Development of a Mathematical Model for Predicting the Average Molten Zone Thickness of HDPE Pipes During Butt Fusion Welding

Currently, the determination of the molten zone thickness in HDPE pipes during butt fusion welding primarily depends on experimental and numerical methods, leading to high costs and reduced efficiency. In this study, a mathematical (MM) model based on Neumann's solution for the melting of a semi-infinite region was developed to efficiently predict the average molten zone (AMZ) thickness of HDPE pipes under varying heating temperatures and heating times while incorporating the effects of heat convection. Additionally, a two-dimensional CFD model was constructed using finite element analysis (FEA) to validate the MM model. Welding pressure was not considered in this study. The effects of heating temperature, heating time, and heat convection on the AMZ thickness in HDPE pipes were systematically analyzed. The heating temperature at the heated end of HDPE ranged from 190 °C to 350 °C in 20 °C increments, with a temperature of 28 °C as the ambient and initial setting, and the heating time was set to 180 s for both the MM and CFD models. The results demonstrate a strong correlation between the AMZ thickness predictions from the MM and CFD models. The relative error between the MM and CFD models ranges from 0.280% to 10,830% with heat convection and from -2.398% to 8.992% without heat convection. Additionally, for the MM model, the relative error between cases with and without heat convection ranges from 0.243% to 0.433%, whereas for the CFD model, it varies between 1.751% and 3.189%. These findings confirm the reliability of the MM model developed in this study and indicate that thermal convection has a minimal impact on AMZ thickness prediction for large-diameter, thick-walled HDPE pipes.