Time periodic second grade fluid flow in an infinite strip

Abstract

Time periodic Poiseuille type solutions are studied for equations of the non-Newtonian second grade fluid in the two dimensional infinite strip. We prove the existence and uniqueness of the solution. Moreover, we obtain estimates of the solution in Sobolev spaces and show the relationships between the flux and the pressure drop.

Keywords

• the second grade fluids
• Poiseuille flow
• flux condition
• Fourier series