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One-dimensional Model for Fluids of Third-grade in Tubes with Constant Radius

Fernando Carapau, Paulo Correia


Our goal in this paper is to extend previous results obtained for Newtonian and secondgrade fluids to third-grade fluids in the case of an axisymmetric, straight, rigid and impermeable tube with constant cross-section using a one-dimensional hierarchical model based on the Cosserat theory related to fluid dynamics. In this way we can reduce the full threedimensional system of equations for the axisymmetric unsteady motion of a non-Newtonian
incompressible third-grade fluid to a system of equations depending on time and on a single spatial variable. Some numerical simulations for the volume flow rate and the the wall shear stress are presented.


one-dimensional model, third-grade model, Cosserat theory, volume flow rate, mean pressure gradient.

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