## 6 Validity of This Study  
Table 1 is designed to present the comparative analysis of the obtained results with [PERSON] et al. [37]; an examination which probed the unsteadiness flowing of Powell-Eyring liquid via an angled stretchable plate was investigated in this paper by employing the homotopy analysis technique in the existence of thermal radiation. Additionally, we compared our results with a non-uniformly heat-generating study by [PERSON] et al. [38], which elaborated on the unsteadiness magnetic hydrodynamical (MHD) stagnating point, flowing via a porousness shrinkable plate of Casson fluid, flowing with radiative fluxing transference by the shooting method. We also compared our results with [PERSON] et al. [39], an investigation which discussed the Soret effects on unsteady magnetohydrodynamics flowing across a semi-infinite vertical penetrable moveable plate with thermal radiative, heat absorptive, and homogeneous chemically reactive samples exposed to changing suction by the Runge-Kutta 4 th-order computational technique, in limiting cases by taking variation in unsteady parameter \(A\). From the table, it is observed that the obtained computational outcomes for the case of the present model with the utilization of the current numerical technique are in good agreement with the available literature. Figure 15: (**a**,**b**). Linkage of \(Sc\) with concentration distribution at \(\omega=0\) and \(\omega=\pi/3\). Figure 17 investigates the effect of \(We\) and \(\theta_{r}\) on the frictional force coefficient. The surface drag coefficient decreases by increasing \(We\) and \(\theta_{r}\). The viscosity of fluid increases by rising \(We\) and the fluid becomes more viscous by increasing \(\theta_{r}\). As a result, the skin friction coefficient diminishes. The effect of Grashof number \(G\) and power-law index on the surface drag coefficient is highlighted in Figure 18. The buoyancy forces dominate the viscous fluid by increasing \(G\), which amplifies the skin friction coefficient, and the density of fluid lessens by improving the power-law index, which strengthens the surface drag coefficient phenomenon. Figure 17: (a,b) \(We\) and \(\theta_{r}\) attachment with skin friction. Figure 18: \(Cont.\)  
Figure 19 investigated the influence of \(\theta_{w}\) and \(\theta_{r}\) on the Nusselt number. A positive change in \(\theta_{w}\) amplifies the nonlinear thermal radiation phenomenon which amplifies the heat transmission rate. The heat transmission rate diminishes by enhancing \(\theta_{r}\). The impact of both \(N_{t}\) and \(N_{t}\) on the heat transfer rate is displayed n Figure 20. Both \(N_{t}\) and \(N_{b}\) are important parameters of the Buongiorno nanofluid model. It is well established that the addition of nanoparticles in the base fluid amplifies the heat transmission phenomenon. That is why a variation in \(N_{t}\) and \(N_{b}\) amplifies the Nusselt number. A positive variation in \(N\) and \(Pr\) deprecates the Nusselt number as shown in Figure 21. A continuous supply of nonlinear thermal radiation excites the conduction process among the molecules of the fluid. Molecules of the fluid collide more randomly. The Nusselt number is a ratio of heat transfer by convection to heat transfer by conductivity. The Nusselt number is inversely related to the conduction phenomenon. So, an increment in \(N\) deprecates the heat transfer Nusselt number. Thermal diffusivity lessens by augmenting \(Pr\) which diminishes the heat transfer rate. Figure 21: _Cont._  
Figure 20: (a,b) \(N_{t}\) and \(N_{b}\) attachment with Nusselt number. Figure 22 investigates the impact of thermal conductivity \(\varepsilon_{1}\) and molecular diffusivity \(\varepsilon_{2}\) on the Nusselt number. Diffusivity is related to concentration. A positive variation in diffusivity increases the concentration which amplifies the concentration and diminishes the liquid temperature and heat transmission rate. A variation in thermal conductivity magnifies the temperature within the liquid and depreciates the heat transfer rate phenomenon.