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Three-dimensional thermal-mechanical models for the prediction of heat transfer coefficient distributions with different size beams are investigated. H300 × 300, H250 × 250, and H200 × 200 H-shape steel beams are investigated in a controlled cooling process to obtain the design requirements for maximum uniform temperature distributions and minimal residual stress after controlled cooling. An algorithm developed with the conjugated-gradient method is used to optimize the heat transfer coefficient distribution. In a comparison with the three group results, the numerical results indicate that, with the same model and under the same initial temperature (T=850°C) and final temperature (T=550±10°C), the heat transfer coefficients obtained with the conjugated-gradient method can produce more uniform temperature distribution and smaller residual web stress, with objective functions of the final average temperature Tave±ΔT and maximum temperature difference to minimum min⁡ΔTmax(x,y). The maximum temperature difference is decreased by 57°C, 74°C, and 75°C for Case  1, Case  2, and Case  3, respectively, the surface maximum temperature difference is decreased by 60~80°C for three cases, and the residual stress at the web can be reduced by 20~40 MPa for three cases

Optimal Heat Transfer Coefficient Distributions during the Controlled Cooling Process of an H-Shape Steel Beam