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In this work, we investigate the estimation of the transient mold-slab heatflux in continuous casting molds given some thermocouples measurements in themold plates. Mathematically, we can see this problem as the estimation of aNeumann boundary condition given pointwise state observations in the interiorof the domain. We formulate it in a deterministic inverse problem setting.After introducing the industrial problem, we present the mold thermal model andrelated assumptions. Then, we formulate the boundary heat flux estimationproblem in a deterministic inverse problem setting using a sequential approachaccording to the sequentiality of the temperature measurements. We considerdifferent formulations of the inverse problem. For each one, we develop noveldirect methodologies exploiting a space parameterization of the heat flux andthe linearity of the mold model. We construct these methods to be divided intoa computationally expensive offline phase that can be computed before theprocess starts, and a cheaper online phase to be performed during the castingprocess. To conclude, we test the performance of the proposed methods in twobenchmark cases.

Novel Methodologies for Solving the Inverse Unsteady Heat Transfer Problem of Estimating the Boundary Heat Flux in Continuous Casting Molds