The process of conversion in Linz-Donawitz converters is a crucial stage in the production of steel; oxygen is blown on the surface of the melted bath in order to reduce the carbon concentration. At the same time, suitable amounts of coolants are added in order to govern the increase of the bath temperature and reduce the impurities (favoring the slag formation). The aim is to direct the bath of melted steel to the desired final condition, in terms of temperature and carbon content. At around 92-93% of the complete process of conversion, the oxygen blowing is suspended and the In-Blow is performed, i.e. a steel sample is collected by means of a lance introduced in the melted bath and its carbon percentage and temperature measured. A dynamic model, through two characteristic equations, describes the evolution of the carbon percentage and temperature of the melted steel during the final phase of the conversion process, i.e. from the In-Blow until the end. Based on this model, the volume of oxygen to be blown during this phase and the amount of coolant to be added in order to reach the required final (End-Point) conditions of carbon percentage and temperature can be calculated. The model is nonlinear and depends on four parameters to be estimated. Based on a dimensional analysis and on a large set of experimental data, the nominal model has been modified introducing the hypothesis that the parameters are not constant, but depend on the temperature. Within this framework the novel model is identified exploiting Least Squares (LS) methods and its output is compared with the existing practice. (C) 2015 Elsevier Ltd. All rights reserved.