Unsteady flow of an Oldroyd-B fluid induced by a constantly accelerating plate

We study the start-up flow of an Oldroyd-B fluid between two infinite parallel plates, one of them at rest and the other one being subject, after time zero, to a constant acceleration A. The solutions that are obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. They reduce to those for a Maxwell, Second grade or Navier–Stokes fluid as a limiting case.