Abstract
The purpose of this research is to examine thin-film nanomaterial movement in three dimensions over a stretchable rotating inclined surface. Similarity variables are used to transform fundamental systems of equations into a set of First-order Differential Equations. The Runge-Kutta Fourth Order approach is utilized for numerical purpose solution. Variable thickness., Unsteadiness parameter., Prandtl number., Schmidt number., Brownian-motion parameter., and Thermophoretic parameter have all been seen to have an impact. Physically and statistically, the indispensable terms namely Nusselt as well as Sherwood numbers are also investigated. As the dimensionless factor \(S\) grows, the temperature field decreases. The momentum boundary layer is cooled when the parameter \(S\) is improved, and the opposite effect is observed for Nusselt number. A greater Schmidt number Sc reduces the Sherwood number by increasing the kinematic viscosity as well as Concentration of the chemical species. Further, the RK4 method is also validated with the HAM approach. Furthermore, we verified the acquired results by establishing a comparison with previous literature, and we discovered an outstanding match, confirming the accuracy of the current communication.