7.1 Comparison of different models of thermoelasticity

In this subsection, the distributions of the physical fields for different models of thermoelasticity (CTE, LS , DPL and SFLS) together with the modified fractional model with two parameters\(\alpha,\ \beta\) and dual phase-lags (2FDPL) are studied. The obtained results are represented in Tables (1-3) and Figs.(1-3) for the field quantities corresponding to different values of the parameters\(\alpha,\ \beta\) within the distance \(x(0\leq x\leq 4\)) at\(t=0.15\), when the dual phase-lags\(\tau_{\theta}=0.03,\tau_{q}=0.05\) and the presence of external body force \(\omega=5\). These tables emphasize that the physical quantities depend not only on the time \(t\) and the distance \(x\), but also on the fractional parameters \(\alpha\) and \(\beta\).
Table 1 : The effect of the fractional parameters\(\alpha\), \(\beta\) on the temperature \(\theta\)