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Starting solutions for some unsteady unidirectional flows of Oldroyd-B fluids. (English) Zbl 1101.76006
Summary: Using Fourier sine transform, we derive analytical expressions for velocity fields corresponding to the motion of an Oldroyd-B fluid due to oscillations of an infinite flat plate as well as those induced by an oscillating pressure gradient and pressure jumps. The corresponding solutions for Maxwell and Newtonian fluid appear as limiting cases of the solutions established here. Relevant physical properties of the flows and their dependence on material and geometry parameters are discussed.

MSC:
76A10 Viscoelastic fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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