Thin Film Flow of Non-Newtonian Third Grade Fluid Down an Inclined Plane by Variation of Parameter Method
Keywords:
non-Newtonian fluid, thin film flow, third-grade fluid, Variation of Parameters Method (VPM)Abstract
In this study, a non-Newtonian third-grade fluid flow down an inclined parallel plate held horizontally against each other are investigated. As the nonlinear differential equation which governs the flow model can be obtained by using the conversation of laws, the Variation of Parameters Method (VPM) is then applied to solve the aforementioned differential equation. The proposed VPM is applied without any discretization, perturbation, transformation or restrictive assumptions and is free from round off errors and calculation. Analytical solution solved by Runge-Kutta numerical solution and the VPM show excellent agreement. Effects of flow parameters β and m on the velocity field are demonstrated graphically with comprehensive discussions. Numerical results reveal the complete reliability of the proposed VPM.
