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Analysis of a heterogeneous functionally graded material with a spherical void exposed to time-dependent ramp-type heating according to the TPL heat conduction model

Crossref DOI link: https://doi.org/10.1038/s41598-025-11471-3

Published Online: 2025-07-24

Update policy: https://doi.org/10.1007/springer_crossmark_policy

Authors

Megahid, Sami F.
Funding

Funding for this research was provided by:

Mansoura University
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Text and Data Mining valid from 2025-07-24

Version of Record valid from 2025-07-24
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Article History

Received: 24 May 2025

Accepted: 10 July 2025

First Online: 24 July 2025

Declarations

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: The authors declare that they consent to publish the article.

: The authors declare no competing interests.

: The submitted work is original, and the manuscript has not been submitted to another journal for simultaneous consideration.

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