Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials

Abstract

This study proposes a comprehensive heat conduction model that incorporates fractional time derivatives and two-phase lags to describe the behavior of non-simple thermoelastic materials accurately. Generalized fractional differential operators with non-singular kernels are introduced. This type of fractional derivative includes the Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives. The model also consists of the two-temperature idea, which considers the effect of microstructure through a two-stage delay approach. Interactions of a thermoelastic nature caused by the rapid heating of an isotropic substance under the influence of an external body force were studied as a practical application of the new concept. There has been some discussion about the effect of the discrepancy index and fractional differential operators. Finally, the graphical representations obtained from the numerical simulations were used to explain the behavior of the studied physical fields. The generalized fractional heat transfer model is demonstrated to be capable of producing a temperature forecast that is in close agreement with experimental data. As a result, the proposed model may be useful for solving difficulties in heat transfer, anomalous transport, and other branches of engineering analysis.

Keywords

• fractional thermoelasticity
• two-temperature
• phaselags
• non-singular kernels