Novel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting molds

Morelli, Umberto EmilBarral, PatriciaQuintela Estévez, PeregrinaRozza, GianluigiStabile, Giovanni2023-06-232023-06-232023Morelli UE, Barral P, Quintela P, Rozza G, Stabile G. Novel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting molds. Int J Numer Methods Eng. 2023;124(6):1344-1380. doi: 10.1002/nme.71670029-5981http://hdl.handle.net/10347/30766In this article, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann boundary condition given pointwise state observations in the interior of the domain. We formulate it in a deterministic inverse problem setting. After introducing the industrial problem, we present the mold thermal model and related assumptions. Then, we formulate the boundary heat flux estimation problem in a deterministic inverse problem setting using a sequential approach according to the sequentiality of the temperature measurements. We consider different formulations of the inverse problem. For each one, we develop novel direct methodologies exploiting a space parameterization of the heat flux and the linearity of the mold model. We construct these methods to be divided into a computationally expensive offline phase that can be computed before the process starts, and a cheaper online phase to be performed during the casting process. To conclude, we test the performance of the proposed methods in two benchmark caseseng© 2022 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.http://creativecommons.org/licenses/by/4.0/Boundary condition estimationContinuous castingData assimilationHeat transferInverse problemOptimal controlNovel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting moldsjournal article10.1002/nme.71671097-0207open access