A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

摘要

In this communication, we utilize some basic symmetryreductions to transform the governing nonlinear partial differentialequations arising in the study of third-grade fluid flows into ordinarydifferential equations. We obtain some simple closed-form steady-statesolutions of these reduced equations. Our solutions are valid for the wholedomain [0,∞) and also satisfy the physical boundary conditions. Wealso present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the floware presented and discussed.