## 5 Conclusions  
This study presents the numerical outcomes of the MHD free convective motion of Walters-B liquid past a permeable accelerating surface with the contribution of [PERSON] and Dufour. The equations of motion PDEs, which modeled the problem under investigation, were evaluated into fourth-order coupled and highly nonlinear total differential equations with suitable similarity functions. We solved the transformed fourth-order coupled and highly nonlinear ordinary differential equations in Equations (19)-(21) using SHAM. SHAM uses the traditional HAM in conjunction with the Chebyshev pseudospectral method to solve differential equations. Spectral methods are now an essential instrument for scientist and engineers to solve complex problems. Detailed explanations of SHAM are presented in the previous section. The present results show that the application of magnetism gives rise to a drag-like force (i.e., Lorentz force), thereby lowering the fluid velocity. This study also explains the application of the MHD flow of viscoelastic fluid in biomechanics, the petroleum industry, etc. The present results reveal that the velocity decreases drastically with an increase in the viscoelastic parameter (\(\beta\)). Furthermore, this study shows that an increase in the Dufour parameter intensifies the fluid velocity alongside temperature. This is owing to the energy flux, which rises due to the concentration gradient, which is inversely proportional to the velocity. In the same vein, a higher Soret term increases the velocity and concentration field. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\beta\) & \(\mathbf{G}t\) & \(\mathbf{C}f\) & \(\mathbf{N}u\) & \(\mathbf{S}h\) \\ \hline
0.0 & 0 & 0.35362 & 0.65313 & 0.92109 \\  & 0.5 & 0.53971 & 0.67986 & 0.94349 \\  & 1 & 0.72152 & 0.70418 & 0.96415 \\  & 2 & 1.07430 & 0.74707 & 1.001256 \\
0.01 & 0 & 0.35618 & 0.65291 & 0.92095 \\  & 0.5 & 0.54379 & 0.67981 & 0.94351 \\  & 1 & 0.72714 & 0.70430 & 0.96431 \\  & 2 & 1.08301 & 0.74750 & 1.00168 \\
0.05 & 0 & 0.36766 & 0.65212 & 0.92051 \\  & 0.5 & 0.56172 & 0.67975 & 0.94369 \\  & 1 & 0.75155 & 0.70493 & 0.96508 \\  & 2 & 1.12046 & 0.74942 & 1.00358 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numeric values of local skin friction, local Nusselt, and local Sherwood numbers for distinct values of viscoelastic parameter (\(\beta\)) and thermal Grashof number when M = 1.0, R = 0.5, Pr = 0.71, E = 0.01, S\({}_{w}\) = 0.1, \(\alpha\) = 0.01, Sr = 0.2, Df = 0.3, Sc = 0.61. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(\beta\) = 0, \(\mathbf{S}w\) = 0.02} & \multicolumn{4}{c}{\(\beta\) = 0.01, \(\mathbf{S}w\) = 0.06} \\ \hline \(\alpha\) & \(\mathbf{S}r\) & \(\mathbf{C}f\) & \(\mathbf{N}u\) & \(\mathbf{S}h\) & \(\mathbf{C}f\) & \(\mathbf{N}u\) & \(\mathbf{S}h\) \\ \hline
0.0 & 0 & 1.09417 & 0.70364 & 1.01421 & 1.05091 & 0.74833 & 1.06656 \\  & 0.5 & 1.13712 & 0.74918 & 0.88981 & 1.09354 & 0.79586 & 0.92930 \\  & 1 & 1.18712 & 0.80057 & 0.74683 & 1.14279 & 0.84920 & 0.77128 \\  & 2 & 1.31471 & 0.92566 & 0.38704 & 1.26665 & 0.97771 & 0.37455 \\
0.02 & 0 & 1.09968 & 0.69008 & 1.01670 & 1.05523 & 0.73602 & 1.06848 \\  & 0.5 & 1.14095 & 0.73666 & 0.89450 & 1.09652 & 0.78449 & 0.93333 \\  & 1 & 1.18941 & 0.78945 & 0.75314 & 1.14456 & 0.83905 & 0.77707 \\  & 2 & 1.31473 & 0.91886 & 0.39461 & 1.26665 & 0.97114 & 0.38196 \\
0.08 & 0 & 1.11955 & 0.64363 & 1.02623 & 1.06975 & 0.69593 & 1.07521 \\  & 0.5 & 1.15414 & 0.69539 & 0.91000 & 1.10609 & 0.74877 & 0.94608 \\  & 1 & 1.19652 & 0.75529 & 0.77245 & 1.144970 & 0.80902 & 0.79406 \\  & 2 & 1.31363 & 0.90744 & 0.40934 & 1.26587 & 0.95815 & 0.39801 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numeric values of local skin friction, local Nusselt, and local Sherwood numbers for distinct values of heat generation parameter (\(\beta\)) and Soret number (\(\beta\)) when M = 1.0, R = 0.5, Pr = 0.71, E = 0.01, S\({}_{w}\) = 0.1, Sr = 0.2, Df = 0.3, Sc = 0.61.