7. Numerical results and
verification
This section is devoted to describe and confirm the results achieved in
the preceding sections. Also, we present the numerical results using the
value of the Copper material at \(T_{0}=293\ K\) as [27]
\(\par
\begin{matrix}\lambda=7.76\times 10^{10}\text{kg\ }m^{-1}s^{-2},\ \ \ \mu=3.86\times 10^{10}\text{kg\ }m^{-1}s^{-2},\ \ \ \rho=8954\ kg\ m^{-3},\\
K=386\ W\ m^{-1}K^{-1},\ \ \ C_{e}=3.381\ J\ kg\ K^{-1},\ \ \ \varepsilon=0.0168.\\
\end{matrix}\)
The obtained results are accessible in Tables (1-4) and graphically in
Figs. 1-9 at several values of the distance \(x(0\leq x\leq 4\)) and
distinct values of the two fractional parameters\(\ \ \alpha,\ \ \beta\)at \(t=0.15\), when the dual phase-lags \(\tau_{\theta}=0.03\) and\(\tau_{q}=0.05\) in the present external body forces\(F_{x}=e^{-\text{ωx}}\). The Mathematica programming Language is
used within our numerical calculations. Comparisons are accomplished
with the expected results predicted by all the models mentioned.
Furthermore, the numerical calculations are prepared for three
directions.