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Magneto-thermoelastic behaviour of a finite viscoelastic rotating rod by incorporating Eringen’s theory and heat equation including Caputo–Fabrizio fractional derivative

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Abstract

This paper addresses a modified constitutive equation by incorporating the size effect of nanostructured materials and a new formulation of Fourier's law including Caputo–Fabrizio fractional heat conduction equation with a non-singular kernel. The Kelvin–Voigt model is used to characterize the viscoelastic behavior of the material. In the absence of mechanical relaxation and nonlocal effects, the results of different generalized theories of thermoelasticity can be achieved as specific cases. The presented model is then applied to analyze the magneto-thermoelastic interactions in a viscoelastic rotating rod subject to a moving heat source. The analytical solutions are obtained through Laplace transform method and its reversal followed by residue calculations. Several illustrations are presented to evaluate the effects of system parameters, fractional order, nonlocal and vicsocity parameters, magnetic field and the velocity of heat source on the features of physical variables.

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Acknowledgements

The authors would like to sincerely thank Mr. Ali H. Shirazi for his cooperation in producing the quality image for the considered problem. H.M. Sedighi is grateful to the Research Council of the Shahid Chamran University of Ahvaz for its financial support (Grant No. SCU.EM1400.98).

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Authors and Affiliations

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

    Ahmed E. Abouelregal

  2. Basic Sciences Research Unit, Jouf University, Sakaka, Saudi Arabia

    Ahmed E. Abouelregal

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

    Ahmed E. Abouelregal

  4. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

  5. ‏Drilling Center of Excellence and Research Center, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Hamid M. Sedighi

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Abouelregal, A.E., Sedighi, H.M. Magneto-thermoelastic behaviour of a finite viscoelastic rotating rod by incorporating Eringen’s theory and heat equation including Caputo–Fabrizio fractional derivative. Engineering with Computers 39, 655–668 (2023). https://doi.org/10.1007/s00366-022-01645-2

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