Artificial Neural Network Analysis on the Heat Transfer and Friction Factor of the Double Tube with Spring Insert

Transcription

1 Artificial Neural Network Analysis on the Heat Transfer and Friction Factor of the Double Tube with Spring Insert P. Naphon* Thermo-Fluids and Heat Transfer Enhancement Laboratory (TFHT), Department of Mechanical Engineering, Faculty of Engineering, Srinakharinwirot University, Ongkarak, Nakhon-Nayok, Thailand. T. Arisariyawong Thermo-Fluids and Heat Transfer Enhancement Laboratory (TFHT), Department of Mechanical Engineering, Faculty of Engineering, Srinakharinwirot University, Ongkarak, Nakhon-Nayok, Thailand. T. Nualboonrueng National Science and Materials Technology Development Center, National Science & Materials Technology Development Agency,4 Thailand Science Park, Phahonyothin Rd., Khlong Luang, Pathum Thani, 0, Thailand Abstract The paper focus is the application of artificial neural networks to analyze the heat transfer and friction factor of the horizontal double tube heat exchanger with spring insert. The optimal artificial neural network model for predicting the heat transfer coefficient and friction factor of the double tube with spring insert is considered. The developed artificial neural network model shows the mean square error (MSE) of and the correlation coefficient (R) of in modeling of overall experimental dataset. The predicted results obtained from the optimize ANN model are verified with the testing experimental data and good agreement is obtained with errors of ±.5%,-5%-+7.5% for heat transfer coefficient and friction factor, respectively. In addition, the predicted results are also validated with those from the other correlations in various literatures. The ANN model results are found to be more accurate than the predicted results obtained from the published correlation. Keywords: ANN; heat transfer coefficient; friction factor; spring insert Introduction Due to providing better and more reasonable solution, ANN have been applied in many engineering applications. There are many researches on the ANN application in the thermal system analysis. Sablani [] developed a non-iterative procedure of an artificial neural network to determine the fluid-to-particle heat transfer coefficient. Mittal and Zhang [] predicted the food thermal process parameters using artificial neural networks. Islamoglu [3,4] applied a new approach of an artificial neural network model for predicting the heat transfer rate of the wire-on-tube type heat exchanger. Wang et al. [5] proposed the generalized neural network correlation for flow boiling heat transfer of R and other refrigerants inside horizontal smooth tubes. Compared with the experimental data, it is much better than that of the existing correlations. Scalabrin et al. [6] proposed a new model of artificial neural networks for predicting the flow boiling heat transfer of the mixtures. Yigit and Ertunc [7] predicted the outlet air temperature and humidity of the wire-on-tube type heat exchanger by using neural networks. Zdaniuk et al [8] used an artificial neural network approach to determine the Colburn j- factors and fanning friction factors of the liquid flow in straight tubes with internal helical fins. Ermis et al. [9] studied the feed-forward back-propagation artificial neural network algorithm to analyze the phase change heat transfer in a finned-tube, latent heat thermal energy storage system. Xie et al. [0,3] analyzed the heat transfer characteristics for shelland-tube heat exchangers and laminar-turbulent heat transfer and flow characteristics of heat exchangers by using artificial neural networks approach. Kurt et al. [] predicted the thermal performance of hot box type solar cooker by using artificial neural network. Tahavvor and Yaghoubi [] applied the ANN to determine the natural convection heat transfer and flow characteristics of a cooled horizontal circular cylinder with constant surface temperature. Taymaz and Islamoglu [4] predicted the laminar convective heat transfer in converging diverging tube by using back-propagation neural network. Alizadehdakhel et al. [5] applied the CFD and artificial neural network modeling for predicting the twophase flow pressure drop. Gao et al. [6] predicted the performance of wet cooling tower using artificial neural network under cross-wind conditions. Bar et al. [7] predicted the pressure drop of non-newtonian liquid flow through piping components using artificial neural network with back propagation algorithm. The proposed approach towards the prediction is done using a multilayer perceptron. Kumar and Balaji [8] estimated the heat generation from multiple protruding heat sources on a vertical plate under conjugate mixed convection by using artificial neural networks. Wu et al. [9] predicted the performance characteristics of a cooling tower under cross flow conditions. Kiran and Rajput [0] studied proposed the effectiveness model for predicting the thermal performance of indirect evaporative cooling by using artificial neural network. Bacilar et al. [] applied the optimize ANN technique for predicting the condensation heat transfer characteristics during downward annular flow of 354

2 R34a in smooth tube. Vaferi et al. [] investigated the thermal behavior of nanofluids flowing through a circular tube by using artificial neural network. As mentioned above, the numerous papers presented the thermal process analysis by using artificial neural networks. From the reviews papers, however, there is no paper presents the heat transfer and flow analysis of the tube with spring insert using ANN. The primary advantages of ANN than conventional regression analysis are: free of linear supposition, have large degrees of freedom, and more effectively deal with non-linear functional forms. The main objective of this study is devoted to find the optimal configuration of ANN model and its topology. The obtained optimal ANN model with the smallest size which show the best performance for predicting the heat transfer coefficient and the friction factor in the double tube heat exchanger with coiled wire insert. The results obtained from the optimal ANN model are verified with the measured data and some reliable published correlations. Experimental Apparatus and Method Experimental Apparatus A schematic diagram of the experimental apparatus used for the heat transfer and friction factor is presented in Fig. which the details presentation of the design, fabrication of the experimental apparatus and evaluation of the data are available in [3]. After the temperature of the cold and hot water are adjusted to achieve the desired level, the water of each loop is pumped out of the storage tank, and is passed through a flow meter, test section, and returned to the storage tank. The test section is made from the straight copper tube with the length of 000 mm as shown in Fig.. The experiments are performed with the test section with three different coiled pitches. The inner diameter and outer diameter of the inner tube are 8.0 and 9.54 mm, respectively. The thermocouples are used to measure the water temperature distribution by extending inside the tube and at the same cross section, the tube wall temperature are measured by mounting on the tube wall and fixed with special glue applied to the outside surface of the inner tube. All the thermocouples are pre-calibrated by dry-block temperature calibrator with 0.0 o C precision. The pressure drop across the test section is measured by the differential pressure transducer (YOKOKAWA, MT0) with the accuracy of 0.0% of full scale. Figure : Schematic diagram of experimental apparatus Figure Schematic diagram of the test section Experimental procedure Experiments were conducted with various inlet temperatures and flow rates of hot water and cold water entering the test section. In the experiments, the hot water flow rate was increased in small increments while the cold water flow rate, inlet cold water and hot water temperatures were kept constant. The inlet hot and cold water temperatures were adjusted to achieve the desired level by using electric heaters controlled by temperature controllers. Before any data were recorded, the system was allowed to approach the steady state. The temperature at each position and pressure drop across the test section were recorded three times. Data Reduction and Uncertainty Analysis Data reduction The data reduction of the measured results is available in [3]. An average heat transfer rate, Q, used in the calculation is ave determined from the hot water-side and cold water-side. The tube-side heat transfer coefficient, h, can be calculated from i an average heat transfer rate obtained from Qave hi Ai T s,ave Tw,ave () where T is an average wall temperature, and s,ave T is an w,ave average water temperature, and A i is the inside surface area of tube. Friction factor for the tube with spring insert, f, can be calculated from P f () u L d i where P is the pressure drop across the test section, is the density of water, d i is the inner diameter of tube, u is the velocity of water, and L is the length of tube. Uncertainty analysis The uncertainty and accuracy of the measurement are available in [3]. The uncertainties of measurements data and the relevant parameters obtained from the data reduction process are calculated. The maximum uncertainties of the relevant parameters in the data calculation are based on Coleman and Steel method [4]. The maximum uncertainties of relevant parameters are ±5% for Reynolds number, ±7.5% for the Nusselt number and ±7.5% for friction factor. 3543

3 Artificial Neural Networks Approach Due to its simplicity, flexibility, availability a various training algorithms as well as its large modeling capacity [4,5-7], the non-linear mathematical models of artificial neural network get great attention. The processors are analogous to biological neurons in human brain which are connected to each other by weighted links over which signals can pass. General, neuron receives multiple input parameters from other neurons in proportion to their connection weights and generates a single output parameters which may be propagated to several other neurons [8]. There are many types of artificial neural networks, the feed forward neural network has been become the most popular in engineering applications [9], which is somewhat simple in structure and easily analyzed mathematically. While the back propagation network is the first and most commonly used feed forward neural network because there exists a mathematically strict learning scheme to train the network and guarantee mapping between input parameters and output results. As shown in Fig. 3, this ANN configuration has one input layer, one hidden layer and one output layer. During the feed forward stage, a set of input parameter is supplied to the input nodes and the information is transferred forward through the network to the nodes in the output layer. The nodes perform non-linear input output transformations by means of sigmoid activation function. The mathematical background, the procedures for training and testing the optimize ANN model, and account of its history can be found in the text by Haykin [30]. ANN configuration model as shown in Fig. 3, the input parameters are the hot and cold water mass flow rates, hot and cold water inlet temperatures, H/d while the output parameters are the heat transfer coefficient and friction factor. Figure 3: Proposed optimal ANN model configuration For training and testing the neural networks results, input data patterns and corresponding targets are required. In developing a ANN model, the available data set (70 80% of the data [3]) is divided into two dataset: the first dataset is used to train the ANN model, and then it is validated with the another dataset [3]. The training process of the ANN model can be done by comparing with the predicted results of the ANN model to the input data. The weights and biases are changed in order to minimize the error between the predicted output results and the input data. The scheme used in this study is the back propagation algorithm. The proposed ANN model configuration is set by selecting the number of hidden layer and the number of nodes in hidden layer. The number of nodes in the input and output layers can be determined from physical variables which the calculation procedure of the optimize ANN model is shown in Fig. 3. Results and Discussion ANN performance analysis Based on the predicted results, the optimize ANN model performance can be evaluated by a regression analysis between the network outputs. In order to obtain the accuracy of the ANN model, the correlation coefficient (R) and the mean square error (MSE) are used as the characteristic parameters to obtain the agreement of training and predicting process of the ANN model. Correlation coefficient is a measurement of how well the variation in the predicted outputs which is explained by the measured data, and the R value between the measured data and predicted output results is defined by [6,33] as follows: cov( a, p ) R (3) cov( a,a ) cov( p, p ) where cov(a, p) is the covariance between a and p sets which represent the measured data and the predicted results obtained from ANN, respectively, and is calculated from: cov( a, p ) E a a p p (4) where E is the expected value, µ a and µ p are the mean value of a set and p set, respectively. In addition, cov(a, a) and cov(p, p) are the auto covariances of a and p sets, respectively, and are expressed as follows: cov( a,a ) E a a (5) cov( p, p ) E p p (6) The correlation coefficient ranges between and +. The R values closer to + indicate a stronger agreement of training and predicted results, while the values closer to indicate a stronger negative relationship between training and predicting process. The mean square error is calculated from [6,33,4] as follows: N i i (7) N i MSE a p where a i and p i are the experimental results and predicted results of i set, and N is the number of data patterns. 3544

4 Backward propagation algorithm selection There are many training functions can be adopted in the training process, including trainlm, trainrp, traingcgb, traingcgf, and traincgp which the backward propagation algorithms are used in the present study. For all backward propagation algorithms, a three-layer ANN model with a tangent sigmoid transfer function (tansig) for hidden layer and a linear transfer function (purelin) for output layer are used. The nine neurons are used in the hidden layer for all backward propagation algorithms (Fig. 3). The Levenberg Marquardt algorithm with a minimum MSE and R is used to act as the training function. This is because it has higher stability and faster convergence rate than other training algorithms [9]. ANN structure optimization Determination of the optimal number of hidden layers and the numbers of neuron in each hidden layers are the most important step in development of an ANN model. In general, the suitable numbers of hidden neurons are not known and often determined by trial and error process. Determination of an optimal number of hidden neurons is a difficult task while it depends on three external issues: () correlation complexity between independent and dependent variables being handled by ANN, () number of training and testing dataset which are available and (3) amount of noise which exists in the dataset [,35]. Large numbers of hidden neurons require high computation times and often result in over-fitting, while low numbers of hidden neurons cannot relate dependent/dependent to independent/independent variables with acceptable accuracy [,36]. Although, smaller network, which has fewer weights and biases usually have better generalization capability, two different strategies, i.e., network growing and network pruning are proposed [,35] for the evaluation of an optimal number of hidden neurons. The network growing method starts with a small network and increases hidden neurons until a desired accuracy is achieved, while the network pruning strategy commences with a large number of hidden units, and then reduces the extra neurons through the training stage [,37]. Network growing strategy is more efficient than pruning algorithms where the majority of the learning time devoted to the networks which are bigger than necessary []. In this section, the heuristic design principle of acquiring decision factors to determine the quantity of hidden nodes and the configuration of hidden layers is presented. There are three empirical correlations for determination of number in hidden layer [38] as follows; n i CN k (8) i0 i where K is the simple number, if i > N, CN 0 = 0. N m n c (9) where c is a constant which belongs to [,0]. N log n (0) For one hidden layer of ANN model, the correlation for calculation of node number in hidden layer is proposed by [39] as follows; N mn () For put forward, the empirical correlation [40] for determination the node number in hidden layer can be expressed as; N 0. 43mn 0. m. 54n 0. 77m () Which N is the node number in hidden layer, n is the node number in input layer and m is the node number in output layer. According to above formulas, the node number in hidden is calculated and in the range of 3-4. The three neurons are used in the hidden layer as an initial guess. With an increase in the number of neurons, the networks give several correlation coefficient (R) and different mean square error (MSE) values for the training process. Figures 4-5 show the variation of mean square error (MSE) and correlation coefficient (R) of the optimize ANN model with number of hidden layer for testing and overall (training+testing) dataset. It can be seen that the MSE and R values tend to decrease and to increase with increasing hidden layer from 3 to 9, respectively. With 9 hidden layers, the MSE reaches it minimum value as well as maximum R. When the number of hidden layers exceeded 9, the MSE and R tend to increase and to decrease, respectively. It can be said that increasing the number of hidden layer more than nine results in over-fitting of the ANN model over training dataset and also cannot generalize the rules to test dataset as well. Therefore, the neural network containing 9 hidden layers is chosen as the best case. The training process is stopped after 50 iterations for the Levenberg Marquardt algorithm because the MSE and R values converge after 50 epochs as shown in Figure 6. Mean squared errors (MSE) R value Overall dataset MSE Testing dataset MSE Number of hidden neurons Figure 4: MSE of various ANN models for testing and overall (training + testing) data set Overall dataset R Testing dataset R Number of hidden neurons Figure 5: R values of various ANN models for testing and overall (training + testing) data set 3545

5 Mean squared errors (MSE) Best training performance point Epochs Figure 6: MSE variation versus epochs for optimal ANN model in training process Comparison of optimal ANN model with the measured training data subset A computer program with C++ software has been developed by using the back propagation algorithm. ANN model sensitivity is examined for ten different networks with 3, 5, 8, 9,, 3, 5, 7, 9 and neural nodes in the hidden layer. Table shows the values of MSE and R which existed between the experimental data and the predicted results obtained from optimal ANN model over training, testing as well as overall overall dataset (training+testing). According to Table, the optimize ANN model shows the beast predictive capability for the prediction of the convective heat transfer coefficient and friction factor data, MSE and R of and , respectively. These values of statistical criteria and error indexes confirm the excellent agreement between the measured data and the predicted results obtained from the optimal ANN model. Figure 7 shows the comparison between those values of friction factor which are obtained from the optimal ANN model and experimental training data subset. The optimal ANN model shows the R= between the predicted results and the experimental results of the training dataset. The optimal ANN model has predicted the friction factor of a training subset with MSE of Again, Figure 8 presents the comparison between the measured heat transfer coefficient training dataset and the predicted results from the optimal ANN model. It can be seen that the ANN model prediction for the heat transfer coefficient yield a MSE of , a R of with the experimental training dataset. Figure 8 also is provided with a straight line indicating perfect prediction. Table : Evaluation of the optimal ANN model through statistical accuracy analysis Hidden neuron Data set Statistical accuracy analysis MSE R 3 Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Training Testing Overall Predicted friction factor Equality line Friction factor R = MSE = Experimental friction factor Figure 7: Comparison between the measured friction factor and the predicted results from ANN model over the training subset Predicted heat transfer coefficient Equality line Heat transfer coefficient R = MSE = Experimental heat transfer coefficient Figure 8: Comparison between the measured heat transfer coefficient and the predicted results from ANN model over the training subset 3546

6 Comparison of the optimal ANN model with the measured testing data subset A plot of the predictions as a function of the experimental testing dataset is shown in Fig. 9. It can be seen that the maximum error of the friction factor between the predicted results obtained from the optimal ANN model and the measured testing dataset is less than-5%-+7.5%. Similarly, the predicted heat transfer coefficient results obtained from the optimal ANN model are compared with those from the experimental testing dataset as shown in Fig. 0. It can be seen that the predicted results are as good as those obtained from the experimental data within ±.5% error band % Experimental results -5% Figure 9: Comparison between the measured friction factor and the predicted results from ANN model over the testing subset 5 optimal ANN model. It can be seen from the figure that the deviation is in the range of ±5%. Naphon [3] proposed an empirical heat transfer coefficient correlation for water flowing through the horizontal double tube with coiled wire insert. As shown in Fig., the predicted results using the proposed correlation are reasonable agreement with the predicted results obtained from the optimal ANN model and the deviation is in the range of ±0%. Again, the predicted heat transfer coefficient results obtained from the optimal ANN model are verified with those from the reliable published correlations [36]. It can be seen that the predicted results from the correlation [36] are higher than those from the optimal ANN model. Reasonable agreement is obtained and lie within 0%-+40% as shown in Fig. 3. Predicted results from correlation Correlation from [3] +5% -5% Figure : Comparison between the predicted friction factor from ANN model And the predicted results from correlation [3] % Experimental results -.5% Predicted results from correlation Correlation from [3] +0% -0% Figure 0: Comparison between the measured heat transfer coefficient and the predicted results from ANN model over the testing subset Comparison of optimal ANN model with the published correlations Figure shows the comparison between the predicted friction factor results obtained from the published correlation [3] and the predicted friction factor results obtained from the Figure : Comparison between the predicted heat transfer coefficient from ANN model and the predicted results from correlation [3] 3547

7 Predicted results from correlation Correlation from [36] +40% 0% Figure 3: Comparison between the predicted heat transfer coefficient from ANN model and the predicted results from correlation [36] Conclusion In this paper, the application of feed-forward and backpropagation artificial neural network algorithm for analysis the heat transfer coefficient and friction factor are presented. Due to its simplicity, flexibility, availability a various training algorithms as well as its large modeling capacity, the nonlinear mathematical models of artificial neural network get great attention in the thermal process analysis. The present obtained from the optimal ANN model are verified by comparing with the experimental results and from published correlations. It is found that the optimal ANN model provides better agreement with the experimental results data, compared to the correlation results. Nomenclatures A area f friction factor h heat transfer coefficient, kw/(m o C) m mass flow rate, kg/s Q heat transfer rate, kw T temperature, o C density, kg/m 3 d tube diameter, m H spring pitch, m L length, m P pressure, kpa Re Reynolds number u velocity, m/s Subscripts ave average h hot in inlet out outlet w water c cold i inside o outside t tube Acknowledgements The authors would like to express their appreciation to the Excellent Center for Sustainable Engineering (ECSE) of the Srinakharinwirot University (SWU) for providing financial support for this study. References [] S.S. Sablani, A neural network approach for noniterative calculation of heat transfer coefficient in fluid particle systems, Chemical Engineering and Processing 40 (00) [] G.S. Mittal, J. Zhang, Prediction of food thermal process evaluation parameters using neural networks, International Journal of Food Microbiology 79 (00) [3] Y. Islamoglu, A new approach for the prediction of the heat transfer rate of the wire-on-tube type heat exchanger use of an artificial neural network model, Applied Thermal Engineering 3 (003) [4] Y. Islamoglu, A. Kurt, Heat transfer analysis using ANNs with experimental data for air flowing in corrugated channels, International Journal Heat and Mass transfer 47 (004) [5] W.J. Wang, L.X. Zhao, C.L. Zhang, Generalized neural network correlation for flow boiling heat transfer of R and its alternative refrigerants inside horizontal smooth tubes, International Journal of Heat and Mass Transfer 49 (006) [6] G. Scalabrin, M. Condosta, P. Marchi, Mixtures flow boiling: modeling heat transfer through artificial neural networks, International Journal of Thermal Sciences 45 (006) [7] K.S. Yigit, H.M. Ertunc, Prediction of the air temperature and humidity at the outlet of a cooling coil using neural networks, International Communications in Heat and Mass Transfer 33 (006) [8] G.J. Zdaniuk, L.M. Chamra, D.K. Walters, Correlating heat transfer and friction in helicallyfinned tubes using artificial neural networks, International Journal of Heat and Mass Transfer 50 (007) [9] K. Ermis, A. Erek, I. Dincer, Heat transfer analysis of phase change process in a finned-tube thermal energy storage system using artificial neural network, International Journal of Heat and Mass Transfer 50 (007) [0] G.N. Xie, Q.W. Wang, M. Zeng, L.Q. Luo, Heat transfer analysis for shell-and-tube heat exchangers with experimental data by artificial neural networks approach, Applied Thermal Engineering 7 (007) [] H. Kurt, K. Atik, M. Özkaymak, Z. Recebli, Thermal performance parameters estimation of hot box type solar cooker by using artificial neural network, International Journal of Thermal Sciences 47 (008)

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