Different families of new exact solutions for planar and nonplanar second grade fluid flows

Abstract

Three different families of new exact solutions for second grade fluid flows are derived in this paper. First family of two dimensional exact solutions are obtained by assuming a novel form for the stream function and these solutions contain spatially periodic as well as non-periodic solutions. The subclass of periodic solutions extends the rectangular array of Taylor vortices to more complex structures of two dimensional vortices. Second family of planar solutions are also having vortex structures similar to Taylor vortices. Third family of exact solutions are pseudo planar flows of second kind. All these exact solutions reduce to corresponding new exact solutions for Newtonian fluid flows when the normal stress moduli are absent.