Explicit reconstruction of space- and time-dependent heat sources with integral transforms

This work addresses an explicit methodology based on integral transforms for the inverse problem of reconstructing space and time dependent heat sources. The basic idea is to perform an integral transformation of the heat conduction equation and obtain an explicit expression for the integral transfo...

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Bibliographic Details
Published in:Numerical heat transfer. Part B, Fundamentals Fundamentals, 2021-04, Vol.79 (4), p.216-233
Main Authors: Negreiros, Anny R., Knupp, Diego C., Abreu, Luiz A. S., Silva Neto, Antônio J.
Format: Article
Language:English
Subjects:
Conduction heating
Conductive heat transfer
Eigenvectors
Heat sources
Integral transforms
Inverse problems
Noise levels
Time dependence
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Summary:This work addresses an explicit methodology based on integral transforms for the inverse problem of reconstructing space and time dependent heat sources. The basic idea is to perform an integral transformation of the heat conduction equation and obtain an explicit expression for the integral transformed heat source in terms of the integral transformed temperatures. Once temperature measurements within the medium are available, they are transformed with the same kernel and readily employed in the derived expressions for the representation of the sought heat source as an eigenfunction expansion. In order to critically illustrate the approach, one- and two-dimensional examples are considered, with different functional forms of the sought heat source and different noise levels in the simulated experimental data.
ISSN:1040-7790
1521-0626
DOI:10.1080/10407790.2020.1850148