`Mathematical Problems in EngineeringVolume 2006, Article ID 23754, 12 pageshttp://dx.doi.org/10.1155/MPE/2006/23754`

## Mathematical study of transport phenomena along a tuyere of the Teniente converter

1Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMR 2071 CNRS-UChile, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170/3, Santiago, Chile
2Instituto de Innovación en Minería y Metalurgia SA,, Avenida del Valle 738, Ciudad Empresarial, Huechuraba, Chile

Received 14 March 2005; Revised 29 July 2005; Accepted 24 August 2005

Copyright © 2006 J. San Martín et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a comprehensive mathematical model of transport phenomena which occur along a tuyere of the Teniente converter during injection of oxygen-enriched air. Inlet pressure, gas velocity and temperature, the dimensions of the tuyere, and the properties of gas are the basic data. From these inputs, temperature distribution of the refractory walls of the converter around the tuyere as well as the velocity, pressure, and the Mach number along the pipe can be calculated. In this model, the heat transfer through the metal jacket of the tuyere and the refractory lining are duly taken into account. More precisely, a mathematical model is developed where the equations of momentum and energy of the gas are coupled with the equations of heat transfer inside the solid part. This new model couples a partial differential equation in the solid part with four ordinary differential equations in the gas flow.