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The dissolution of Ti additions in liquid steel during secondary steelmaking occurs in a two step process. In the first step, a steel shell solidifies around the initial cold addition, whereas in the second step, after this shell has remelted, the Ti dissolves directly in the steel bath. The initial presence of this steel shell modifies the position of dissolution and influences the local concentration and thus the inclusion formation. Further complications arise from the fact that part of the Ti will dissolve while enclosed by the steel shell, altering the alloy composition first released in the ladle and effectively shortening the subsequent free dissolution period. The duration of the steel shell period and the fraction of predissolved Ti have been investigated using a conservative one-dimensional sharp interface model solving the coupled heat and mass transfer in a cylindrical shell/addition composite. The influence of the convection conditions and the original Ti radius was evaluated in a parametric study. A pronounced effect of the convective heat transfer on the shell melting time was found. It is thus concluded that the dissolution behaviour is strongly dependent on the local flow conditions, which is determined by factors such as stirring conditions and addition characteristics.