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Effect of the photothermal Moore–Gibson–Thomson model on a rotating viscoelastic continuum body with a cylindrical hole due to the fractional Kelvin-Voigt model

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Abstract

According to recent research, the theoretical consequences of viscoelastic materials may be adequately described using fractional calculus. A novel model for the fractional time derivative of the Kelvin-Voigt type of viscoelastic semiconductor material has been provided in this study. The Atangana and Baleanu (AB) fractional derivatives operator is utilized, which employs the generalized Mittag–Leffler function as a nonlocal and non-singular kernel and respects all features of fractional derivatives. The Moore–Gibson–Thompson (MGT) photothermal heat transfer model has also been considered to explain the mechanism of photosensitive heat transfer and the interplay between plasma, elastic, and heat signals. This fractional model is used to explore thermal and photoacoustic interactions when an infinite viscoelastic rotating material with a circular cylindrical hole is exposed to a time-dependent variable heat in the presence of an axial constant magnetic field. The solutions of photothermal field variables are obtained using Laplace transform methods, and the technique of Fourier series expansions is applied to obtain the inversions. Results have been listed to examine how the fractional-order and mechanical viscoelastic relaxation parameters affect different photo-thermoelastic variables that have physical meaning.

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Abbreviations

\(\lambda_{0} ,\mu_{0}\) :

Lam´e’s constants

\(\alpha_{t}\) :

Thermal expansion coefficient

\(C_{E}\) :

Specific heat

\(\gamma_{0} = \left( {3\lambda_{0} + 2\mu_{0} } \right)\alpha_{t}\) :

Thermal coupling parameter

\(T_{0}\) :

Reference temperature

\(\theta = T - T_{0}\) :

Temperature increment

T :

Absolute temperature

\(\overrightarrow {{\text{u}}}\) :

Displacement vector

\(e = {\text{div}}\overrightarrow {{\text{u}}}\) :

Cubical dilatation

\(\sigma_{ij}\) :

Stress tensor

\(e_{ij}\) :

Strain tensor

\(\delta_{ij}\) :

Kronecker’s delta function

\(n_{0}\) :

Equilibrium carrier concentration

\(\vec{H}\) :

Magnetic field

\(\vec{h}\) :

Induced magnetic field

\(d_{0} = \left( {3\lambda_{0} + 2\mu_{0} } \right)d_{n}\) :

Diffusion coupling parameter

\(\mu_{v} ,\lambda_{v} ,\gamma_{v} ,d_{v}\) :

Viscoelastic relaxation times

K :

Thermal conductivity

\(\rho\) :

Material density

\(\alpha\) :

Fractional order

\(D_{t}^{\alpha }\) :

Fractional operator

\(\vec{E}\) :

Induced electric field

N :

Carrier density

\(\tau_{0}\) :

Relaxation time

\(\tau_{ij}\) :

Maxwell stress

\(E_{g}\) :

Semiconducting energy gap

\( d_{n}\) :

Electronic deformation coefficient

\(D_{E}\) :

Diffusion coefficient

\(\vec{q}\) :

Heat flux vector

\(\kappa\) :

Thermal activation coupling parameter

\(\tau\) :

Ifetime of photogenerated electron

\(\vec{J}\) :

Current density

\(\mu_{0}\) :

Magnetic permeability

G :

Carrier photogeneration source

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Authors and Affiliations

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

    Husam Alfadil & Ahmed E. Abouelregal

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

    Ahmed E. Abouelregal

  3. Research Center for Interneural Computing, China Medical University, Taichung, Taiwan

    Ömer Civalek

  4. Department of Mechanical Engineering, Technology Faculty, Fırat University, Elazig, Turkey

    Hakan F. Öztop

Authors
  1. Husam Alfadil
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  2. Ahmed E. Abouelregal
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  3. Ömer Civalek
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  4. Hakan F. Öztop
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All authors discussed the findings, and the final version of the manuscript was reviewed and approved by all.

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Correspondence to Hakan F. Öztop.

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Alfadil, H., Abouelregal, A.E., Civalek, Ö. et al. Effect of the photothermal Moore–Gibson–Thomson model on a rotating viscoelastic continuum body with a cylindrical hole due to the fractional Kelvin-Voigt model. Indian J Phys 97, 829–843 (2023). https://doi.org/10.1007/s12648-022-02434-9

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