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A modified mathematical model for thermo-viscous thermal conduction incorporating memory-based derivatives and the Moore–Gibson–Thomson equation

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Abstract

Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier’s equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors.

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Acknowledgements

The authors present their appreciation to King Saud University for funding the publication of this research through the Researchers Supporting Program (RSP2024R167), King Saud University, Riyadh, Saudi Arabia.

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Researchers Supporting Project number (RSP2024R167), King Saud University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    Ahmed E. Abouelregal

  2. Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, Romania

    Marin Marin

  3. Academy of Romanian Scientists, Bucharest, Romania

    Marin Marin

  4. Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Sameh S. Askar & Abdelaziz Foul

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  1. Ahmed E. Abouelregal
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Correspondence to Ahmed E. Abouelregal.

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Abouelregal, A.E., Marin, M., Askar, S.S. et al. A modified mathematical model for thermo-viscous thermal conduction incorporating memory-based derivatives and the Moore–Gibson–Thomson equation. Continuum Mech. Thermodyn. (2024). https://doi.org/10.1007/s00161-024-01284-6

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