Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study
1
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA
2
Computational Science Division and Leadership Computing Facility, Argonne National Laboratory, Lemont, IL 60439, USA
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(24), 9080; https://doi.org/10.3390/app10249080
Received: 29 October 2020 / Revised: 7 December 2020 / Accepted: 14 December 2020 / Published: 18 December 2020
(This article belongs to the Special Issue Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures)
Pipe flow is one of the most commonly used models to describe fluid dynamics. The concept of fractional derivative has been recently found very useful and much more accurate in predicting dynamics of viscoelastic fluids compared with classic models. In this paper, we capitalize on our previous study and consider space-time dynamics of flow velocity and stress for fractional Maxwell, Zener, and Burgers models. We demonstrate that the behavior of these quantities becomes much more complex (compared to integer-order classical models) when adjusting fractional order and elastic parameters. We investigate mutual influence of fractional orders and consider their limiting value combinations. Finally, we show that the models developed can be reduced to classical ones when appropriate fractional orders are set.
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Keywords:
fractional calculus; Riemann-Liouville fractional derivative; viscoelasticity; pipe flow; fractional Maxwell model; fractional Zener model; fractional Burgers model
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MDPI and ACS Style
Gritsenko, D.; Paoli, R. Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study. Appl. Sci. 2020, 10, 9080. https://doi.org/10.3390/app10249080
AMA Style
Gritsenko D, Paoli R. Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study. Applied Sciences. 2020; 10(24):9080. https://doi.org/10.3390/app10249080
Chicago/Turabian StyleGritsenko, Dmitry; Paoli, Roberto. 2020. "Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study" Appl. Sci. 10, no. 24: 9080. https://doi.org/10.3390/app10249080
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