Modelo matemático preditivo para caracterização da resposta térmica temporal de tubos temperados por imersão em um tanque de água

• Ano de defesa: 2017
• Autor(a) principal: Pedro Henrique Vasconcellos Apipe
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Estudo experimental; Processo de têmpera; Modelo matemático; Volumes finitos; Aço Tratamento termico; Método dos elementos finitos; Modelos matemáticos; Engenharia mecânica
• Link de acesso: http://hdl.handle.net/1843/BUOS-AU6HCN

The knowledge of the cooling curve during the quenching process in steel is essential to define the mechanical properties and the final quality of the material. As these properties vary considerably as a function of the cooling rate, it is fundamental to monitor and control the thermal response during this treatment. This work presents the development of a one-dimensional predictive mathematical model for the characterization of the temporal thermal response in the wall of quenched pipes by immersion in a water tank. In this model, the pipe wall was divided into several control volumes. The heat conduction equation was applied for each volume during a given time step and the rate of heat transfer by conduction on the inner and outer surface of the pipe was considered equal to the convective heat transfer rate between the pipe and water. The equations of the model were solved by the finite volume method through totally implicit scheme. In parallel, a simplified analytical solution was developed to perform the numerical validation of the model. Mesh tests revealed that meshes with time steps equal to 0.2s and number of control volumes equal to 100 presented an excellent compromise between the computational efforts and the obtained results. Mean relative errors less than 8% between the numerical solution and the simplified analytical solution proved the numerical validation of the model. For the physical validation of the model, tests on a heat treatment line with a pipe that had been immersed in a water tank were performed. The specimen (pipe) was instrumented with type K thermocouples, which were arranged along its length and close to its internal and external surface. Using average heat transfer coefficients between 1000 (W/m².K) and 25000 (W/m².K), numerical solutions were generated and compared to the results obtained experimentally. The average relative errors for the entire cooling process were less than 14.5% and close to 7% for cooling until 62% of the total time. The main conclusion of this work was that the model, fed through the combination of constant average heat transfer coefficients, presented a good precision in the forecast of the cooling curve, especially until the second third of the process.