Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

The aim of this note is to present the exact solutions corresponding to two types of unsteady flows of an Oldroyd-B fluid in a channel of rectangular cross-section. The solutions that have been obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For λr or λ→0 they tend toward similar solutions for a Maxwell or second-grade fluid. If both λr and λ→0, the solutions for Navier-Stokes fluids are recovered.