Stabilization of boundary conditions obtained from the solution of the inverse problem during the cooling process in a furnace for thermochemical treatment
[ 1 ] Instytut Energetyki Cieplnej, Wydział Inżynierii Środowiska i Energetyki, Politechnika Poznańska | [ P ] employee
2024
scientific article
english
- gas nitriding
- cooling control inside a furnace for thermochemical treatment
- inverse heat conduction problem IHCP
- modified Tikhonov regularization
- heat transfer coefficient (HTC)
EN Heating and cooling inside a furnace intended for thermochemical treatment is the basis for the execution of processes characterized by lower energy consumption, and, thus, lower costs. Precise control of the thermochemical treatment requires knowledge of the temperature, heat flux, and the heat transfer coefficient (HTC) on the boundaries of the treated elements. The mentioned boundary conditions have been established in this paper for the cooling stage inside the furnace for thermochemical treatment by solving the inverse heat conduction problem. The paper analyzes the impact of regularization of the inverse problem on the stability of the calculated boundary conditions during cooling. Numerical tests were performed for the Tikhonov and Tikhonov-Phillips regularization as well as their modification. The computational method presented in the paper was developed for online control of thermochemical treatment processes. Online control necessitates minimizing computation time. The paper investigated the impact of the regularization term on the solution of the inverse problem with a constant value of the regularization parameter. The choice of regularization method was based on a norm that measures the oscillation of the solution of the inverse problem. The approach presented in the paper allowed for a reduction in computation time and the obtaining of a stable solution to the inverse heat conduction problem for both numerical tests and experimental data.
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