Mathematical model for the temperature profiles of steel pipes quenched by water cooling rings

The quenching process is one of the most important steps in steel heat treatment and has a significant impact on the quality of the product. In systems with water cooling rings, there are several operational parameters that affect the performance of the heat treatment, such as the longitudinal and angular speeds of the pipe, the water flow rate and pressure. Mathematical models have been developed to predict the temperature profile in the steel pipe, to investigate the causes of defect formation and to allow a better control of the cooling conditions. In the present work, two-dimensional (2D) and tridimensional (3D) models were developed to simulate the heat transfer during the cooling of the pipe. The models were verified, and the tridimensional model was validated by industrial tests. Several simulations have been carried out to compare the 2D and 3D approaches and the effect of the angular speed of the pipe was investigated. The results indicated that the temperatures calculated using the 2D and 3D models are different. It was demonstrated that an increase in the rotation speed of the pipe leads to a more uniform temperature distribution. However, for rotation speeds superior to 6 rad/s, no significative effect in the temperature profile is obtained by increasing the speed of rotation. Keywords: Temperature profile, Quenching, Heat transfer, Mathematical modelin