Thermoelastic reactions in a long and thin flexible viscoelastic cylinder due to non-uniform heat flow under the non-Fourier model with fractional derivative of two different orders

Ahmed Abouelregal; Meshari Alesemi; Husam Alfadil; Ahmed Abouelregal; Meshari Alesemi; Husam Alfadil

doi:10.3934/math.2022474

AIMS Mathematics

2022, Volume 7, Issue 5: 8510-8533. doi: 10.3934/math.2022474

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Thermoelastic reactions in a long and thin flexible viscoelastic cylinder due to non-uniform heat flow under the non-Fourier model with fractional derivative of two different orders

1.
Department of Mathematics, College of Science and Arts, Al-Qurayyat, Jouf University, Saudi Arabia
2.
Basic Sciences Research Unit, Jouf University, Saudi Arabia
3.
Department of Mathematics, College of Science, University of Bisha, Bisha, Saudi Arabia

Received: 12 December 2021 Revised: 15 February 2022 Accepted: 16 February 2022 Published: 28 February 2022
MSC : 74A35, 74F05, 80A19, 65M60

In this paper, a new fractional model of non-Fourier heat conduction is presented that includes phase delays and two fractional orders. To derive the proposed model, the fractional integral Atangana-Baleanu (AB) operator with non-singular and non-local kernels was used. The proposed model has been applied to solve a one-dimensional thermoelasticity problem that includes an annular cylinder of a flexible material whose inner and outer surfaces are subjected to a variable heat flux that depends on time and temperature and is free from traction. The Laplace transform approach was applied to find the general solution to the problem and to obtain the expressions for the different physical fields. To estimate the effects of the fractional-order parameters and instantaneous time on the responses of all thermophysical field variables, comparisons are presented in figures and tables.
- fractional-order,
- thermoelasticity,
- annular cylinder,
- phase delays,
- Atangana-Baleanu operator
Citation: Ahmed Abouelregal, Meshari Alesemi, Husam Alfadil. Thermoelastic reactions in a long and thin flexible viscoelastic cylinder due to non-uniform heat flow under the non-Fourier model with fractional derivative of two different orders[J]. AIMS Mathematics, 2022, 7(5): 8510-8533. doi: 10.3934/math.2022474

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Abstract

In this paper, a new fractional model of non-Fourier heat conduction is presented that includes phase delays and two fractional orders. To derive the proposed model, the fractional integral Atangana-Baleanu (AB) operator with non-singular and non-local kernels was used. The proposed model has been applied to solve a one-dimensional thermoelasticity problem that includes an annular cylinder of a flexible material whose inner and outer surfaces are subjected to a variable heat flux that depends on time and temperature and is free from traction. The Laplace transform approach was applied to find the general solution to the problem and to obtain the expressions for the different physical fields. To estimate the effects of the fractional-order parameters and instantaneous time on the responses of all thermophysical field variables, comparisons are presented in figures and tables.

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