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Laminar two-dimensional flow of a viscoelastic fluid of the "Second-Order" type was investigated above a fixed rigid plate. Conventional boundary layer approximations
were invoked to simplify the equations of motion which incorporate several elastic terms in addition to the familiar inertia, viscous and pressure terms. The governing boundary layer equation was realized to be a PDF equation which was further transformed into a nonlinear fourth-Order ODE through the use of the concept of a stream function together with introducing a similarity variable. The xcoordinate could not be eliminated from this equation, and so only local similarity solutions
could be obtained for this flow field. Using a combination of finite difference and shooting methods, this equation was solved numerically for Deborah numbers as high as 1.0. The results showed that the wall shear stress scales with fluid's elasticity, increasing for higher values of fluid's elasticity. The boundary layer thickness was also found to decrease with an in crease in the elastic level of the fluid. Around a Deborah number of 0.4, velocity inside the boundary layer is predicted to exceed that
outside the layer, a prediction which awaits experimental verification.