COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China ©2006 Tsinghua University Press & Springer-Verlag Factor Analysis of Convective Heat Transfer for a Horizontal Tube in the Turbulent Flow Region Using Artificial Neural Network H. K. Tam 1 *, S. C. Tam 2 , A. J. Ghajar 3 , L. M. Tam 1 1. Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, China 2. Department of Mathematics, Faculty of Science and Technology, University of Macau, China 3. School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Oklahoma, USA Email: hktam@umac.mo Abstract Artificial neural network (ANN) has shown its superior predictive power compared to the conventional approaches in many studies. However, it is always treated as a ‘black box’ because it provides little explanation to the relative influence of the independent variables in the prediction process. Ghajar et al. [1] used the ANN method to develop an empirical correlation for the heat transfer data in a horizontal tube with a reentrant inlet under uniform wall heat flux boundary condition in the transition region. In their work, the least and the most important variables were examined using the coefficient matrices based on a single training. However, the method was only applied to one set of experimental data. The applicability of their method to other data sets is not known. In this study, the method proposed in the previous study is modified and a new set of experimental data for different inlet configurations (square-edged and bell-mouth) from the work of Ghajar and Tam [2] in the turbulent region are used to further verify this method. An index of contribution is defined in this study. Furthermore, the gradient method used and the number of neurons and iterations for each training are carefully examined. Using the revised method and the index of contribution defined in this study, an ANN correlation is established and the Reynolds number (Re) and the Prandtl number (Pr) are observed as the most important parameters. The length-to-diameter ratio (x/D) and the viscosity ratio (µ b /µ w ) 0.14 are found to be the least important parameters. Key words: convective heat transfer, artificial neural network, turbulent flow, index of contribution *Student paper competition INTRODUCTION Heat transfer inside horizontal tubes in the transitional and turbulent flow regimes have been studied experimentally by various researchers in the past. Usually, the research results are presented in the form of heat transfer correlations. The form of the correlations is based either on different theoretical models or they are completely empirical. The coefficients of the correlations are usually determined by the conventional least squares method. Kakac et al. [3] documented some of the most well accepted correlations in the transition and turbulent flow regions. Recently, Ghajar et al. [1] proposed a new correlation in the transition region based on the method of artificial neural network (ANN) with excellent accuracy. In their paper, it was mentioned that ANN can also be used in the determination of the most and least important variables using the coefficient matrices obtained from the weight and bias matrices of the ANN correlation. However, there are some unanswered questions regarding this technique, such as (1) applicability of this technique to other data sets and (2) besides the most important variables, i.e., the normalized Reynolds and Grashof numbers, and least important variables, i.e., the normalized Sieder and Tate factor (µ b /µ w ) 0.14 , the importance of the normalized Prandtl number can not be seen. Therefore, this method is modified and then verified by using a different set of experimental data, the turbulent heat transfer data for uniformly heated horizontal tube fitted with different inlet configurations of Ghajar and Tam [2]. Furthermore, the gradient method selected, the number of neurons and iterations used for training will be analyzed and defined systematically in this study. Based on the defined network parameters, the index of contribution for each independent variable will be found from the ANN correlation by the revised method.