Exact solutions of flow problems of an Oldroyd-B fluid

摘要

Exact analytical solutions of the following six problems of flow of an Oldroyd-B fluid between two boundaries are obtained: (i) unsteady Couette flow, (ii) unsteady flow for rigid and free boundaries, (iii) flow between two parallel plates suddenly set in motion with same speed, (iv) unsteady Poiseuille flow, (v) unsteady generalized Couette flow and (vi) unsteady generalized Couette flow for rigid and free boundaries. The viscoelasticity of the fluid increases the order of the differential equation. It is shown that the solutions exist for all values of non-Newtonian parameters. The solutions for the second grade, Maxwell and Newtonian fluids can be obtained from those for fluids of Oldroyd-B fluid as the limiting cases.