Visco Elastic Fluids

Navier-Stokes equations are the most fundamental equations in Newtonian fluid mechanics. But for the last few decades it has been generally accepted that the Newtonian fluid flow models are not able to explain certain phenomena which has been reported for the fluids flow in industry and other technological applications. Indeed it is the non-Newtonian fluid models which best describe these phenomena. Among the several non-Newtonian fluid models, the second and third grade fluids have received the attention of many researches. Particularly, non-Newtonian fluids with magnetic field under the influence of Hall currents have been investigated more, mainly due to their abundant applications in various industries and different engineering disciplines. The equations describing the motion of these fluids are highly non-linear partial differential equations and therefore present a special challenge to engineers, physicists and mathematicians. Furthermore, due to the non-linearity there are only a few analytical solutions available in the literature. In this report we present some analytic solutions for Oldroyd-B, second and third grade fluids under different geometrical configurations.