Inverse finite element technique for identification of thermal resistance of gas-gap between the ingot and mould in continuous casting of metals

Identification of thermal resistance of the gas-gap between the ingot and mould during continuous casting of metals is the subject of the present article. Analysed parameter estimation problem of the steady-state heat conduction belongs to the group of inverse problems. The present work shows the possibility of applying the least square adjustment method with a priori data for identification of thermal resistance as well as the interphase location and the temperature field within the ingot and mould. The most important feature of the approach is that the unknown thermal resistance is identified by solving appropriate inverse problem from the temperature measurements at the number of sensor located in the wall of the mould. The validity of the solution of the inverse problem is checked by comparison with the results of direct problem. In the present 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 to build the mathematical model of the heat transfer process. Such an approach makes us possible to find solid-liquid interface location, because it is the integral part of the solution of the considered problem. Due to the strong convective nature of the boundary problem (casting velocity, thermal parameters) the special up-wind technique is applied to avoid the oscillation of numerical results.