Computation of flow of a second grade fluid near a rotating disk

The steady laminar Bow of a second grade fluid near a rotating disk is considered. The viscoelasticity of the fluid gives rise to a boundary value problem in which the order of the differential equation is seven but there are only five boundary conditions. It is shown that a series solution involving exponentially decaying functions characterizes the problem. Its existence is used to reduce the range of integration to unity. The transformed differential equations are solved numerically for arbitrary non-negative values of K, the viscoelasticity of the fluid. The exact numerical solution reveals that the solution exists for all values of K. A perturbation solution valid for small Pt, and an asymptotic solution valid for large K are also developed. Their respective domains of applicability are discussed. (C) 1997 Elsevier Science Ltd.