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Generalized Heat Equation with the Caputo–Fabrizio Fractional Derivative for a Nonsimple Thermoelastic Cylinder with Temperature-Dependent Properties

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Abstract

In the current paper, a generalized thermoelastic model with two-temperature characteristics, including a heat transfer equation with fractional derivatives and phase lags, is proposed. The Caputo–Fabrizio fractional differential operator is used to derive a new model and to solve the singular kernel problem of conventional fractional models. The suggested model is then exploited to investigate responses of an isotropic cylinder with variable properties and boundaries constantly exposed to thermal or mechanical loads. The elastic cylinder is also assumed to be permeated with a constant magnetic field and a continuous heat source. The governing partial differential equations are formulated in dimensionless forms and then solved by the Laplace transform technique together with its numerical inversions. The effects of the heat source intensity and fractional order parameter on the thermal and mechanical responses are addressed in detail. To verify the integrity of the obtained results, some comparative studies are conducted by considering different thermoelastic models.

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The authors received no financial support for the research, authorship, and publication of this paper.‎

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Authors and Affiliations

  1. Department of Mathematics, College of Science and Arts, Jouf University, 75911, Al-Qurayyat, Saudi Arabia

    A. E. Abouelregal

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

    A. E. Abouelregal

  3. Coordination of General Courses, Istanbul Ticaret University, 34445, Istanbul, Turkey

    A. H. Sofiyev

  4. Scientific Research Center for Composition Materials, Azerbaijan State Economic University, 1001, Baku, Azerbaijan

    A. H. Sofiyev

  5. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, 61357-43337, Ahvaz, Iran

    H. M. Sedighi

  6. Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, 61357-43337, Ahvaz, Iran

    H. M. Sedighi

  7. Department of Mathematics, Jamoum University College, Umm Al-Qura University, Jamoum, 25371, Makkah, Saudi Arabia

    M. A. Fahmy

  8. Department of Basic Sciences, Faculty of Computers and Informatics, Suez Canal University, 41522, Ismailia, Egypt

    M. A. Fahmy

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  1. A. E. Abouelregal
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  2. A. H. Sofiyev
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Correspondence to H. M. Sedighi.

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Translated from Fizicheskaya Mezomekhanika, 2022, Vol. 25, No. 6, pp. 135–151.

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Abouelregal, A.E., Sofiyev, A.H., Sedighi, H.M. et al. Generalized Heat Equation with the Caputo–Fabrizio Fractional Derivative for a Nonsimple Thermoelastic Cylinder with Temperature-Dependent Properties. Phys Mesomech 26, 224–240 (2023). https://doi.org/10.1134/S1029959923020108

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