Abstract
In this paper, the authors discuss an inverse boundary problem for the axi-symmetric steady-state heat equation, which arises in monitoring the boundary corrosion for the blast-furnace. Measure temperature at some locations are used to identify the shape of the corrosion boundary.
The numerical inversion is complicated and consuming since the wear-line varies during the process and the boundary in the heat problem is not fixed. The authors suggest a method that the unknown boundary can be represented by a given curve plus a small perturbation, then the equation can be solved with fixed boundary, and a lot of computing time will be saved.
A method is given to solve the inverse problem by minimizing the sum of the squared residual at the measuring locations, in which the direct problems are solved by axi-symmetric fundamental solution method.
The numerical results are in good agreement with test model data as well as industrial data, even in severe corrosion case.
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* Project supported by the National Natural Science Foundation of China (No. 10431030).
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Tan, Y., He, R. Boundary Identification for a Blast Furnace*. Chin. Ann. Math. Ser. B 28, 571–582 (2007). https://doi.org/10.1007/s11401-006-0014-x
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DOI: https://doi.org/10.1007/s11401-006-0014-x