Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: Parametric Study

Abstract

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.

Keywords

• fractional calculus
• Riemann-Liouville fractional derivative
• viscoelasticity
• pipe flow
• fractional Maxwell model
• fractional Zener model