Prediction of Heat Transfer Rates for Shell-and-Tube Heat Exchangers by Artificial Neural Networks Approach Qiuwang WANG Gongnan XIE Ming ZENG Laiqin LUO State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Shaanxi, Xi’an 710049, China

This work used artificial neural network (ANN) to predict the heat transfer rates of shell-and-tube heat exchangers with segmental baffles or continuous helical baffles, based on limited experimental data. The Back Propagation (BP) algorithm was used in training the networks. Different network configurations were also studied. The deviation between the predicted results and experimental data was less than 2%. Comparison with correlation for prediction shows ANN superiority. It is recommended that ANN can be easily used to predict the performances of thermal systems in engineering applications, especially to model heat exchangers for heat transfer analysis.

Keywords: heat transfer rate, Artificial Neural Network, shell-and-tube heat exchanger, back propagation CLC number: TK124 Document code: A Article ID: 1003-2169(2006)03-0257-06 Introduction

Artificial Neural Networks (ANNs) have been developed for about two decades, and now widely used in various application areas such as pattern recognition, system identification, dynamic control and so on. ANN offers a new way to simulate non-linear, or uncertain, or unknown complex system without requiring any explicit knowledge about input/output relationship. ANN has more attractive advantages that, it can approximate any continuous or nonlinear function by using certain network configuration, can be used to learn complex nonlinear relationship from a set of associated input/output vectors, can be implemented to dynamically simulate and control unknown or uncertain process. The Computational Intelligence (CI) technique, e.g. ANNs, Genetic Algorithms (GAs), Fuzzy Logic (FL), has been successfully applied in many scientific researches and engineering practices. In recent years, ANNs have been used in thermal systems for heat transfer analysis, performance prediction and dynamic control. For example, Thibault et al. [1] used a neural network (NN) for heat transfer data analysis, Jambunathan et al. [2] evaluated heat transfer coefficients from experimental data by using a NN, Bittanti et al. [3] used a NN to identify and control heat exchanger, Yang and Sen [4,5] reviewed works in dynamic modeling and controlling of

heat exchangers using ANNs and GAs, Diaz et al. [6-10] did lots of works in steady/dynamic simulation and control of heat exchangers using ANNs, Parcheco-Vega et al. [11-14] also did many works in analysis for fin-tube heat exchanger with limited experimental data using soft computing and global regression, Islamoglu et al. [15,16] predicted heat rate for the wire-on-tube heat exchanger and made heat transfer analysis for air flow in corrugated channels. Other researches about heat exchangers control by means of ANNs were reported in references [17-19]. From aforementioned successful applications, it is shown that ANNs are well suitable to thermal analysis in engineering systems, especially in heat exchangers.

In many experimental studies and engineering applications of thermal science, researchers and engineers expect to reduce experimental data into one or more simple and compact dimensionless heat transfer correlations. The disadvantages of the correlation methods are that heat transfer coefficients strongly depend on their definitions and temperature difference, and inevitably need iterative method to obtain correlations when fluid properties are dependent on fluid temperature [20]. However, ANN does not need definition of correlations and iterative method, only needs input/output samples for training a special neural network, in turn, obtaining output results as test samples

Received: March 13, 2006 Qiuwang WANG: Professor

J. of Thermal Science Vol.15, No.3

Nomenclature Qe Experimental heat transfer rate (W) Dc Diameter of center tube (mm) Qp Predicted heat transfer rate by ANN (W) Er Relative error Rew number in water-side M Number of sets of data for train Reo Reynolds number in oil-side N Number of sets of data for test rms Root-mean-squares error Nb Number of baffle Sb Baffle pitch (mm) Nt Number of tube Tw,in Inlet temperature in water-side (K) Pr Prandtl number To,in Inlet temperature in oil-side (K)

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fed into trained network. In the above-mentioned literature, most works were done in thermal analysis for fin-tube heat exchangers, while for shell-and-tube heat exchangers there were few in open literature. For this reason, the objective of this paper is to apply ANN to predict heat transfer rates of shell-and-tube heat exchangers by using experimental data based on back propagation algorithm, and different network configurations were studied, in addition, the predicted results by ANN were compared with those by correlations.

Physical model and experimental data

The three shell-and-tube heat exchangers were experimentally tested by Peng [21]. A detailed description of designed experimental system and manufactured heat exchangers can be found in reference [21]. One is heat exchanger with segmental baffles (hereafter, the heat exchanger is called HX1), as shown in Fig.1 (a), the other two are heat exchangers with continuous helical baffles, as shown in Fig.1 (b). The difference between the latter two heat exchangers is that inlet-outlet flow manner of fluid in shell-sides, of which the structure of the one is middle-in-middle-out (called HX2) and the structure of the other is side-in-side-out (called HX3).

The heat exchangers are 1-2 type, with hot oil flows in shell-side and cold water flows in tube-side. Except for different baffles located in shell-sides, the obvious difference between HX1 and HX2, HX3 is that the latter two have blocked center tubes while the former has not, as shown in Fig.1. There are other differences in geometric parameters such as, total tube number Nt, total baffle number Nb, baffle pitch Sb and diameter of center tube Dc.

Experiments were performed in the Reynolds number ranging from 300 to 7000 in the shell-side, 3000

Fig.1 Shell-and-tube heat exchangers (Made in software SMARTDRAW)

—4000 in the tube-side. Heat transfer rate varied from 20 kW to 50 kW. 39 sets of experimental data were obtained in reference [21]. Trained data of geometric parameters and Reynolds number are listed in Table.1. Note that for sake of brief list each set of experimental dynamic data was only written in Reo. Detailed information can be found in next section. It should be noted that the diameter of center tube in HX1 is zero since there is no center tube. Tested data were listed in Table.2, in which each heat exchanger has two, three and four data samples respectively.

Table.1 Experimental data for training the network (unit: mm) Type Sb Nb Dc Nt Reo

HX1 70 7 0 176 296 525 697 821 1102 1253 1399 1486 1693 1825

HX2 48 9 48 158 1148 1413 3121 4365 4979 5669 5843 6702 6996

HX3 48 9 48 158 571 745 981 1950 2591 2565 3045 3507 4949 5536 7018

Note: Dc=0 in HX1 since it has no center tube.

Qiuwang WANG et al. Prediction of Heat Transfer Rates for Shell-and-Tube Heat Exchangers by Artificial Neural Networks Approach 259

Neural network configuration

ANNs comprise of a great number of interconnected neurons. Fig.2 illustrates a typical network configuration such an ANN consisting of a series of layers, each with a number of nodes. The node (circle point in Fig.2) sometimes called neuron is the basic processor of neural network. Each connection between two nodes with a real value is called weight. Nodes are gathered together into column called layer. For each node, there exists an activation and a bias associated it. Among the various types of ANNs, the feedforward or multilayer perception neural network is widely used in engineering applications. The input information is propagated forward through the network. As shown in Fig.2, the first and last layers are called input layers and output layer with eight nodes and one node respectively, while the others in the middle are called hidden layers. The configuration in Fig.2 has two hidden layers with six and five nodes respectively.

Fig.2 Neural network configuration used for modeling heat exchanger

(Made in software SMARTDRAW) The Back Propagation (BP) algorithm is widely used

to train the network. The main idea of this algorithm is to minimize an error function by steepest descent method to add small changes in the direction of minimization. It simply consists of back-propagating output errors to the network by modifying the weight matrices. More descriptions of BP algorithm can be found in references [1,5]. The drawback of BP algorithm is that it may get stuck in a local minimum and it needs a long time to arrive

at convergence. Varying the learning rate dynamically or using momentum terms can improve the convergence speed. The mathematical background, the procedures for training and testing the ANN, and the description of BP algorithm can be found in the references [22,23].

For the heat exchangers at hand, eight independent parameters were fed into the input layer of the network (as shown in Fig.2): Reynolds numbers, inlet temperature in each sides Rew, Reo ,Tw,in, To,in, total tube number Nt, center tube diameter Dc, baffle number Nb, baffle pitch Sb. The main reason for selection these input variables is that, heat transfer rate is affected by inlet mass flow rate, temperature on each side, and structure of heat exchanger core due to the aforementioned differences among the three exchangers. The effects of tube and baffle arrangements can be considered as that of hydraulic diameter, which was included in Reynolds number. The output layer contains a parameter, heat transfer rate Qp, as the objective of the present study.

A total of 39 sets of data were run in the network, of which M=30 sets of experimental data, as listed in Table.1, were applied to train the network, while the rest N=9 data, as listed in Table.2, were used to test the network. Note that 77% of the experimental data were used for training the network. In Table.1 and Table.2, a set of input variables such as Rew, Reo, Tw, in, To,in , were briefly expressed in Reo, meaning that a Reo refer to a set of dynamic parameters. The selection of test data from each heat exchanger may be somewhat arbitrary, however these data are based on approximate uniform variation of Reo from 300 to 7000 and based on total number of data from each heat exchanger.

Results and discussions

As aforementioned, drawback of BP algorithm is that it may get stuck in a local minimum, therefore the learning rate was being changed during the training process of the network. As this result, the learning rate was finally set to 0.4 based on previous tested experiences [7-13]. The training of the neural network was terminated when the maximum number of training cycles was reached. Note that the selection of the number is a trail process in which it may be changed if the performance of the network during the training is not good enough. In the present study, after a series of trail tests the number of training cycles was chosen 200,000,

Table.2 Experimental data for testing the network

Reo

378a 912a 1371c 1978b 2610b 3480b 4251c 5761c 6625c

Note: superscripts a, b and c refer data from HX1, HX2 and HX3 respectively.

260 Journal of Thermal Science, Vol.15, No.3, 2006

where the maximum relative error between the output of the network and the target output was less than 2.0%. The relative error was defined by

Er=(Qe-Qp)/Qe (1)

where Qp is the predicted results, output of ANN, the Qe

is the experimental data, target output. Note that all of the input/output pairs were normalized in the (0.15, 0.85) range [7-13].

During the training the network, the performance of the network was evaluated by calculating the root-mean-square (rms) values of the output errors

2

1

1 e pM

ei

Q QrmsM Q=

⎛ ⎞−= ⎜ ⎟

⎝ ⎠∑ (2)

As an example, the errors during training 8-6-5-1 network configuration, with two hidden layers with 6 and 5 nodes respectively, were shown in Fig.3 (a). Training was carried out to 200,000 cycles in the present study, based on trail experience. I t can be seen

Fig.3 Training error for configuration 8-6-5-1 ANN (Made in software ORIGIN)

that the maximum error asymptotes at about 100,000 cycles, while the rms error is reached at 80,000 cycles. At the end of training process, the relative errors for training data were shown in Fig.3 (b). Most of all are within 1% region, and the maximum relative error is about 1.7%.

To observe the effects of network configuration, eleven different ANN configurations were studied, as shown in Table.2. R and σare defined by

1 1

1 1 eN N

i Pi i

QR RN N Q= =

= =∑ ∑ (3)

2

1

( )Ni

i

R RN

σ=

−= ∑ (4)

R reflects the average accuracy of the prediction while σreflects the scatter of the prediction. Both quantities are important for an assessment of the relative success of the ANN analysis [5]. For three layers, when the number of hidden node is increased to 6, R is much closer to unity, while R begins to be far from unity when the number is increased from 7. This indicates that adding more hidden node may not improve the predicted results. From Table.3, the configurations with four layers have more accuracy of prediction than those with five layers. It is also noted that adding more hidden layers may not make the prediction better. Thus, in this case, configuration 8-6-5-1 is selected for testing, with R=1.002959 andσ=0.02117, and the maximum relative error is less than 1.7%.

In this study, the predicted heat transfer rates obtained by configuration 8-6-5-1 ANN, and those by dimensionless correlations from Peng [21], were compared. The results are shown in Fig.4. For most of the data, the ANN error is within ±2% while the correlation error is within ±8%. This shows that ANN is superior to correlation for prediction.

Fig.4 Comparison of 8-6-5-1 ANN and correlation for

shell-an-tube heat exchangers (Made in software ORIGIN)

Qiuwang WANG et al. Prediction of Heat Transfer Rates for Shell-and-Tube Heat Exchangers by Artificial Neural Networks Approach 261

Prediction of heat exchanger performance is one of the important objectives to a designer or engineer so as to understand the performance before perform the experimental investigations. There are many approaches to predict the performance. As usual, for example, the data information obtained by experiment can be compressed as compact form in correlation such as Nusselts number vs. Reynolds number and Prandtl numbers, Nu=f (Re, Pr), sometimes including geometric factors. However, there exist some assumptions in deriving the correlation, which generally are not quite valid for real problem. For example, most researchers often consider that the heat transfer coefficient along the wall is constant, the temperature of the wall between the hot and cold side is constant, and the fluid properties are independent on fluid temperature. These assumptions do not hold for an actual heat exchanger. As shown in above figure, the precision of ANN is much better than that of simplified correlation. It can be seen that we can directly obtain the heat transfer rates from the input information through the network, instead of using them to get Nusselt number from correlations and in turn indirectly obtaining the heat transfer rates. The ANN approach is useful and convenient for engineers or researchers to predict the performance of a given heat exchanger with limited experimental data, without needing an accurate and detailed mathematical formulation, and without correlating the information into compact form. Once the ANN was trained, the weights and biases from the network, which corresponding to a practical heat exchanger, can be transferred to engineers or researchers who are going to use the tested data for prediction.

Conclusions

In the present study, the ANN is applied to predict heat transfer rates for shell-and-tube heat exchangers. BP algorithm is used to train the network. The results show that the predicted heat transfer rates by ANN approach are much closer to experimental data, indicating that ANN technique is more suitable in the prediction of heat transfer rates than empirical correlations. It is recommended that ANNs can be applied to simulate thermal systems, especially for engineers to model heat exchangers in engineering applications.

Acknowledgements

This work was supported by Higher Academy Young Teacher Foundation Project of Fok Ying-Tung Education Foundation (Grant No. 91056) and Program for New Century Excellent Talents in University of China (Grant No. NCET-04-0938).

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Table.3 Comparison of errors by different ANN configurations Train error Test error

Configuration max(Er) (%) rms (%) R σ

8-3-1 2.0391 0.8446 1.006639 0.04752

8-4-1 2.0333 0.753 1.004873 0.03467

8-5-1 1.7868 0.6886 1.005505 0.04161

8-6-1 1.2911 0.509 0.995436 0.03145

8-7-1 1.2209 0.5996 0.993042 0.03590

8-4-4-1 1.7431 0.753 1.025406 0.06203

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8-6-5-4-1 1.6543 0.7598 1.010841 0.02424

8-6-5-5-1 1.5535 0.6908 1.013189 0.02916

Note: max(Er) is the maximum relative error

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