The analysis of the stability of the Cauchy problem in the cylindrical double-layer area
[ 1 ] Instytut Energetyki Cieplnej, Wydział Inżynierii Środowiska i Energetyki, Politechnika Poznańska | [ 2 ] Instytut Mechaniki Stosowanej, Wydział Inżynierii Mechanicznej, Politechnika Poznańska | [ P ] employee
[2.9] Mechanical engineering[2.10] Environmental engineering, mining and energy
2023
scientific article
english
- Cauchy problem
- quasiregularization method
- protective layer
- cylindrical double-layer area
EN Ceramic protective coats, for instance, on turbine blades, cre ate a double-layer area with various thermophysical properties and they require metal temperature control. In this paper, it is implemented by for mulating a Cauchy problem for the equation of thermal conductivity in the metal cylindrical area with a ceramic layer. Due to the ill posed problem, a regularization method was applied consisting in the notation of thermal balance for the ceramic layer. A spectral radius for the equation matrix was taken as the stability measure of the Cauchy problem. Numerical calcula tions were performed for a varied thickness of the ceramic layer, with consid eration of the non-linear thermophysical properties of steel and a ceramic layer (zirconium dioxide). A polynomial was determined which approximates temperature distribution in time for the protective layer. The stability of solutions was compared for undisturbed and disturbed temperature values, and thermophysical parameters with various ceramic layer thickness. The obtained calculation results confirmed the effectiveness of the proposed regu larization method in obtaining stable solutions at random data disturbance.
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