Identification of the heat fluxes and thermal resistance on the ingot-mould surface in continuous casting of metals

Abstract

Identification of thermal resistance of the gas-gap between the ingot and mould, as well as the heat flux distribution on the phase change from the solid side during continuous casting of metals is the subject of this article. Analysed parameter estimation problems of the steady-state heat conduction belong to the group of inverse problems. The presented work shows the possibility of applying the least square adjustment method with a priori data for the identification of thermal resistance, the interphase location as well the heat flux distribution on the phase change from the solid side and the temperature field within the ingot and mould. The most important feature of the approach is that the unknown thermal resistance of the gas-gap is obtained from the temperature measurements at a number of sensors located in the wall of the mould, and some sensors located in the ingot, by solving the appropriate inverse problem. The validity of the solution of the inverse problem is checked by comparison with the results of direct problem. In this work, a front-tracking method with an automatic mesh generation finite element technique (so called deforming or moving finite-elements) for steady-state equation conduction-advection problems is developed. Such an approach makes it possible to find the exact solid-liquid interface location, because it is the integral part of the solution. Due to the strong convective nature of the problem (casting velocity, thermal parameters) the special up-wind technique is applied.

Keywords:

• inverse problems
• Stefan problem
• heat conduction

Acknowledgements

The financial assistance of the National Committee for Fundamental Research, Poland, within the grant O R00 0022 06 and O R00 0021 06 is gratefully acknowledged herewith.