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herschel–bulkley

European Journal of Applied Mathematics (1)

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1 results

Creeping flow of a Herschel–Bulkley fluid with pressure-dependent material moduli
L. FUSI, F. ROSSO
Journal:

European Journal of Applied Mathematics / Volume 29 / Issue 2 / April 2018

Published online by Cambridge University Press:

11 July 2017, pp. 352-368
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We model the axisymmetric unidirectional flow of a Herschel–Bulkley fluid with rheological parameters that depend linearly on pressure. Adopting an appropriate scaling, we formulate the mathematical problem in cylindrical geometry exploiting an integral formulation for the momentum equation in the unyielded part. We prove that, under suitable assumptions on the data of the problem, explicit solutions can be determined. In particular, we determine the position of the yield surface together with the pressure and velocity profiles. With the aid of some plots, we finally discuss the dependence of the solution on the physical parameters of the problem.