## 4 Discussion
The comparison of the present work and published work [22] has been shown in Figures 12 and 13, where the common parameters have been counted and dissimilar parameters have been ignored. In the published work the plate moves vertically while in the present work the plate moves at an incline, with the same physical conditions. The gravitational parameter in the published work is known as stock number \(S_{t}\) and in the present work it has been denoted by \(m\). In Figure 12, the larger values of the second grade parameter \(\alpha\) and Williamson number \(W_{e}\) show that the results only match at the boundaries. However, in Figure 13, if we reduce the values of these two parameters, the graphical comparison becomes very close which specifies the validation of this work. The comparison of OHAM and ADM methods for the velocity field and temperature distribution have been shown in Figures 14 and 15. It is clear from Figure 14 that the OHAM and ADM agree with each other initially, and the fast convergence of OHAM solution is clear at the boundary. Similarly, in Figure 15, the boundary conditions are more clearly satisfied by OHAM as compared to ADM. Tables 1 and 2 show the numerical comparison of the present work with published work [22]. The absolute error is larger for higher values of the second grade parameter \(\alpha\) and Williamson number \(We\), as shown in Table 1, but this error reduces for small values of these parameters. Tables 3 and 4 demonstrate the agreement of OHAM and ADM for velocity and temperature profiles, respectively, and the closed convergence of OHAM has been obtained. Figure 1: The physical configuration of the problem considering thin film flow of the Williamson fluid passing over an inclined, oscillating, and moving belt. Figure 2.0 The view of the fluid motion at time level \(\omega t\in(0,6\pi)\) in 3D, when \(m=0.3\), \(M=0.2\), \(W_{e}=0.1\). Figure 2.1 The view of the fluid motion at time level \(\omega t\in(-3\pi,3\pi)\) in 2D, when \(m=0.3\), \(M=0.2\), \(W_{e}=0.1\). Figure 2.2 The 3D presentation of temperature distribution at time level \(\omega\ t\in(0,50\pi)\), when \(\omega=0.2\), \(m=0.10\), \(M=0.2\), \(W_{e}=0.1\), \(Ec=9\). Figure 2.3 The 2D presentation of temperature distribution at time level \(\omega t\in(-4\pi,4\pi)\), when \(\omega=0.2\), \(m=0.10\), \(M=0.2\), \(W_{e}=0.1\), \(Ec=9\). Figure 2.4 The magnetic effect during fluid motion, when. \(\omega=0.6\); \(m=0.5\); \(W_{e}=5\); \(t=5\). Figure 2.5 The effect of the Williamson number during fluid motion, when \(\omega=0.3;m=0.5;M=5\); \(t=20\). Figure 2.6 The effect of the oscillating parameter \(\omega\) during fluid motion, when \(m=0.5;W_{e}=5\); \(M=1.6\); \(t=1\). Figure 2.7 The effect of the Eckert number during temperature distribution, when \(m=0.5;\ W_{e}=5;\ M=0.6;\ \omega=0.7;t\ =\ 1.\)  
Figure 2.8 The effect of the gravitational parameter during fluid motion, when \(\omega=0.6;\ W_{e}=5;\ M=0.6;\ t\ =3.5.\)  
Figure 2.9 The effect of the Williamson number during temperature distribution, when \(m=0.5\); \(Ec=8\); \(M=0.5\); \(\omega=0.3;t=1\). Figure 4.0 The comparison of the velocity profile of the present work and published work [18], when. \(\alpha=0.5\); \(W_{e}=0.3\); \(S_{t}=m=1\); \(M=\lambda=0\); \(a=\xi=1\); \(\omega=0.3;t=0.6\). \begin{table}
\begin{tabular}{c c c c} \hline
**Y** & **Published Work** & **Present Work** & **Absolute Error** \\ \hline
0 & 1.99281 & 1.99281 & 0. \\
0.2 & 1.51428 & 1.22328 & 0.290999 \\
0.4 & 1.07569 & 0.6983 & 0.377391 \\
0.6 & 0.677106 & 0.355481 & 0.321626 \\
0.8 & 0.318544 & 0.139077 & 0.179467 \\
1 & \(6.245\times 10^{-18}\) & 0. & \(6.245\times 10^{-18}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The numerical agreement of the present work and published work [22] with absolute error, when \(\alpha=0.5;W_{e}=0.3;S_{t}=m=1;M=\lambda=0;a=\xi=1;\omega=0.3;t=0.6\).