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

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.