title: A note on the solutions of some nonlinear equations arising in third-grade fluid flows: an exact approach.
abstract: In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.
authors.affiliation: Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa.
authors.forename: Taha
authors.identifier: 0000-0003-0519-1320
authors.initials: T
authors.lastname: Aziz
authors.affiliation: Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa ; School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia.
authors.forename: F M
authors.initials: FM
authors.lastname: Mahomed
mesh_terms: D008962:Models, Theoretical; D014783:Viscosity