New classes of periodic and non-periodic exact solutions for Newtonian and non-Newtonian fluid flows

Abstract

Two different families of planar exact solutions for second grade fluid flows are derived in this paper. Exact solutions for Newtonian fluid flows are derived as particular case when normal stress moduli vanish. The novelty of the solutions is that they are obtained by assuming the stream functions as a finite sum of functions with different arguments. An important property of the derived solutions is that solutions in a given family are all superposable flows. The first family of solutions can be considered as a generalization of rectangular array of Taylor vortices as these classical solutions are special cases of the derived exact solutions. A subfamily of spatially periodic exact solutions for both Newtonian and non-Newtonian fluid flows are also derived. The complex structures of the two dimensional vortices are illustrated in several cases. • Two new families of exact solutions for second grade fluid flows are derived. • These solutions are classified as generalized Taylor vortices. • The solutions in a given family are superposable flows. • Subfamily of spatially periodic solutions are constructed. • Exact solutions for Newtonian flows are also derived.