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The spectral collocation method based on the Vieta-Lucas polynomials is introduced here for the flow of non-Newtonian Powell-Eyring fluid. The attentiveness is focused on some physical characteristics that emerge for numerical simulation of flows with thermal radiation, magnetic field, and slip velocity phenomenon. In addition, the most significant-physical assumptions to handle in this study are the presence of the thermal stratification phenomenon and the handling of the heat generation term in the energy equation. The Vieta-Lucas spectral collocation method is implemented to present an approximate formula for the n-order derivative and solve numerically the proposed model. This method is employed to convert the system of ODEs that describes the problem to a non-linear system of algebraic equations. This system is constructed as a constrained optimization problem and optimized to get the unknown coefficients of the series solution. We state some theorems to study the convergence of the method. The results reveal that raising the viscosity parameter or the slip velocity parameter reduces the velocity distribution, but increasing the heat generation parameter or thermal conductivity parameter increases the temperature distribution.