Contribution analysis of dimensionless variables for laminar and turbulent flow convection heat transfer in a horizontal tube using artificial neural network

The artificial neural network (ANN) method 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 this study, the ANN method was used to develop empirical correlations for laminar and turbulent heat transfer in a horizontal tube under the uniform wall heat flux boundary condition and three inlet configurations (re-entrant, square-edged, and bell-mouth). The contribution analysis for the dimensionless variables was conducted using the index of contribution defined in this study. The relative importance of the independent variables appearing in the correlations was examined using the index of contribution based on the coefficient matrices of the ANN correlations. For the turbulent heat transfer data, the Reynolds and Prandtl numbers were observed as the most important parameters, and the length-to-diameter and bulk-to-wall viscosity ratios were found to be the least important parameters. The method was extended to analyze the more complicated forced and mixed convection data in developing laminar flow. The dimensionless parameters influencing the heat transfer in this region were the Rayleigh number and the Graetz number. The contribution 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 of this study clearly indicated that the contribution analysis method can be used to provide correct physical insight into the influence of different variables or a combination of them on complicated heat transfer problems.