Different Formulations to Solve the Giesekus Model for Flow between Two Parallel Plates

• Published in: Applied sciences 2021-11, Vol.11 (21), p.10115
• Main Authors: da Silva Furlan, Laison Junio, de Araujo, Matheus Tozo, Brandi, Analice Costacurta, de Almeida Cruz, Daniel Onofre, de Souza, Leandro Franco
• Format: Article
• Language: English
• Subjects: Approximation; Constitutive models; exact solution; flow between two parallel plates; Fluid dynamics; Fluid flow; Fluid mechanics; Fluids; Formulations; Giesekus model; high Weissenberg number; high-order approximations; Independent variables; Mathematical models; Newtonian fluids; Non Newtonian fluids; Numerical integration; numerical solution; Parallel plates; Reynolds number; Solvents; Velocity; Velocity distribution; Viscoelastic fluids; Viscoelasticity; Viscosity
• ISSN: 2076-3417; 2076-3417
• DOI: 10.3390/app112110115

This work presents different formulations to obtain the solution for the Giesekus constitutive model for a flow between two parallel plates. The first one is the formulation based on work by Schleiniger, G; Weinacht, R.J., [Journal of Non-Newtonian Fluid Mechanics, 40, 79–102 (1991)]. The second formulation is based on the concept of changing the independent variable to obtain the solution of the fluid flow components in terms of this variable. This change allows the flow components to be obtained analytically, with the exception of the velocity profile, which is obtained using a high-order numerical integration method. The last formulation is based on the numerical simulation of the governing equations using high-order approximations. The results show that each formulation presented has advantages and disadvantages, and it was investigated different viscoelastic fluid flows by varying the dimensionless parameters, considering purely polymeric fluid flow, closer to purely polymeric fluid flow, solvent contribution on the mixture of fluid, and high Weissenberg numbers.