heat transfer analysis for shell-and-tube heat exchangers

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Applied Thermal Engineering 27 (2007) 1096–1104

Heat transfer analysis for shell-and-tube heat exchangerswith experimental data by artificial neural networks approach

G.N. Xie, Q.W. Wang *, M. Zeng, L.Q. Luo

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Shaanxi, Xi’an 710049, China

Received 21 March 2006; accepted 11 July 2006Available online 24 October 2006

Abstract

This work applied Artificial Neural Network (ANN) for heat transfer analysis of shell-and-tube heat exchangers with segmental baf-fles or continuous helical baffles. Three heat exchangers were experimentally investigated. Limited experimental data was obtained fortraining and testing neural network configurations. The commonly used Back Propagation (BP) algorithm was used to train and testnetworks. Prediction of the outlet temperature differences in each side and overall heat transfer rates were performed. Different networkconfigurations were also studied by the aid of searching a relatively better network for prediction. The maximum deviation between thepredicted results and experimental data was less than 2%. Comparison with correlation for prediction shows superiority of ANN. It isrecommended that ANN can be used to predict the performances of thermal systems in engineering applications, such as modeling heatexchangers for heat transfer analysis.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Heat transfer rate; Outlet temperature difference; Artificial neural network; Shell-and-tube heat exchanger; Segmental baffles; Continuoushelical baffles

1. Introduction

The Computational Intelligence (CI) techniques, such asArtificial Neural Networks (ANNs), Genetic Algorithms(GAs), Fuzzy Logic (FL), have been successfully appliedin many scientific researches and engineering practices.ANNs have been developed for about two decades andnow widely used in various application areas such as pat-tern recognition, system identification, dynamic controland so on. ANN offers a new way to simulate nonlinear,or uncertain, or unknown complex system without requir-ing any explicit knowledge about input/output relation-ship. ANN has more attractive advantages. It canapproximate any continuous or nonlinear function byusing certain network configuration. It can be used to learncomplex nonlinear relationship from a set of associatedinput/output vectors. It can be implemented to dynami-

1359-4311/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2006.07.036

* Corresponding author. Tel./fax: +86 29 82663502.E-mail address: [email protected] (Q.W. Wang).

cally simulate and control unknown or uncertain process.In recent years, ANNs have been used in thermal systemsfor heat transfer analysis, performance prediction anddynamic control. For example, Thibault and Grandjean[1] earlier used a Neural Network (NN) for heat transferdata analysis, Jambunathan et al. [2] evaluated heat trans-fer coefficients from experimental data by using a NN, Bitt-anti and Piroddi [3] used a NN to identify and control heatexchangers, Yang and Sen [4,5] reviewed works in dynamicmodeling and controlling of heat exchangers using ANNsand GAs, Diaz et al. [6–10] did lots of works in steady/dynamic simulation and control heat exchangers usingANNs, Parcheco-Vega et al. [11–14] also did many worksin analysis for fin-and-tube heat exchangers with limitedexperimental data using soft computing and global regres-sion, Islamoglu et al. [15,16] predicted heat transfer rate fora wire-on-tube heat exchanger and made heat transferanalysis for air flowing in corrugated channels. Otherresearches about heat exchangers control by meansof ANNs were reported in references [17–19]. From

mailto:[email protected]

Nomenclature

Dc diameter of center blocked tube (mm)Do outside diameter of tube (mm)Er relative errorM number of sets of data for training networkN number of sets of data for testing networkNb number of baffleNt number of tubePr Prandtl numberU heat transfer rate (W)R evaluation factor for average accuracy, Eq. (3)Rew, Reo Reynolds number in water-side, oil-siderms Root-mean-squares errorSb baffle pitch (mm)C coefficient of heat transfer correlationm exponent of heat transfer correlation

Nu Nusselt numberPr Prandtl numberTw,in, To,in inlet temperature in water-side, oil-side (K)umax velocity at minimum cross-section (m/s)DTo,out temperature difference in oil-side (K)DTw,out temperature difference in water-side (K)r evaluation factor for scatter accuracy, Eq. (4)m kinematic viscosity

Superscriptse, p experimental, predicted

Subscripts

o, w oil, waterin, out Inlet, outlet

G.N. Xie et al. / Applied Thermal Engineering 27 (2007) 1096–1104 1097

aforementioned successful applications, it is shown thatANNs are well suitable to thermal analysis in engineeringsystems, especially in heat exchangers.

In many experimental studies and engineering applica-tions of thermal science, researchers and engineers expectto reduce experimental data into one or more simple andcompact dimensionless heat transfer correlations. The dis-advantages of the correlation methods are that heat trans-fer coefficients strongly depend on their definitions andtemperature differences, and inevitably need iterativemethod to obtain correlations when fluid properties aredependent on fluid temperatures [20]. However, ANN doesnot need definition of correlations and iterative method,only needs input/output samples for training a special neu-ral network, in turn, obtaining output results as test sam-ples fed into trained network. In the above-mentionedliterature, most works were done in thermal analysis forfin-tube heat exchangers, while for shell-and-tube heatexchangers only few works were done in open literature.For this reason, the objective of this paper is that, settingup experimental system for investigation on three shell-and-tube heat exchangers, and applying ANN for heattransfer analysis of heat exchangers with experimental databased on back propagation algorithm to train the network.The predicted outputs of ANN are temperature differencesof two sides and heat transfer rate. Different network con-figurations were studied for searching an optimal network.In addition, the predicted results by ANN were comparedwith those by correlations from references.

2. Physical model and experimental data

2.1. Experimental system

The experimental loop is shown in Fig. 1, which wasdesigned by our research group and built at school ofEnergy and Power Engineering, Xi’an JiaoTong Univer-

sity. There are three sub-loops (an oil loop, a cold waterloop and a cooling water loop) for achieving the heatexchange of the experimental loop in the present study.

In Fig. 1, 41 is the tested heat exchanger. We can carryout oil–water (by oil loop and cold water loop) or water–water (by hot water loop and cold water loop) heat exchan-ger on the experimental loop. The cooling water loop isused to cool the heated water of the cold water loop.

More detailed description of the experimental systemand tested heat exchangers can be found in Ref. [21].

2.2. Data acquisition

Three main parameters, mass flow rate, temperature andpressure drop are obtained, for both hot and cold workingmedium of the tested heat exchangers. The heat balancesbetween water and oil are less than 8% by on-line calcula-tions for all studied cases. If the heat balance were well sat-isfied, all the corresponding experimental data were savedand averaged on a computer for data reduction. The uncer-tainties of obtained temperature difference, flow rate, heattransfer rate and heat transfer coefficient are less than2%, 0.15%, 2.5% and 4%, respectively.

The three tested heat exchangers are shown in Fig. 2.Fig. 2(a) is a heat exchanger with segmental baffles (hereaf-ter, the heat exchanger is called HX1), the other two areheat exchangers with continuous helical baffles, as shownin Fig. 2(b) and Fig. 2(c). The only difference between thelatter two helical heat exchangers is the inlet–outlet flowmanner of shell-side fluid. One is middle-in-middle-out(so called HX2, Fig. 2(b)) and the other one is side-in-side-out (so called HX3, Fig. 2(c)). The cores of HX2and HX3 are same (i.e., the layouts of tubes and bafflesare identical), and the only difference between the HX2and HX3 is the position/location of inlets and outlets ofshell-side flows. The positions of inlet and outlet of HX2are on the middle of the shell side, which is normal to shell,

Fig. 1. Experimental loop.

1098 G.N. Xie et al. / Applied Thermal Engineering 27 (2007) 1096–1104

while the positions of inlet and outlet of HX3 are on theside of the shell side, which is tangential to shell. It shouldbe noted that for helical heat exchangers (HX2, HX3) thereis a blocked center tube.

The heat exchangers are 1–2 type, with hot oil flowing inshell-side and cold water flowing in tube-side. The detailparameters for the three tested heat exchangers are shownin Table 1. Note that the helical characteristics are deter-mined by helical pitch (herein is baffle pitch, Sb) and bafflediameter, instead of helix angle, because the helical bafflesare continuous. One cycle of continuous helical baffle isfirstly produced, and each cycle occupies one circle of theexchanger, and spires for one helical pitch.

Experiments were performed for Reynolds numberranging from 300 to 7000 in the shell-side, 3000 to 4000in the tube-side. Heat transfer rate varied from 20 kW to50 kW. Thirty nine sets of experimental data were obtainedand divided into two parts: one part is used for trainingnetworks (as listed in Table 2), the other is used for testingnetworks (as listed in Table 3). It should be noted that thediameter of center tube in HX1 is zero since there is no cen-ter tube. In this study, the shell-side Reynolds number isdefined by

Reo ¼umaxDo

mð1Þ

where Do is the outer diameter of tube, umax is the velocityat minimum cross-section of shell-side, m is kinematic vis-cosity of oil. It should be noted that the properties of oiland water are determined at the mean temperature (aver-aged by inlet and outlet temperature).

3. Neural network configuration

ANNs comprise of a great number of interconnectedneurons. Fig. 3 illustrates a typical full-connected networkconfiguration. Such an ANN consists of a series of layerswith a number of nodes. The nodes (circle points inFig. 3) sometimes called neuron are the basic processorsof neural network. Each connection between two nodeswith a real value is called weight. Nodes are gatheredtogether into a column called layer. For each node, thereexist an activation and a bias associated it. Among varioustypes of ANNs, the feedforward or multilayer perception

neural network is widely used in engineering applications.The input information is propagated forward through thenetwork, while the output error is back propagatedthrough the network for updating the weights. As shownin Fig. 3, the first layer with eight nodes and last layer withthree nodes are called input layer and output layer respec-tively, while the others in the middle are called hidden lay-

ers. The configuration in Fig. 3 has two hidden layers,

Oil

(a) HX1

(b) HX2

(c) HX3

Oil

OilOil

OilOil

Water

Water

Water

Blockedcenter tube

Blockedcenter tube

Fig. 2. Shell-and-tube heat exchangers.

Table 1Geometrical parameters of heat exchangers

Parameters Unit Value

Inner diameter of shell mm 207Outer diameter of tube mm 10Inner diameter of tube mm 8Arrangement of tube – TriangleEffective length of tube mm 620Number of tubes (helical) – 158Number of tubes (segmental) – 176Outer diameter of inlet tube in water-side mm 57Inner diameter of inlet tube in water-side mm 50Outer diameter of outlet tube in water-side mm 57Inner diameter of outlet tube in water-side mm 50Outer diameter of inlet tube in oil-side mm 57Inner diameter of inlet tube in oil-side mm 50Outer diameter of outlet tube in oil-side mm 57Inner diameter of outlet tube in oil-side mm 50Length of heat exchanger mm 670


which has six and five nodes respectively. There are manyways to implement ANNs. It is difficult to find an optimalnetwork, considering the uniqueness of a real problem.Thus, a priori choice, such as selection of network topol-

ogy, training algorithm and network size should be madebased on experience in order to keep the task to a manage-able proportion.

The back propagation (BP) algorithm is widely used totrain the networks. The main idea of this algorithm is tominimize cost function by steepest descent method to addsmall changes in the direction of minimization. It simplyconsists of back-propagating the output errors to the net-work by modifying the weight matrices. More descriptionsof BP algorithm can be found in Refs. [1,5]. The drawbackof BP algorithm is that it may get stuck in a local minimumand it needs a great of time to arrive at convergence. Vary-ing the learning rate dynamically or using momentumterms can improve the convergence speed. The mathemat-ical background, the procedures for training and testing theANN, and description of BP algorithm can be found in ref-erences [22,23]. Although the BP algorithm needs long timeto converge, the algorithm has gained a remarkable popu-larity in neural network community, because it is relativelyeasy to be implemented in engineering applications.

For the heat exchangers at hand, eight independentparameters were fed into the input layer of the network

Table 2Experimental data for training the network

No. Reo To,in (�C) Rew Tw,in (�C) Nt Nb Dc (mm) Sb (mm)

1a 296 59.6 3010 30.2 176 7 0 702a 525 58.7 3014 28.1 176 7 0 703c 571 58.4 3358 30.7 158 9 48 484a 697 60.3 2942 27.7 176 7 0 705c 745 59.1 3706 32.9 158 9 48 486a 821 60.5 3033 29.3 176 7 0 707c 981 58.5 3814 34.3 158 9 48 488a 1102 59.6 3121 30.2 176 7 0 709b 1148 61 3887 33.6 158 9 48 4810a 1253 59.4 2954 26.7 176 7 0 7011a 1399 58.9 3168 30.8 176 7 0 7012b 1413 61 3391 26 158 9 48 4813a 1486 59.4 3022 27.9 176 7 0 7014a 1693 59.1 3165 30.6 176 7 0 7015a 1825 59.8 3094 29.3 176 7 0 7016c 1950 59.3 3369 26.7 158 9 48 4817c 2565 59 3488 27.9 158 9 48 4818c 2591 59.4 3742 31.6 158 9 48 4819c 3045 59.2 3607 29.4 158 9 48 4820b 3121 60.8 3705 29.7 158 9 48 4821c 3507 59.6 3811 32.7 158 9 48 4822b 4365 60.1 3832 31.3 158 9 48 4823c 4949 60.7 3862 33.1 158 9 48 4824b 4979 61 3997 33.4 158 9 48 4825c 5536 61.4 3820 32.2 158 9 48 4826b 5669 61.6 3907 32 158 9 48 4827b 5843 60.9 4203 33.9 158 9 48 4828b 6702 62 4103 34.8 158 9 48 4829b 6996 61.8 4091 34.5 158 9 48 4830c 7018 62.2 4000 34.6 158 9 48 48

Note: Dc = 0 indicates that there exists no center tube in the heat exchanger.Superscripts a, b, c refer to the data from HX1, HX2, HX3 respectively.

Table 3Experimental data for testing the network

No. Reo To,in (�C) Rew Tw,in (�C) Nt Nb Dc (mm) Sb (mm)

1a 378 59.9 2911 26.5 176 7 0 702a 912 59.8 2794 24.1 176 7 0 703c 1371 58 3319 26.1 158 9 48 484b 1978 59.8 3537 27.9 158 9 48 485b 2610 60.2 3596 28.5 158 9 48 486b 3480 59.1 3923 33.3 158 9 48 487c 4251 60.7 3721 31.1 158 9 48 488c 5761 61 3936 34.1 158 9 48 489c 6625 61.5 4015 35.3 158 9 48 48

Note: Dc = 0 indicates that there exists no center tube in the heat exchanger.Superscripts a, b, c refer to the data from HX1, HX2, HX3 respectively.


(as shown in Fig. 3): Reynolds numbers and inlet tempera-ture in each side Rew, Reo, Tw,in, To,in, total number oftubes Nt, diameter of center tube Dc, total number of baf-fles Nb and baffle pitch Sb. The main reason for selection ofthese input variables is that, heat transfer rate as well asoutlet temperature are affected by inlet mass flow rate, inlettemperature on each side, and structure of heat exchangerscore due to the aforementioned differences between thethree heat exchangers. The effects of tube and baffle

arrangements can be considered into the hydraulic diame-ter, which is included in Reynolds number. The outputlayer contains three parameters: heat transfer rate, Up, tem-perature differences in each side, DT p

o;out, DT pw;out. It is

noticed that the ANN prediction is off-line carried out afterall of the dynamic parameters, including Re, thermal prop-erties, heat transfer rate, have been post-handled. Thus,once the flow rate has been measured, Re can be obtainedthrough its definition, so can the heat transfer rate and

Reo

,o inT

,w inT

tN

bN

bS

cD

pΦ

pTΔ

,p

w outTΔ

Rew

o,out

Fig. 3. 8-6-5-3 neural network configuration used for modeling heat exchangers.


temperature differences. In other words, when all experi-mental data have been reduced, the ANN predictions canbe off-line conducted.

A total of 39 set of data were run in the network, ofwhich M = 30 sets of experimental data, as listed in Table2, were used to train the network, while the rest of N = 9data, as listed in Table 3, were used to test the network.Note that 77% of the experimental data were used fortraining the network. The selection of test data from eachheat exchanger may be somewhat arbitrary, however thesedata are based on approximately uniform variation of Reo

from 300 to 7000 and based on total number of data fromeach heat exchanger.

In the present study, the popular used sigmoid functionwas adopted in hidden layers and output layer. It should benoted that the sigmoid function has the asymptotic limitsof [0,1]. It is desirable to normalize all the input/outputdata with the largest and smallest values of each of the datasets, since the variables of input/output data have differentphysical units and range sizes. Thus, to avoid any compu-tational difficulty, all of the input/output pairs were nor-malized in range of [0.15, 0.85] based on previousexperience [7–13].

4. Results and discussion

As aforementioned, drawback of BP algorithm is that itmay get stuck in a local minimum, therefore the learningrate was being changed during the training process of thenetwork. In the present study, the learning rate was finallyset to 0.4 based on previous tested experience [7–13]. Thetraining of the neural network was terminated when themaximum number of training cycles was reached. Notethat the selection of the number is a trail-and-error processin which it may be changed if the performance of neuralnetwork during the training is not good enough. In this

study, after a series of trail tests the number of trainingcycles was chosen to be 1,000,000, where the maximum rel-ative error between the output of the network and the tar-get output was less than 2%. The relative error of everypredicted output was defined by

Er ¼ jAe � Apj=Ae ð2Þ

where Ap is the predicted results (that is, the output ofANN), Ae is the experimental data (that is, the target out-put. The maximum error was determined by maximum va-lue of the maximum relative errors of the three outputvariables.

During the training process of neural network, the per-formance of the network was evaluated by calculating theroot-mean-square (rms) values of the output errors

rms ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

M

XM

i¼1

Ae � Ap

Ae

� �2

vuut ð3Þ

Then rms error was determined by maximum value of therms error of the three output variables. As an example,the errors during training 8-6-5-3 network configuration(as shown in Fig. 3), with two hidden layers with 6 and 5nodes respectively, are shown in Fig. 4(a). It can be seenthat the maximum error asymptotes at about 800,000 cy-cles, while the rms error is reached at 100,000 cycles. Atthe end of training process, the relative errors for trainingdata are shown in Fig. 4(b). Most of errors are within1% region, and the maximum relative error is about 1.5%.

Generalization is an important quality of ANN. It is theability to provide accurate output results when the inputdata that have never been used for training were fed intothe trained network. The network topology and size, suchas selection of number of hidden layer and number of hid-den node, will affect the predicted performance. The perfor-mance of the trained network is evaluated by comparing its

0 200,000 400,000 600,000 800,000 1,000,0000

2

4

6

8

10

Cycles

maximum error

rms

0 5 10 15 20 25 300.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Erro

r (%

)Er

ror (

%)

NoRelative error

Training process

Fig. 4. Training error for configuration 8-6-5-3 ANN: (a) Trainingprocess and (b) relative error DTo,out (j), DTw,out (m) and Q (w).

Table 4Comparison of errors by different ANN configurations

Configuration Train error Test error

Er (%) rms (%) R r

8-4-3 5.1347 1.5891 1.1282 0.129208-5-3 3.8703 1.0828 1.1084 0.122728-6-3 4.2666 0.8151 1.1914 0.194888-7-3 4.0109 0.8442 1.1904 0.193918-8-3 2.3681 0.5448 1.1226 0.129478-6-4-3 1.3852 0.5306 1.0893 0.132598-6-5-3 1.4471 0.5276 1.0890 0.13872

8-7-5-3 1.0657 0.4831 1.0958 0.135318-6-5-3-3 2.1113 0.8686 1.0595 0.145408-7-5-3-3 1.8007 0.7028 1.0925 0.13764

Note: the error is the maximum value among from the error of the threeoutput variables.

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

ΔTp o,

out

-10%

ΔTeo,out

+10%

0 2 4 6 8 100

2

4

6

8

10

ΔTp w

,out

ΔTew,out

+10%

-10%

(°C)

(°C)

(°C

)(°

C)

Fig. 5. Predicted temperature difference vs. experimental data (�C): (a)predicted temperature difference in oil-side and (b) predicted temperaturedifference in water-side.


prediction with the data set aside for testing. Thus, in thisstudy, by the aid of searching a relatively good configura-tion for prediction, ten different ANN configurations werestudied, as shown in Table 4. R and r are defined by

R ¼ 1

N

XN

i¼1

Ri ¼1

N

XN

i¼1

Ae

Ap ð4Þ

r ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

i¼1

ðR� RiÞ2

N

vuut ð5Þ

Note that in Table 4, R and r is the maximum value whichwere determined from R and r of the three output variablesrespectively. R reflects the average accuracy of the predic-tion, while r reflects the scatter of the prediction. Bothquantities are important for an assessment of the relativesuccess of the ANN analysis [5]. For three layers, whenthe number of hidden nodes is increased to 5, R is muchcloser to unity. This indicates that adding more hiddennodes may not improve the predicted results. From Table4, network with R close to unity is 8-6-5-3-3, however, itsr is larger than that of 8-6-5-3, in this sense, the configura-tions with four layers have higher accuracy of predictionthat those with five layers. It is also noted that adding morehidden layers may not make the prediction better. Thus, inthis case, configuration 8-6-5-3 is selected for testing, with

Table 5Constants of C and m in correlations for tested HX

Heat exchanger C m Error (%)

HX1 0.16442 0.65582 3.528HX3 0.06801 0.57861 2.28HX2 0.34571 0.62296 1.76

0 10,000 20,000 30,000 40,000 50,0000

10,000

20,000

30,000

40,000

50,000

ANN

Φp (W

)

Φe (W)

Correlations

+10%

-10%

Fig. 6. Comparison of 8-6-5-3 ANN and correlation for heat transfer rate(W).


smallest R = 1.089 and r = 0.1387 and the maximum rela-tive error is less than 1.5%.This selection agrees well withthat in Ref. [24].

The predicted temperature differences for two sides ofheat exchangers from trained and tested ANN plottedagainst experimental data is shown in Fig. 5. It can be seenthat both predicted results are well close to the correspond-ing measured variables. In this study, the predicted heattransfer rates obtained by configuration 8-6-5-3 ANN,and those by dimensionless correlations from Peng [21],were compared. It is noted that heat transfer correlations inshell-side could be shown as ln(Nu/Pr1/3) = C + m ln(Re),and the constants C and m are listed in Table 5 [21]. Thecomparison results are shown in Fig. 6. For most of data,the ANN error is within ±2% while the correlation error iswithin ±8%. The ANN predictions are much better thanthose of correlations. Thus, for the tested heat exchangersat hand, ANN is superior to correlation for prediction.

Prediction performance of heat exchanger is one ofimportant objective to a designer or engineer so as tounderstand the performance before performing the experi-mental investigations. There are many approaches, whichcan be used. As usual, for example, the data informationobtained by experiments can be compressed as a compactform in correlation such as Nusselt number vs. Reynoldsnumber and Prandtl numbers, Nu = f (Re,Pr), sometimesincluding geometrical factors. However, there exist someassumptions in deriving the correlation, which generallyare not quite valid for real problem. For example, it is very

often to assume the heat coefficient along heat transfer wallto be constant and the temperature difference between hotand cold fluid to be constant, and fluid properties are oftenindependent on fluid temperature. In fact, these assump-tions do not always hold for an actual heat exchanger.As shown in the above figures, the precision of ANN ismuch better than that of simplified correlation. It is canbe seen that we can directly obtain the heat transfer ratesfrom the input information through the network, insteadof using them to get Nusselt numbers from correlations,and then in turn indirectly obtain the heat transfer rates.On the other hand, when designing a heat exchanger undergiven inlet mass flow rate and temperature, the outlet tem-perature or sometimes temperature difference should beevaluated. Under this case, the heat transfer rate needs tobe predicted. The ANN approach is useful and convenientfor engineers or researchers to predict the performance of agiven heat exchanger with limited experimental data. Itdoes not need to provide accurate and detailed mathemat-ical formulations as well as compact form of correlations.Once the ANN is trained, the weights and biases fromthe network corresponding to a practical heat exchangercan be transferred to engineers or researchers who aregoing to use the test data for prediction. Then engineersmay simply feed these data into the trained network andtherefore quickly make accurate prediction of thermal per-formance for the practical heat exchanger. However, somelimitation should be considered for ANNs, since they donot provide any knowledge about physical phenomena.

5. Conclusions

In the present study, an experimental system for investi-gation on performance of shell-and-tube heat exchangers isset up, and limited experimental data is obtained. TheANN is applied to predict temperature differences and heattransfer rate for heat exchangers. BP algorithm is used totrain and test the network. It is shown that the predictedresults are close to experimental data by ANN approach.Comparison with correlation for prediction heat transferrate shows ANN is superior to correlation, indicating thatANN technique is a suitable tool for use in the predictionof heat transfer rates than empirical correlations. It is rec-ommended that ANNs can be applied to simulate thermalsystems, especially for engineers to model the complicatedheat exchangers in engineering applications.

Acknowledgements

This work was supported by National Defense Scienceand Technology Key Laboratory Foundation of Chnia(Grant No. 51482100204JW0801) and Program for NewCentury Excellent Talents in University of China (GrantNo. NCET-04-0938).


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heat transfer analysis for shell-and-tube heat exchangers

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