The purpose of this study is to develop mathematical models to explore the mixing and its related phenomena in converter bath. Specifically, first, a mathematical model of a physical model converter, which was scaled down to 1/6th of a 30 t vessel, was developed in this study. A number of parameters were studied and their effects on the mixing time were recorded in a top blown converter. Second, a mathematical model for a combined top-bottom blown was built to investigate the optimization process. Then, a side tuyere was introduced in the combined top-bottom blown converter and its effects on the mixing and wall shear stress were studied. Moreover, based on the above results, the kinetic energy transfer phenomena in a real converter were investigated by applying the mathematical models. A simplified model, in which the calculation region was reduced to save calculation compared to simulations of the whole region of the converter, was used in the mathematical simulation. In addition, this method was also used in the simulation of real converters. This approach makes it possible to simulate the Laval nozzle flow jet and the cavity separately when using different turbulence models. In the top blown converter model, a comparison between the physical model and the mathematical model showed a good relative difference of 2.5% and 6.1% for the cavity depth and radius, respectively. In addition, the predicted mixing time showed a good relative difference of 2.8% in comparison to the experimental data. In an optimization of a combined top-bottom blown converter, a new bottom tuyere scheme with an asymmetrical configuration was found to be one of the best cases with respect to a decreased mixing time in the bath. An industrial investigation showed that the application effects of the new tuyere scheme yield a better stirring condition in the bath compared to the original case. Furthermore, the results indicated that the mixing time for a combined top-bottom-side blown converter was decreased profoundly compared to a conventional combined top-bottom blown converter. It was found that the side wall shear stress is increased by introducing side blowing, especially in the region near the side blowing plume. For a 100 t converter in real, the fundamental aspects of kinetic energy transfer from a top and bottom gas to the bath were explored. The analyses revealed that the energy transfer is less efficient when the top lance height is lowered or the flowrate is increased in the top blowing operations. However, an inverse trend was found. Namely, that the kinetic energy transfer is increased when the bottom flowrate is increased in the current bottom blowing operations. In addition, the slag on top of the bath is found to dissipate 6.6%, 9.4% and 11.2% for the slag masses 5, 9 and 15 t compared to the case without slag on top of the surface of the bath, respectively. / <p>QC 20151015</p>