On the flow of an elastico-viscous fluid near a rotating disk

摘要

The steady laminar flow of an elastico-viscous fluid near a rotating disk is considered. The constitutive equations of the fluid are modeled by those for a Walter B′ fluid. They give rise to a boundary-value problem in which the order of the system of differential equations is seven but there are only five boundary conditions. Nevertheless, without augmenting any boundary condition at infinity, it is possible to obtain an exact numerical solution for any value of k, the viscoelastic fluid parameter. The solution also takes into account and eliminates the error introduced by replacing numerical infinity with a finite value.It is shown that solutions exist for all values of k. A perturbation solution valid for small values of k, and an asymptotic analytical solution valid for large values of k are also derived, each up to the third order. By comparing them with the exact solution, a critical assessment is undertaken of their respective domains of usefulness.