The analysis of the stability of the Cauchy problem in the cylindrical double-layer area

• Autorzy: Ciałkowski Michał , Joachimiak Magda , Mierzwiczak Magdalena , Frąckowiak Andrzej , Olejnik Aleksander , Kozakiewicz Adam

Identyfikatory

DOI

10.24425/ather.2023.149735

• Języki publikacji: EN

Abstrakty

EN

Ceramic protective coats, for instance, on turbine blades, create a double-layer area with various thermophysical properties and they require metal temperature control. In this paper, it is implemented by formulating 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 calculations were performed for a varied thickness of the ceramic layer, with consideration 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 regularization method in obtaining stable solutions at random data disturbance.

Słowa kluczowe

EN

cauchy problem; quasiregularization method; protective layer; cylindrical; double-layer area

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2023
• Tom: Vol. 44, no 4
• Strony: 563--579
• Opis fizyczny: Bibliogr. 46 poz., rys.

Twórcy

autor

Ciałkowski Michał

• Poznan University of Technology, Institute of Thermal Engineering, Piotrowo 3a, 60-965, Poznań, Poland

autor

Joachimiak Magda

• Poznan University of Technology, Institute of Thermal Engineering, Piotrowo 3a, 60-965, Poznań, Poland

autor

Mierzwiczak Magdalena

• Poznan University of Technology, Institute of Applied Mechanics, Jana Pawła II 24, 60-965, Poznań, Poland

autor

Frąckowiak Andrzej

• Poznan University of Technology, Institute of Applied Mechanics, Jana Pawła II 24, 60-965, Poznań, Poland

autor

Olejnik Aleksander

• Military University of Technology, Sylwestra Kaliskiego 2, 00-908 Warszawa, Poland

autor

Kozakiewicz Adam

• Military University of Technology, Sylwestra Kaliskiego 2, 00-908 Warszawa, Poland

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