Conclusion
In the context of this paper, a modified fractional model with a
dual-phase-lag and two parameters \(\alpha,\ \beta\) (2FDPL) is
introduced. In the limited cases, the proposed model reduces to various
classical, generalized and fractional thermoelasticity models (CTE, LS,
DPL and SFLS). According to this new model, the distributions of the
physical quantities for a half-plane (\(x>0\)) are discussed.
Numerical simulation results yield the following conclusions:
- The studied fields are observed to be very sensitive to the fractional
parameters \(\alpha,\ \beta\).
- The numerical results show that the fractional model 2FDPL provides
physically acceptable and accurate results, especially for\(\alpha=0.75,\ \beta=0.75\) .
- The effects of the fractional parameter \(\alpha,\ \beta\) on all the
physical fields under consideration are very obvious.
- The existence of the external body force has a clear effect on the
temperature, displacement and the stress.
- The results of our study differ from the classical model (CTE) of the
phenomenon of limited velocities of the propagation of heat waves.
- The obtained results are very useful for the material science
researchers and material designers who are working on the development
of the thermoelasticity and fractional thermoelasticity models.
- The technique introduced in this study is important in real-life
engineering problems and mathematical biology models according to the
fractional-time-derivative.