Fractional heat transfer DPL model incorporating an exponential Rabotnov kernel to study an infinite solid with a spherical cavity

Ahmed E. Abouelregal; Faisal Alsharif; Hashem Althagafi; Yazeed Alhassan; Ahmed E. Abouelregal; Faisal Alsharif; Hashem Althagafi; Yazeed Alhassan

doi:10.3934/math.2024896

AIMS Mathematics

2024, Volume 9, Issue 7: 18374-18402. doi: 10.3934/math.2024896

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Research article

Fractional heat transfer DPL model incorporating an exponential Rabotnov kernel to study an infinite solid with a spherical cavity

1.
Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia
2.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
3.
Mathematics Department, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Received: 09 February 2024 Revised: 16 May 2024 Accepted: 21 May 2024 Published: 31 May 2024
MSC : 35B35, 37L30, 74F05, 74H10, 80A19

The objective of this study was to investigate the thermodynamic reactions of thermoelastic materials by utilizing a modified mathematical fractional thermoelastic model. This model combines a fractional derivative with Rabotnov's exponential kernel and the idea of a two-phase delay, which makes it possible to show thermoelastic behavior more accurately. The model was utilized to investigate an unbounded material with a spherical cavity subjected to a decreasing and shifting heat flux on its inner surface. The problem was solved using analytical approaches, with a strong focus on the Laplace transform. The transform was numerically inverted to provide time-domain results. The study presented graphs that compared the outcomes of utilizing a single kernel fractional derivative with the results obtained using the Rabotnov kernel and fractional order. These graphs showed how the Rabotnov kernel and fractional order affected the physical fields under investigation. This novel theoretical framework has the potential to be advantageous in diverse domains, including engineering, solid mechanics, and materials science.
- fractional heat conduction,
- Rabotnov's exponential kernel,
- phase delays,
- non-singular kernel,
- heat flux
Citation: Ahmed E. Abouelregal, Faisal Alsharif, Hashem Althagafi, Yazeed Alhassan. Fractional heat transfer DPL model incorporating an exponential Rabotnov kernel to study an infinite solid with a spherical cavity[J]. AIMS Mathematics, 2024, 9(7): 18374-18402. doi: 10.3934/math.2024896

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Abstract

The objective of this study was to investigate the thermodynamic reactions of thermoelastic materials by utilizing a modified mathematical fractional thermoelastic model. This model combines a fractional derivative with Rabotnov's exponential kernel and the idea of a two-phase delay, which makes it possible to show thermoelastic behavior more accurately. The model was utilized to investigate an unbounded material with a spherical cavity subjected to a decreasing and shifting heat flux on its inner surface. The problem was solved using analytical approaches, with a strong focus on the Laplace transform. The transform was numerically inverted to provide time-domain results. The study presented graphs that compared the outcomes of utilizing a single kernel fractional derivative with the results obtained using the Rabotnov kernel and fractional order. These graphs showed how the Rabotnov kernel and fractional order affected the physical fields under investigation. This novel theoretical framework has the potential to be advantageous in diverse domains, including engineering, solid mechanics, and materials science.

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