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Article


Title

Solution of Inverse Problem of Non-Stationary Heat Conduction Using a Laplace Transform

Authors

[ 1 ] Instytut Energetyki Cieplnej, Wydział Inżynierii Środowiska i Energetyki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.9] Environmental engineering, mining and energy

Year of publication

2022

Published in

Heat Transfer Engineering

Journal year: 2022 | Journal volume: in press

Article type

scientific article

Publication language

english

Keywords
EN
  • inverse heat conduction problem
  • Laplace transform
  • Cauchy problem
  • stability of solution to the inverse problem
Abstract

EN This paper presents some solutions to the one-dimensional Cauchy-type transient inverse heat conduction problem. Based on known courses of temperature and the heat flux on one of the boundaries of the region, courses of temperature and heat flux on the opposite boundary of the region were determined with the use of the Laplace’s transform. Solution of the inverse problem does not require determination of temperature distribution on subsequent time moments inside the region. Stability of the solution to the inverse problem of the Cauchy type was investigated by means of determining the minimal time step ensuring the stability of the solution. Two examples of one-dimensional transient inverse problems were solved. The first one is related to the reconstruction of shock temperature change on the boundary of the region based on known courses of temperature and heat flux on the opposite boundary. The second one concerned the reconstruction of the heat flux acting on one of the boundaries through a period of time. In both considered problems the reconstructed boundary conditions were discontinuous. Stable results were obtained for both investigated examples, however, the stability of the inverse problem depended on the length of time step.

Pages (from - to)

1 - 11

DOI

10.1080/01457632.2022.2113445

URL

https://www.tandfonline.com/doi/abs/10.1080/01457632.2022.2113445

Ministry points / journal

70.0

Impact Factor

2.431 [List 2021]

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