Abstract
The generation of the steady rectilinear flow of an Oldroyd B fluid in a rectangular duct is considered. The Laplace transform is used to separate out the time dependence from the governing equations and a Fourier series is used to solve the resulting Poisson problem in the space variables. It is seen that the presence of elasticity in the fluid gives rise to velocity ‘overshoot’. The solution of Waters and King for the planar channel is recovered at large aspect ratios.
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Akyildiz, F.T., Jones, R.S. The generation of steady flow in a rectangular duct. Rheol Acta 32, 499–504 (1993). https://doi.org/10.1007/BF00396181
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DOI: https://doi.org/10.1007/BF00396181