Abstract
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 λ r or λ → 0 they tend toward similar solutions for a Maxwell or second-grade fluid. If both λ r and λ → 0 , the solutions for Navier–Stokes fluids are recovered.
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