  In the present work, we consider the industrial problem of estimating in
real-time the mold-steel heat flux in continuous casting mold. We approach this
problem by first considering the mold modeling problem (direct problem). Then,
we plant the heat flux estimation problem as the inverse problem of estimating
a Neumann boundary condition having as data pointwise temperature measurements
in the interior of the mold domain. We also consider the case of having a total
heat flux measurement together with the temperature measurements. We develop
two methodologies for solving this inverse problem. The first one is the
traditional Alifanov's regularization, the second one exploits the
parameterization of the heat flux. We develop the latter method to have an
offline-online decomposition with a computationally efficient online part to be
performed in real-time. In the last part of this work, we test these methods on
academic and industrial benchmarks. The results show that the parameterization
method outclasses Alifanov's regularization both in performance and
computational cost. Moreover, it proves to be robust with respect to the
measurements noise. Finally, the tests confirm that the computational cost is
suitable for real-time estimation of the heat flux.
