## 8 Final Outcomes  
In this study, we theoretically investigated the thermal and entropy performance of third-grade nanofluid. The governing equations are converted to ordinary differential equations and numerically resolved using the Galerkin finite element method. All of the findings have been thoroughly examined and debated. As a result of this research, the following conclusions can be drawn:  
* The velocity profile can be increased by adjusting the Deborah number (\(\beta_{2}\), \(\beta_{3}\)) and injection parameters, although porous media, volume fraction nanoparticles, velocity slide, and force parameters reduce the speed of the movement.
* The Deborah number (\(\beta_{1}\)), porous media, volume fraction nanoparticle, velocity slip, Biot number, radiation, thermal conductivity, and injection parameter increase the temperature profile, whereas Deborah number (\(\beta_{2}\)) and the suction parameter reduce the temperature profile of both nanofluids.
* Porous media, volume fraction nanoparticles, Biot number, radiation, suction, Reynolds number, and Brinkmann support entropy in the system. However, only velocity slip and injection parameters can reduce flow entropy.
* The local Nusselt number is determined as a result of the volume fraction nanoparticle, Biot number, and radiation parameter, although it is reduced by the velocity slip parameter.
* The SWCNT-CMC is a better heat conducting, whereas the MWCNT-CMC is a better heat absorber.  
Future applications of the G-FEM include a range of physical and technological difficulties [66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77]. According to [78; 79; 80; 81; 82; 83; 84; 85; 86; 87], there have been several recent advancements with respect to the importance of the research domain under consideration.  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \(B_{\xi}\) & \(\Lambda\) & \(S\) & \(\phi\) & \(Nr\) & \(Pr\) & \(N_{n}Re_{x}^{\frac{\pi\lambda}{2}}\) & \(N_{n}Re_{x}^{\frac{\pi\lambda}{2}}\) \\  & & & & & & & **MWCNT-CMC** & **SWCNT-CMC** \\ \hline
0.1 & 0.2 & 0.1 & 0.1 & 0.1 & 0.8 & 0.0907 & 0.1209 \\
0.2 & & & & & & 0.1735 & 0.2302 \\
0.3 & & & & & & 0.2492 & 0.3291 \\  & 0.1 & & & & & 0.0860 & 0.1021 \\  & 0.2 & & & & & 0.0907 & 0.1209 \\  & 0.3 & & & & & 0.0955 & 0.1408 \\  & 0.1 & & & & & 0.0907 & 0.1209 \\  & 0.2 & & & & & 0.0952 & 0.1387 \\  & 0.3 & & & & & 0.0981 & 0.1454 \\ \hline  & & & & & & 0.0652 & 0.0979 \\  & & & & & & 0.0780 & 0.1009 \\  & & & & & & 0.0907 & 0.1209 \\  & & & & & 0.1 & 0.0907 & 0.1209 \\  & & & & & 0.2 & 0.0920 & 0.1513 \\  & & & & & 0.0982 & 0.1625 \\  & & & & & 0.8 & 0.0907 & 0.1209 \\  & & & & & 7.8 & 0.0959 & 0.1598 \\  & & & & & 6450 & 0.0972 & 0.1853 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Calculation of Nusselt number \(=N_{n}Re_{x}^{\frac{\pi\lambda}{2}}\) for \(Pr=0.8\).  
**Author Contributions:** Conceptualization, I.U.; Data curation, I.U.; Formal analysis, N.A.A.M.N. and R.W.I.; Funding acquisition, S.M.H. and M.K.; Investigation, W.J.; Methodology, W.J. and S.M.H.; Project administration, M.B.H.; Resources, M.B.H.; Software, F.S.; Supervision, M.K.; Validation, R.W.I.; Visualization, N.A.A.M.N.; Writing--original draft, R.S. and R.W.I.; Writing--review & editing, E.S.M.T.E.D. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
**Data Availability Statement:** All the used data is provided in the manuscript.  
The authors are grateful to the Deanship of Scientific Research, Islamic University of Madinah, Ministry of Education, KSA, for supporting this research work through a research project grant under Research Group Program/1/804.  
The authors declare no conflict of interest.