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

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 for...

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Bibliographic Details
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
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Summary: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.
ISSN:2076-3417
2076-3417
DOI:10.3390/app112110115