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Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area.

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Title: Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area.
Authors: Ciałkowski, Michał1 (AUTHOR), Joachimiak, Magda1 (AUTHOR) magda.joachimiak@put.poznan.pl, Mierzwiczak, Magdalena2 (AUTHOR), Frąckowiak, Andrzej1 (AUTHOR), Olejnik, Aleksander3 (AUTHOR), Kozakiewicz, Adam3 (AUTHOR)
Source: Heat Transfer Engineering. 2025, Vol. 46 Issue 22, p2005-2017. 13p.
Subjects: Cauchy problem, Heat conduction, Numerical calculations, Thermal equilibrium, Inverse problems, Thermal properties, Protective coatings
Abstract: Various types of protective coatings, such as ceramics, are used to increase the efficiency of metal parts that are exposed to high heat loads. Maintaining mechanical properties and acceptable thermal stresses requires temperature control for components such as turbine blades, gun barrels or combustion chambers. This paper presents a new method for controlling thermal parameters by solving a non-stationary Cauchy problem for the heat conduction equation. The solution is presented in a cylindrical two-layer area considering the variation of the thermophysical parameters of the metal and ceramic. The non-linear equation was solved by successive approximation method using differential quotients for the space and time variable. In order to regularize the ill-conditioned inverse problem, a quasi-regularization method was applied by performing an energy balance for the ceramic. Numerical calculations were carried out for different thicknesses of the ceramic layer. The temperature, heat flux density and heat transfer coefficient for the protective layer were calculated. For the same values of the heat transfer coefficient for 0.1 and 0.3 mm thick protective layers, the difference in permissible gas temperature differs by 10.5 °C. [ABSTRACT FROM AUTHOR]
Copyright of Heat Transfer Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 189849710
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area.
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  Data: <searchLink fieldCode="AR" term="%22Ciałkowski%2C+Michał%22">Ciałkowski, Michał</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Joachimiak%2C+Magda%22">Joachimiak, Magda</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> magda.joachimiak@put.poznan.pl</i><br /><searchLink fieldCode="AR" term="%22Mierzwiczak%2C+Magdalena%22">Mierzwiczak, Magdalena</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Frąckowiak%2C+Andrzej%22">Frąckowiak, Andrzej</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Olejnik%2C+Aleksander%22">Olejnik, Aleksander</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kozakiewicz%2C+Adam%22">Kozakiewicz, Adam</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Heat+Transfer+Engineering%22">Heat Transfer Engineering</searchLink>. 2025, Vol. 46 Issue 22, p2005-2017. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Cauchy+problem%22">Cauchy problem</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+conduction%22">Heat conduction</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+calculations%22">Numerical calculations</searchLink><br /><searchLink fieldCode="DE" term="%22Thermal+equilibrium%22">Thermal equilibrium</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink><br /><searchLink fieldCode="DE" term="%22Thermal+properties%22">Thermal properties</searchLink><br /><searchLink fieldCode="DE" term="%22Protective+coatings%22">Protective coatings</searchLink>
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  Label: Abstract
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  Data: Various types of protective coatings, such as ceramics, are used to increase the efficiency of metal parts that are exposed to high heat loads. Maintaining mechanical properties and acceptable thermal stresses requires temperature control for components such as turbine blades, gun barrels or combustion chambers. This paper presents a new method for controlling thermal parameters by solving a non-stationary Cauchy problem for the heat conduction equation. The solution is presented in a cylindrical two-layer area considering the variation of the thermophysical parameters of the metal and ceramic. The non-linear equation was solved by successive approximation method using differential quotients for the space and time variable. In order to regularize the ill-conditioned inverse problem, a quasi-regularization method was applied by performing an energy balance for the ceramic. Numerical calculations were carried out for different thicknesses of the ceramic layer. The temperature, heat flux density and heat transfer coefficient for the protective layer were calculated. For the same values of the heat transfer coefficient for 0.1 and 0.3 mm thick protective layers, the difference in permissible gas temperature differs by 10.5 °C. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Heat Transfer Engineering is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1080/01457632.2024.2416285
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 13
        StartPage: 2005
    Subjects:
      – SubjectFull: Cauchy problem
        Type: general
      – SubjectFull: Heat conduction
        Type: general
      – SubjectFull: Numerical calculations
        Type: general
      – SubjectFull: Thermal equilibrium
        Type: general
      – SubjectFull: Inverse problems
        Type: general
      – SubjectFull: Thermal properties
        Type: general
      – SubjectFull: Protective coatings
        Type: general
    Titles:
      – TitleFull: Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area.
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            NameFull: Ciałkowski, Michał
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            NameFull: Joachimiak, Magda
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            NameFull: Mierzwiczak, Magdalena
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            NameFull: Frąckowiak, Andrzej
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            NameFull: Olejnik, Aleksander
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            – D: 01
              M: 12
              Text: 2025
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              Y: 2025
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              Value: 46
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            – TitleFull: Heat Transfer Engineering
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