Mathematical models for tracking the melting of cored wire during its injection into the steel bath have been developed in the past though important aspects of the formulations have not been discussed in sufficient detail. As a result, it is difficult to use the results of these models to derive benefits for a specific steel melting shop.A general purpose mathematical model has been developed at R & D, Tata Steel, using the finite difference approach with a fully implicit scheme to simulate the process of cored wire injection taking into account the different operating practices encountered in the steel shop. Numerical simulation of this kind of problem, involving moving boundary, typically suffers from the limitation that the progressive solidification of frozen layers that takes place is not made part of the thermal balance till it attains the size of a full node and thus the heat gained or lost by this "partial node" is not accounted for till such time. An alternative numerical formulation has been developed to rectify this.Owing to the difficulty in making a direct validation, this model has been verified through a novel approach. This work suggests that the use of different wire dimensions (13-18 mm diameter and 0.4-0.6 mm casing), depending on the steel grades to be processed, is necessary in order to extract the maximum benefit.KEY WORDS: mathematical model; steelmaking; calcium treatment; cored wire; injection metallurgy; deoxidation; alloy addition.

An essential feature in steel refining is the injection of calcium in the steel ladle in the form of a cored wire for de‐oxidation and inclusion modification. The melting behaviour of these cored wires has an important influence on the efficiency of the injection process, castability of steel and the product quality. The calculation of the time for melting of the casing of the cored wire and the subsequent release of the filling materials into the bath cannot be done without resorting to an elaborate mathematical model due to the complexity of the heat transfer from the bath to the wire. In particular the formation of a solid shell around the wire and consequent lowering of the heat transfer needs to be addressed accurately. A mathematical model for calculating the melting time of the casing has been developed at R & D, Tata Steel. This model describes the freezing and melting process during the travel of the cored wire in the steel bath. The model has been validated against published data. Owing to the complexity of obtaining a direct validation, a novel indirect method has been adopted. The variation in the operating conditions demands variation in the cored wire parameters to make the injection process equally efficient under all conditions. The model has also been used to formulate the specification of cored wire to suit the injection temperature of different grades of steel.

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