Please use this identifier to cite or link to this item: http://hdl.handle.net/10174/36777

Title: A Three-Dimensional Velocity Field Related to a Generalized Third-Grade Fluid Model
Authors: Carapau, Fernando
Correia, Paulo
Rodrigues, Gracino
Keywords: third-grade fluid
shear-thickening viscoelastic fluid
shear-thinning viscoelastic fluid
power-law function
Cosserat theory
Issue Date: 26-Apr-2024
Publisher: MDPI
Citation: Carapau, F.; Correia, P.; Rodrigues, G. A Three-Dimensional Velocity Field Related to a Generalized Third-Grade Fluid Model. Mathematics 2024, 12, 1326. https://doi.org/10.3390/math12091326
Abstract: In this work, we propose a new three-dimensional constitutive equation related to a thirdgrade fluid. This proposal is based on experimental work for which the viscosity term and the terms related to viscoelasticity may depend on the shear rate, in accordance with a power-law type model. The numerical implementation of this fluid model is rather demanding in terms of computational calculation and, in this sense, we use the Cosserat theory related to fluid dynamics, which makes the transition from the three-dimensional fluid model to a one-dimensional fluid model for a specific geometry under study which, in this case, is a straight tube with constant circular cross-section. Based on this approximation theory, the one-dimensional fluid model is solved by assuming an ordinary differential equation involving: an unsteady mean pressure gradient; an unsteady volume flow rate; the Womersley number; and the viscosity and viscoelasticity parameters. Consequently, for specific data, and using the Runge–Kutta method, we can obtain the solution for the unsteady volume flow rate and we can present simulations to the three-dimensional velocity field.
URI: https://www.mdpi.com/2227-7390/12/9/1326
http://hdl.handle.net/10174/36777
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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