCG and CGP [173e175]. But, the LM is themost suitable variant for modeling and simulation of heat ex-changers due to its higher speed and fast convergence whencompared to SCG and CGP. The MLFFNs have certain limitations inoptimizing the network parameters as mentioned in some researchreports [176e178]. AI techniques have been developed to optimizethe network configuration. Limited investigations have been re-ported with a hybrid ANN approach for heat exchanger applica-tions. Hence, further research is required to the hybrid approach ofheat exchanger analysis. WNN overcomes the limitations of MLFFNfor certain heat exchanger applications [67,179]. From the literaturereviewed, it can be understood that MLFFNs are the most suitablenetwork configuration used for modeling and simulation of heatexchangers, estimation of heat exchanger parameters such as Rfo, hand f values, phase change characteristics in heat exchangers andcontrol of heat exchangers with acceptable accuracy.

Table 21Number of ANN used in heat exchanger analysis.

Type of ANN MLFFN GRNN RBFN ANFIS Hybrid Others

Modeling of heat exchangers 58 e 1 4 2 1Estimation of h, Rfo, f 16 e e 5 1 e

Phase change characteristics 21 2 4 2 3 2Control of heat exchangers 8 e 1 e 1

Total 103 2 6 11 6 4

RBFN is another network architecture used in heat exchangeranalysis [61,121,130,133,157,166]. RBFN has a single hidden layer,whereas a MLFFN may have more than one hidden layer, whichneeds to be optimized [180]. In certain applications, RBFN hasbetter prediction capability when compared to MLFFN. RBFN havefaster convergence speed and higher reliability with relatively shortlearning time and less extrapolation errors when compared toMLFFN [181]. The number of hidden neurons in RBFN dependsupon the number of inputs, which require more memory spacewhen there were too many input data [182]. Another drawback ofRBFN is the determination of spread number as reported by Wanget al. [183]. The high value of spread number leads to over fittingand its less value may lead to insufficient learning. The spreadparameter can be optimized using GA as it has done by Zhang andBai [184]. The optimal network parameters were predicted usingPSO in a work reported by Lee and Ko [185]. Due to these draw-backs, limited investigations have been reportedwith RBFN for heatexchanger analysis when compared to MLFFN.

WNN is a new class of networks, which have been widely used[186]. WNN combines the advantages of discrete wavelet transformand neural network processing to attain good non-linear relation-ship, which has been successfully used in fault diagnosis, loadforecasting and functional approximations [186]. The WNN is ageneralized RBFN, which has faster convergence than RBFN [179].The WNN is based on MLFFN, of which the sigmoid transfer func-tionwas replaced bywavelet bases, whereas the activation functionin output layer is sigmoid function. The prediction capability ofWNN was found to be better when compared to MLFFN [67,179]. Ina recent work, a fuzzy integrated WNN was proposed for modelingand optimization applications [187]. The optimization techniquessuch as GA, PSO, SA and ANT colony were also used to optimize thenetwork parameters. Limited investigations have been reportedwith WNN architecture for modeling and simulation of heat ex-changers. Hence, further research is required to explore the possi-bility of using WNN for modeling, simulation, fault diagnosis andcontrol of heat exchangers.

GRNN configuration has radial basis layer and a linear layer asindicated by Specht [188]. Only two research investigations havebeen reported with the application of GRNN for heat exchangers[121,157]. The most significant characteristics of GRNN are its goodfunction approximation ability compared to MLFFN, fast trainingtime and exceptional stability during its prediction stage. GRNN isproposed for function approximation and classification problems.However, the prediction capability of GRNN is affected while thehandling of large training data [189]. GRNN does not require aniterative training procedure as in the back propagationmethod. Theprediction of optimal smoothening parameter and hidden layer sizeare the two major tasks in optimizing the GRNN configuration[190]. GA integrated GRNN was recommended for predicting thesmoothening factor [191]. Moreover, GRNNs are having poorextrapolation capability when compared to the MLFFNs. In acomparative study, it was reported that, GRNN has poor predictioncapability of condensation characteristics when compared toMLFFN, RBFN and ANFIS [121,157]. Due to these drawbacks, GRNNsare not generally used in the thermal analysis of heat exchangers.GRNN is suitable for two phase flow identifications in heat ex-changers handling multiphase flows (such as condensers andevaporators).

The ANFIS configuration combines the learning capabilities of aneural network and reasoning capabilities of fuzzy logic [192e194].ANFIS predictions of heat exchanger performance were found to bebetter when compared to MLFFN as reported by many researchers[23,24,64,77,96,98,113,118,136,157]. However, in certain applica-tions, ANFIS have poor prediction capability for heat exchangerapplications when compared to MLFFNs [77,157]. Selection of


inputs for ANFIS has the influence on prediction capability as re-ported by Jang [195]. Hence it is necessary to select the proper inputparameters carefully. ANFIS prediction capability can be furtherimproved by optimizing the network parameters using GA [113]and PSO [196]. The prediction accuracy of ANFIS is also enhancedby integrating ANFIS with fuzzy weighted preprocessing [197].

5. Limitations of ANN modeling for heat exchangerapplications

The major limitations of ANN for heat exchanger analysisinclude over training errors, extrapolation errors and optimizationof network configuration. Discussions of the limitations of ANNmodeling for heat exchanger analysis are given in the followingsubsections.

5.1. Over training errors

Over training errors occur when the capacity of ANN for trainingis too large or more number of iterations were allowed [198]. Inmost of the engineering applications of ANN, a very high trainingprecision or large number of training cycles is preset to terminatethe training processes. However, in actual engineering systems, fewtraining samples are usually erroneous due to experimental un-certainties. Hence, high precision may over fit the training samplesand degrade the performance prediction of an ANN model. Toovercome the problem of over training with ANN, the number oftraining cycles and number of training data needs to be optimized.To reduce the overtraining error in ANN, EBaLM-OTR was intro-duced and this methodology was elaborated by Wijayasekara et al.[91].

5.2. Extrapolation errors

ANN models are not effective for extrapolation beyond thetraining data as identified by Yin et al. [198]. While preparing thetraining data, the maximum andminimumvalues of the system areto be selected from the experimental results. Some artificialtraining samples can be drawn using empirical correlations whichcover the entire range (as much as possible). The range of thetraining data must be representative of the entire operating rangeof the system in order to reduce the extrapolation errors.

5.3. Network optimization

Selection of optimum network parameters such as, the numberof neurons in hidden layer, number of hidden layers, momentumfactor, learning rate, number of training data and variant are themajor tasks in MLFFN network modeling [199e201]. Trial and errormethod is the widely used approach to optimize the networkconfiguration. The number of neurons in hidden layer can also beoptimized using following equation (1) [202].

Numberof hiddenneurons¼12ðinputneuronsþoutputneuronsÞ

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNumberof trainingdata

p

(1)

However, the trial and error method is time consuming and theresultant ANN configuration may not be optimum. To overcomethis drawback, GA based ANN approach was developed for opti-mizing the network parameters [203,204]. PSO can also beemployed for optimizing the ANN configuration. PSO has fasterconvergence speed with higher accuracy when compared to GA asreported by researchers [205e207]. Similarly, simulated annealing

(SA) [208] and ANTcolony algorithms [209] can be used to optimizethe network parameters. The hybrid optimization technique usingSA and PSO is still more effective than the conventional PSO basedhybrid ANN as reported by Da and Ge [210].

5.4. Training data requirement

ANN is quite suitable to the problems having large number oftraining data [211]. The available data can be split as training data,validation data and testing data. Improper data splitting can lead toa poor prediction capability [212]. Hence, the selection of data fortraining and testing is more important in order to attain high ac-curacy. Experimental uncertainty and theoretical assumptions mayinfluence the reliability of the results in case of handling largetraining data [213]. Hence, the number of training data required forthe network needs to be optimized. Novel optimization techniquesmay be used to minimize the training data requirement.

6. Further research needs

The major research extensions are identified and listed belowbased on the literature reviewed in the area of application of ANNfor the thermal analysis of heat exchangers.

(i) Limited investigations have been reported with the GA in-tegrated ANN approach. Hence, it is essential to extend thesuitability of GA integrated ANN for a wide range of heatexchanger applications.

(ii) PSO approachmay be used to optimize the ANN architecturefor heat exchanger analysis.

(iii) SA approach is also used to optimize the ANN configurationsfor modeling of heat exchangers.

(iv) Need for the optimization of network configuration using anANT colony algorithm.

(v) The hybrid network optimization technique is still moreeffective than GA, PSO and SA techniques. The hybridnetwork optimization approach may be tried for heatexchanger applications.

(vi) The hybrid training algorithm may be tried elaborately forheat exchanger applications [214].

(vii) MLFFN with statistical data weighting pre-processing re-duces the number of training data [215]. Further researchextension of this concept is required for heat exchangerapplications.

(viii) Life cycle assessments of heat exchangers can be carried outin order to investigate its environmental impacts using ANNmodels.

(ix) The quality of water used in heat exchangers may influencethe life of heat exchangers [216]. Hence, the ANN modelingof heat exchangers by considering the water quality can betried.

(x) Pinch analysis of heat exchangers using ANN is one area,which needs a detailed further attention.

(xi) Exergy analysis of heat exchangers using ANN models hav-ing very good future scope for optimizing the size, weight,baffle geometry and cost of heat exchangers [217].

(xii) LMTD and ε-NTU method of heat exchangers are not validfor zeotropic mixtures due to its non-isothermal behavior,which requires a correction factor [20]. Hence, the devel-opment of the ANN model for predicting such correctionfactor needs further research.

(xiii) Frost formation is a major issue in cooling coils [218]. ANNmodel may be developed to control the frost formation incooling coils.


(xiv) ANN modeling of heat exchangers using PCM is a currenttopic, particularly suitable for renewable energy based heatstorage applications such as, solar water heaters and airheaters [219].

(xv) The presence of non-condensable gases in the condensers ofrefrigeration, air conditioning and heat pump systems haveinfluenced its thermodynamic performance [220]. Furtherresearch investigation is required using ANN.

(xvi) The influence of compressor lubricant during boiling andcondensation characteristics of refrigerants in evaporatorsand condensers of refrigeration systems is a topic gainingimportance because of the alternative refrigerant usage[221].

(xvii) The identification of two phase flow instabilities in con-densers and evaporators using ANN is a topic of major in-terest in many heat transfer applications [222].

(xviii) The composition shift and temperature glide are the twospecial attributes of zeotropic mixed refrigerants [20]. Thesuitability of ANN for predicting composition shift andtemperature glide of new environment friendly refrigerantmixtures reported in the literature needs further research toinvestigate its dynamic behavior [223,224].

(xix) ANFIS controls the temperature and humidity in HVACsystems [225]. The suitability of ANFIS may be tried tocontrol the heat exchanger operations.

(xx) ANN models identify the faults in thermal systems withgood accuracy [226e229]. The suitability of using ANN ishaving an excellent scope, particularly with respect to nu-clear reactor applications.

(xxi) The prediction capability of least square support vectormachines is slightly higher than conventional ANN models[230]. Hence, the suitability of least square support vectormachines for heat exchanger control needs further researchinvestigation.

7. Conclusion

Researchers from all over the world have reported manyresearch investigations on thermal analysis of heat exchangersusing ANN. The important research investigations related to ther-mal analysis of heat exchangers using ANN were reviewed in thispaper. The literature discussed in this paper confirmed that, theANN can be successfully used for the modeling, simulation andanalysis of heat exchangers, estimation of heat exchanger param-eters such as, heat transfer coefficient, fouling factor and frictionfactor, estimation of phase change characteristics during boilingand condensation processes of fluids, CHF, void fraction and twophase flow identifications. Also, the control of heat exchangers withacceptable accuracy is possible with ANN compared to conven-tional controllers such as PD, PID, etc.

Multilayer feed forward networks were widely used for pre-dicting the performance of heat exchangers due to its simplicity.However, these are found to be having certain limitations inoptimizing the network configuration. The optimization tech-niques such as GA, PSO, SA, ANT colony algorithm and hybridforms of optimization techniques were recommended for opti-mizing the MLFFN configurations. The hybrid network optimi-zation technique seems to be a more efficient approach tooptimize the network configuration. Limited investigations havebeen reported with RBFN and GRNN due to its drawbacks inperformance prediction, forecasting and estimation. ANFIS isanother hybrid network used for modeling and simulation ofheat exchangers with acceptable accuracy, which needs furtherresearch in heat exchanger control and fault diagnosis

applications. The limitations and future research needs of ANN inthe field of thermal analysis of heat exchangers were identifiedand suggestions to overcome the drawbacks are also discussed.From the detailed review, the authors recommend MLFFN with aback propagation learning algorithm for the thermal analysis ofheat exchangers.

A vast spectrum of investigations is reviewed in this paper onthe topic of ANN application for the thermal analysis of heat ex-changers. Based on the discussions presented here, it can be clearlyunderstood that, ANN offers an excellent alternative methodologyfor the thermal analysis of heat exchangers. The information pro-vided in this paper would be highly beneficial to the researchersworking in the field of heat exchangers and also those using theANN methodology in their studies.

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Glossary

A: areacp: specific heatd: diameter

e: wire coil diameterf: friction factorFr: Froude numberG: mass fluxGr: Grashof numberh: heat transfer coefficientj: Colburn factorjf,: liquid superficial velocityjg: gas superficial velocityL: lengthε-NTU: effectiveness number of transfer unitsm�: mass flow rate

N: number of tube rowsNu: Nusselt numberDp: pressure dropp: pressureph: helical pitchPr: Prandtl numberQ�: heat transfer rate

q: heat fluxR: correlation coefficientRfo: fouling resistanceR2: fraction of absolute varianceRa: Rayleigh numberRe: Reynolds numberT: temperatureDT: temperature differenceU: over all heat transfer coefficientv: velocityWe: Webber numberx: vapor quality

Greek symbols

a: thermal diffusivityb: spiral angle/90m: dynamic viscosityr: densityh: efficiency3: effectiveness

Subscripts

a: airab: ambientb: boilingbu: bulkc: criticalcond: condensationcon: convectiveco: condenserCT: cooling towere: evaporatorfl: flue gasref: refrigerantg: gasi: inletf: fluidfo: foulingh: hydraulicl: liquido: outletr: reduced propertiessat: saturations: shellsur: surfaceth: thermalt: tubew: waterwa: wallwi: water inletwo: water outlet

Abbreviations

AI: artificial intelligenceANFIS: adoptive neuro fuzzy interface systemsANN: artificial neural networksCFD: computational fluid dynamicsCGP: PolaeRibiere conjugate gradientCHF: critical heat fluxCOP: coefficient of performanceCOV: coefficient of variance












































































































CO2: carbon-dioxideDBT: dry bulb temperatureDMNN: direct mapping neural networksDMNN: dynamic neural networksDSU: dynamic synaptic unitsFIS: fuzzy interface systemGA: genetic algorithmGMDH: group method of data handlingGNN: genetic neural networksGRNN: generalized regression neural networksHVAC: heat ventilation and air conditioningKURRI: Kyoto University Research InstituteLM: LevenbergeMarquardtLMTD: logarithmic mean temperature differenceMaRE: maximum relative errorMAE: mean absolute errorMARE: mean absolute relative errorMIMO: multi input-multi outputMISO: multi input-single outputMLFFN: multi layer feed forward network

MRE: mean relative errorMSE: mean square errorNTU: number of transfer unitsPCM: phase change materialsPI: proportional integralPID: proportional integral derivativePNN: probabilistic neural networkPSO: particle swarm optimizationRBFN: radial basis function networkRH: relative humidityRMS: root mean squareRMSE: root mean square errorRMSRE: root mean square relative errorSAH: solar air heaterSA: simulated annealingSCG: scaled conjugate gradientSWH: solar water heaterWBT: wet bulb temperatureWNN: wavelet neural network

international journal of thermal sciences...2014/09/05 · m. mohanraj et al. / international...

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