scholarly journals The Effect of Boundary Slip on the Transient Pulsatile Flow of a Modified Second-Grade Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
N. Khajohnsaksumeth ◽  
B. Wiwatanapataphee ◽  
Y. H. Wu
Keyword(s):  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Boundary Slip ◽  
Fluid Behavior ◽  
Grade Fluid ◽  
Complete Set ◽  
Flow Through

We investigate the effect of boundary slip on the transient pulsatile fluid flow through a vessel with body acceleration. The Fahraeus-Lindqvist effect, expressing the fluid behavior near the wall by the Newtonian fluid while in the core by a non-Newtonian fluid, is also taken into account. To describe the non-Newtonian behavior, we use the modified second-grade fluid model in which the viscosity and the normal stresses are represented in terms of the shear rate. The complete set of equations are then established and formulated in a dimensionless form. For a special case of the material parameter, we derive an analytical solution for the problem, while for the general case, we solve the problem numerically. Our subsequent analytical and numerical results show that the slip parameter has a very significant influence on the velocity profile and also on the convergence rate of the numerical solutions.

scholarly journals Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 123 ◽  
Author(s):  
Mehmet Yavuz ◽  
Ndolane Sene
Keyword(s):  
Heat Balance ◽  
Integral Method ◽  
Fluid Model ◽  
Second Grade ◽  
Physical Analysis ◽  
Second Grade Fluid ◽  
Transform Method ◽  
Heat Balance Integral Method ◽  
Grade Fluid ◽  
The Impact

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

scholarly journals Flow of a Dense Suspension Modeled as a Modified Second Grade Fluid

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 55 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
James Antaki ◽  
Mehrdad Massoudi
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Constitutive Relationship ◽  
Second Grade ◽  
Simple Shear Flow ◽  
Second Grade Fluid ◽  
Dense Suspension ◽  
Grade Fluid

In this paper, a simple shear flow of a dense suspension is studied. We propose a new constitutive relationship based on the second grade fluid model for the suspension, capable of exhibiting non-linear effects, where the normal stress coefficients are assumed to depend on the volume fraction of the particles and the shear viscosity depends on the shear rate and the volume fraction. After non-dimensionalizing the equations, we perform a parametric study looking at the effects of the normal stress coefficients and the variable viscosity. The numerical results show that for a certain range of parameters, the particles tend to form a region of high and uniform volume fraction, near the lower half of the flow.

On some generalizations of the second grade fluid model

2008 ◽  
Vol 9 (3) ◽  
pp. 1169-1183 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Ashwin Vaidya
Keyword(s):  
Fluid Model ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

scholarly journals UNSTEADY TWO-LAYERED BLOOD FLOW THROUGH A -SHAPED STENOSED ARTERY USING THE GENERALIZED OLDROYD-B FLUID MODEL

2016 ◽  
Vol 58 (1) ◽  
pp. 96-118 ◽  
Author(s):  
AKBAR ZAMAN ◽  
NASIR ALI ◽  
O. ANWAR BEG ◽  
M. SAJID
Keyword(s):  
Blood Flow ◽  
Differential Equations ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Initial Boundary ◽  
Momentum Conservation ◽  
Rheological Parameters ◽  
Stenosed Artery ◽  
Flow Through

A theoretical study of an unsteady two-layered blood flow through a stenosed artery is presented in this article. The geometry of a rigid stenosed artery is assumed to be$w$-shaped. The flow regime is assumed to be laminar, unsteady and uni-directional. The characteristics of blood are modelled by the generalized Oldroyd-B non-Newtonian fluid model in the core region and a Newtonian fluid model in the periphery region. The governing partial differential equations are derived for each region by using mass and momentum conservation equations. In order to facilitate numerical solutions, the derived differential equations are nondimensionalized. A well-tested explicit finite-difference method (FDM) which is forward in time and central in space is employed for the solution of a nonlinear initial boundary value problem corresponding to each region. Validation of the FDM computations is achieved with a variational finite element method algorithm. The influences of the emerging geometric and rheological parameters on axial velocity, resistance impedance and wall shear stress are displayed graphically. The instantaneous patterns of streamlines are also presented to illustrate the global behaviour of the blood flow. The simulations are relevant to haemodynamics of small blood vessels and capillary transport, wherein rheological effects are dominant.

scholarly journals On the Steady Flow of a Second-Grade Fluid between Two Coaxial Porous Cylinders

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
M. Emin Erdoğan ◽  
C. Erdem İmrak
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Steady Flow ◽  
Newtonian Fluid ◽  
Velocity Variation ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
The Cross ◽  
Porous Cylinders

An exact solution of an incompressible second-grade fluid for flow between two coaxial porous cylinders is given. The velocity profiles for various values of the cross-Reynolds number and the elastic number are plotted. It is found that for large values of the cross-Reynolds number, the velocity variation near boundaries shows a different behaviour than that of the Newtonian fluid.

Nonorthogonal Stagnation-point Flow of a Second-grade Fluid Past a Lubricated Surface

2016 ◽  
Vol 71 (3) ◽  
pp. 273-280 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

AbstractThe stagnation-point flow of a second-grade fluid past a power law lubricated surface is considered in this paper. It is assumed that the fluid impinges on the wall obliquely. A suitable choice of similarity transformations reduces the governing partial differential equations into ordinary differential equations. The thin lubrication layer suggests that the interface conditions between the fluid and the lubricant can be imposed on the boundary. An implicit finite difference scheme known as the Keller-Box method is employed to obtain the numerical solutions. The effects of slip parameter and Weissenberg number on the fluid velocity and streamlines is discussed in the graphs. The limiting cases of partial-slip and no-slip can be deduced from the present solutions.

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