scholarly journals Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

2011 ◽  
Vol 16 (1) ◽  
pp. 47-58 ◽  
Author(s):  
M. Imran ◽  
M. Kamran ◽  
M. Athar ◽  
A. A. Zafar
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Exact Solutions ◽  
Unit Length ◽  
Time Dependent ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Grade Fluid ◽  
Second Grade Fluids

Exact solutions for the velocity field and the associated shear stress, corresponding to the flow of a fractional second grade fluid between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a time-dependent torque per unit length 2πR1ft2. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1, respectively β → 1 and α1 → 0, the corresponding solutions for ordinary second grade fluids and Newtonian fluids, performing the same motion, are obtained as limiting cases.

scholarly journals Taylor–Couette flow of a generalized second grade fluid due to a constant couple

2010 ◽  
Vol 15 (1) ◽  
pp. 3-13 ◽  
Author(s):  
M. Athar ◽  
M. Kamran ◽  
C. Fetecau
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Unit Length ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Coaxial Cylinders ◽  
Constant Torque ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

The velocity field and the adequate shear stress, corresponding to the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constant torque f per unit length. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1 or β → 1 and α1 → 0, the corresponding solutions for an ordinary second grade fluid, respectively, for the Newtonian fluid, performing the same motion, are obtained as limiting cases.

scholarly journals Exact solutions for the unsteady rotational flow of a generalized second grade fluid through a circular cylinder

2010 ◽  
Vol 15 (4) ◽  
pp. 437-444 ◽  
Author(s):  
M. Kamran ◽  
M. Imran ◽  
M. Athar
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Time Dependent ◽  
Second Grade ◽  
Rotational Flow ◽  
Second Grade Fluid ◽  
Special Cases ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Similar Solutions

Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t = 0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis with a time dependent angular velocity Ωt. The solutions that have been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for the ordinary second grade and Newtonian fluids, performing the same motion, are obtained as special cases of our general solution.

scholarly journals Flow of a second grade fluid with fractional derivatives due to a quadratic time dependent shear stress

2018 ◽  
Vol 57 (3) ◽  
pp. 1963-1969 ◽  
Author(s):  
Nauman Raza ◽  
M. Abdullah ◽  
Asma Rashid Butt ◽  
Aziz Ullah Awan ◽  
Ehsan Ul Haque
Keyword(s):  
Shear Stress ◽  
Fractional Derivatives ◽  
Time Dependent ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

scholarly journals Exact Solutions for Fractionalized Second Grade Fluid Flows with Boundary Slip Effects

2021 ◽  
Vol 26 (1) ◽  
pp. 88-103
Author(s):  
S. Dehraj ◽  
R.A. Malookani ◽  
S.K. Aasoori ◽  
G.M. Bhutto ◽  
L. Arain
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Exact Analytical Solution ◽  
Fluid Flows ◽  
Second Grade ◽  
Physical Parameters ◽  
Second Grade Fluid ◽  
Boundary Slip ◽  
Transform Method ◽  
Grade Fluid

AbstractIn this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under the influence of slip has been obtained. A coupled system of partial differential equations representing the equation of motion has been re-written in terms of fractional derivatives form by using the Caputo fractional operator. The Discrete Laplace transform method has been employed for computing the expressions for the velocity field u(y, t) and the corresponding shear stress τ (y, t). The obtained solutions for the velocity field and the shear stress have been written in terms of Wright generalized hypergeometric function pψq and are expressed as a sum of the slip contribution and the corresponding no-slip contribution. In addition, the solutions for a fractionalized, ordinary second grade fluid and Newtonian fluid in the absence of slip effect have also been obtained as special case. Finally, the effect of different physical parameters has been demonstrated through graphical illustrations.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

2011 ◽  
Vol 27 (2) ◽  
pp. 222-227 ◽  
Author(s):  
Amir Mahmood ◽  
Saima Parveen ◽  
Najeeb Alam Khan
Keyword(s):  
Exact Solutions ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

PRESSURE FLOW OF A SECOND GRADE FLUID THROUGH A CHANNEL OF VARYING WIDTH WITH APPLICATION TO STENOSED ARTERY

2013 ◽  
Vol 06 (03) ◽  
pp. 1350016
Author(s):  
A. M. SIDDIQUI ◽  
T. HAROON ◽  
Z. BANO ◽  
S. ISLAM
Keyword(s):  
Shear Stress ◽  
Flow Behavior ◽  
Second Grade ◽  
Maximum Height ◽  
Second Grade Fluid ◽  
Flow Shear ◽  
Approximate Methods ◽  
Stenosed Artery ◽  
Grade Fluid ◽  
Flow Shear Stress

Analytical solutions are obtained for steady flow of an incompressible second grade fluid in an axisymmetric channel of varying width. Three approximate methods are used depending upon three different geometrical configuration. The results obtained are applied to study the flow of a second grade fluid through a smooth constriction. To understand the flow behavior near stenosis, resistance to the flow, shear stress at the wall and stress at the stenosis throat are calculated. The results obtained are numerically evaluated for different values of dimensionless non-Newtonian parameters λ1 and λ2 and maximum height of the stenosis δm. It is observed that as we increase the value of these parameters the resistance to the flow, wall shear stress and stress at the stenosis throat increase.

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.

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