Approximate analytical solution for the flow of a Phan-Thien–Tanner fluid through an axisymmetric hyperbolic contraction with slip boundary condition

2021 ◽  
Vol 33 (5) ◽  
pp. 053110
Author(s):  
Karen Y. Pérez-Salas ◽  
Gabriel Ascanio ◽  
Leopoldo Ruiz-Huerta ◽  
Juan P. Aguayo
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Hyperbolic Contraction

Analytical Solution of Turbulent Couette Flow by Cosserat Continuum Model and Gradient Theory

2006 ◽  
Author(s):  
H. Ghasvari Jahromi ◽  
G. Atefi ◽  
A. Moosaie ◽  
S. Hormozi ◽  
H. Afshin
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Couette Flow ◽  
Continuum Model ◽  
Slip Boundary Condition ◽  
Cosserat Continuum ◽  
Dimensionless Number ◽  
Gradient Theory ◽  
Slip Boundary ◽  
Cosserat Continuum Model

In present paper the theory of the micropolar fluid based on a Cosserat continuum model has been applied for analysis of Couette flow. The obtained results for the velocity field have been compared with known results from experiments done by Reichardt at Max Plank institute for fluids in Gottingen [1,2] and analytical solution of the problem from Gradient theory by Alizadeh [3]. The boundary condition used here was the no slip one and Trostel’s slip boundary condition [4]. A good agreement between experimental results and the results of the problem for Reynolds near 18000 has beeen found. A new dimensionless number introduced that indicates the theoretical relation between cosserat theory and slip theory and their interaction.

Analytical Solution of Turbulent Problems Using Governing Equation of Cosserat Continuum Model

2006 ◽  
Author(s):  
H. Ghasvari-Jahromi ◽  
Gh. Atefi ◽  
A. Moosaie ◽  
S. Hormozi
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Continuum Model ◽  
Slip Boundary Condition ◽  
Cosserat Continuum ◽  
Dimensionless Number ◽  
Gradient Theory ◽  
Slip Boundary ◽  
Flow Through ◽  
Cosserat Continuum Model

In present paper the theory of the micropolar fluid based on a Cosserat continuum model has been applied for analysis of Couette flow and turbulent flow through rough pipes. The obtained results for the velocity field have been compared with known results from experiments done by Reichardt at Max Plank institute for fluids in Gottingen [1,2] and analytical solution of the problem from Gradient theory by alizadeh[3] for couette problem and with known results from experiments done by Nikuradse (1932). the boundary condition used here was the no slip one and Trostel's slip boundary condition[4].a good agreement between experimental results and the results of the problem for Reynolds near 18000 has beeen found in the couette case also in this case A new dimensionless number introduced that indicates the theoretical relation between cosserat theory and slip theory and their interaction. The solution has been performed for a Reynolds number of 106 for pipes with different values of roughness and the validity analysis approved by the results of Nikuradse's experiments.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

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