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Flow of second-order fluids in curved pipes. (English) Zbl 0972.76009
From the summary: We study flows of incompressible fluids in curved pipes of circular cross-section. The perturbation parameter is the curvature ratio: the cross-sectional radius of the pipe divided by the radius of curvature of the pipe centerline. We obtain closed form solutions for the perturbation equations when the second normal stress difference is non-zero. We show that for a countable number of combinations of non-dimensional parameters a perturbation solution exists but is not unique. For other combinations of parameters, a perturbation solution does not exist.

MSC:
76A05 Non-Newtonian fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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