Abstract
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.
Highlights
The solution for the velocity and extra-stress tensor distribution in a viscoelastic fluid flow using a specific model can be obtained numerically and, sometimes, analytically
The current study presents different formulations to obtain the solution for the Giesekus constitutive model considering the flow between two parallel plates (Poiseuille flow for Newtonian fluid flow)
The paper is divided as follows: Section 2 presents the governing equations; the different formulations to obtain the laminar solution are presented in Section 3, including a semi-analytical solution obtained through the results presented by Schleiniger and Weinacht [10], a formulation to solve considering the independent variable change, and a numerical formulation through the high-order numerical approximation
Summary
The solution for the velocity and extra-stress tensor distribution in a viscoelastic fluid flow using a specific model can be obtained numerically and, sometimes, analytically. Tomé et al [14] presented a solution method for the Giesekus viscoelastic fluid flow based on work by Schleiniger and Weinacht [10], where an analytical solution for the flow between two parallel plates problem was proposed. The current study presents different formulations to obtain the solution for the Giesekus constitutive model considering the flow between two parallel plates (Poiseuille flow for Newtonian fluid flow). The paper is divided as follows: Section 2 presents the governing equations; the different formulations to obtain the laminar solution are presented, including a semi-analytical solution obtained through the results presented by Schleiniger and Weinacht [10], a formulation to solve considering the independent variable change, and a numerical formulation through the high-order numerical approximation.
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