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On dual solutions of stagnation point flow of a viscoelastic fluid. (English) Zbl 0814.76008
Summary: The laminar two-dimensional flow of an incompressible, viscoelastic fluid near a stagnation point is considered. An approximate solution using the orthogonal collocation point method with Laguerre polynomials is developed. It confirms the non-existence of the solutions beyond a critical value of the viscoelastic fluid parameter and the existence of dual solutions for the values of the parameter less than this critical value. A linear stability analysis of the two solutions is presented. The solution corresponding to the smaller value of the shear stress is found to be the stable solution while the other solution is shown to be unstable.

MSC:
76A10 Viscoelastic fluids
76E99 Hydrodynamic stability
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