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.

scholarly journals Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
M. Emin Erdoğan ◽  
C. Erdem İmrak
Keyword(s):  
Reynolds Number ◽  
Hypergeometric Functions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Confluent Hypergeometric Functions ◽  
Moment Coefficient ◽  
Grade Fluid ◽  
Porous Walls ◽  
The Cross ◽  
The Moment

An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for , , and values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.

A series solution of the boundary value problem arising in the application of fluid mechanics

2018 ◽  
Vol 28 (10) ◽  
pp. 2480-2490 ◽  
Author(s):  
Yasir Khan
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Transverse Direction ◽  
Hydrodynamic Flow ◽  
Porous Channel ◽  
Second Grade ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
Content Type ◽  
Grade Fluid

Purpose This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM). Design/methodology/approach The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs. Findings It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number. Originality/value To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.

Application of differential constraint method to exact solution of second-grade fluid

2009 ◽  
Vol 30 (4) ◽  
pp. 403-412 ◽  
Author(s):  
Dao-xiang Zhang ◽  
Su-xiao Feng ◽  
Zhi-ming Lu ◽  
Yu-lu Liu
Keyword(s):  
Exact Solution ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Differential Constraint ◽  
Grade Fluid ◽  
Constraint Method

scholarly journals A note on “Taylor–Couette flow of a generalized second grade fluid due to a constant couple”

2010 ◽  
Vol 15 (2) ◽  
pp. 155-158 ◽  
Author(s):  
C. Fetecau ◽  
A. U. Awan ◽  
M. Athar
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Unsteady Flow ◽  
Couette Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
New Form ◽  
Second Grade Fluids

In this brief note, we show that the unsteady flow of a generalized second grade fluid due to a constant couple, as well as the similar flow of Newtonian and ordinary second grade fluids, ultimately becomes steady. For this, a new form of the exact solution for velocity is established. This solution is presented as a sum of the steady and transient components. The required time to reach the steady-state is obtained by graphical illustrations.

scholarly journals Heat transfer analysis of a second grade fluid over a stretching sheet

1995 ◽  
Vol 18 (4) ◽  
pp. 765-772 ◽  
Author(s):  
C. E. Maneschy ◽  
M. Massoudi
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Stretching Sheet ◽  
Heat Transfer Analysis ◽  
Second Grade ◽  
Temperature Profiles ◽  
Second Grade Fluid ◽  
Grade Fluid

The heat tranfer and flow of a non-Newtonian fluid past a stretching sheet is analyzed in this paper. Results in a non-dimensional form are presented here for the velocity and temperature profiles assuming different kind of boundary conditions.

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