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Mathematical modeling of heat transfer during water spray cooling and controlled slow cooling of steel tubes Mwenifumbo, Steve

Abstract

Mathematical models were developed which incorporate heat flow, phase transformation kinetics, and temperature and composition dependent thermal-physical properties to predict through-thickness temperature evolution during the manufacturing of steel tubular products under industrial cooling conditions. The two industrial cooling conditions investigated were an 'in-line' water quench, used to control austenite grain growth, and controlled slow cooling, applied at the end of the process to produce the desired microstructure and mechanical properties. This investigation combined computer modeling with laboratory measurements on industrial samples (i.e., AISI 5130 as-rolled steel tubes). A 2-D finite-difference axisymmetric accelerated cooling model (ACM) and a 2-D finite-difference circumferential controlled slow cooling model (CSC) were coded to run on a personal computer. The ACM model can handle multi-stage cooling with varying boundary conditions including radiation, natural convection, and forced convection. The model has the capacity to handle temperature and microstructural dependent thermal-physical properties associated with different phases that can form in the material. The CSC is capable of simulating the effects of tube spacing, forced air-cooling, and various ambient conditions. The basic heat diffusion parts of both the ACM and CSC models, including the routines associated with the liberation of latent heat, were validated against a benchmark commercial FEM software package, ABAQUS™. In addition, the results of the CSC model were verified experimentally by acquiring thermal data from a tube instrumented with thermocouples during the slow cooling of 5130 steel tubes. The CSC model predictions agreed reasonably well with the measured data, capturing the various factors affecting heat-transfer between tubes and their surroundings. A sensitivity analysis conducted with the CSC model indicated that the radiation exchange between different components (e.g., adjacent tubes, tubes and the fume hood, tubes and the floor) plays a significant role in heat-transfer. In addition, several factors influenced the effective emissivity within the model, including loose scale formation on the tubes, geometric assumptions in the model to approximate radiation view factors, and assumptions related to the temperature of the surrounding furnace environment.

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