Factor Analysis for Forced and Mixed Convection Laminar Heat Transfer in a Horizontal Tube Using Artificial Neural Network

Artificial neural network (ANN) has shown its superior predictive power compared to the conventional approaches in many studies. However, it has always been treated as a “black box” because it provides little explanation on the relative influence of the independent variables in the prediction process. In our previous work (Tam et al., 2006), an index of contribution extracted from the ANN correlation was primarily introduced to analyze the relative importance of the associated independent variables on our forced convective turbulent heat transfer data in a horizontal tube (Ghajar and Tam, 1994). The most and the least important variables were determined quantitatively and found to be thoroughly conforming to the empirical correlation and physical phenomena. In this study, we have extended the method to a more complicated data set, forced and mixed convection developing laminar flow in a horizontal tube with uniform wall heat flux. The parameters influencing the Nusselt number for this data set were Reynolds number, Grashof number, Prandtl number, the length-to-diameter ratio, and the bulk-to-wall viscosity ratio. Due to the complexity of the problem it is difficult to determine the influence of the individual independent variables. According to literature, for laminar heat transfer involving entrance and mixed convection effects, Rayleigh number and Graetz number are both important. Through the re-arrangement of those variables, the factor analysis clearly showed that the Rayleigh number has a significant influence on the mixed convection heat transfer data and the forced convection heat transfer data is more influenced by the Graetz number. The results clearly indicate that the factor analysis method can be used to provide an insight into the influence of different variables or a combination of them on complicated heat transfer problems.