AXIAL FLOW OF SEVERAL NON-NEWTONIAN FLUIDS THROUGH A CIRCULAR CYLINDER

2010 ◽  
Vol 02 (03) ◽  
pp. 543-556 ◽  
Author(s):  
D. VIERU ◽  
I. SIDDIQUE
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Axial Flow ◽  
Newtonian Fluids ◽  
Time Dependent ◽  
Second Grade ◽  
Material Parameters ◽  
Hankel Transforms ◽  
Dimensionless Variables ◽  
Similar Solutions

The velocity field, the longitudinal and the normal tensions corresponding to the axial flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent stress are determined by means of the Laplace and finite Hankel transforms. The similar solutions for Maxwell, second grade or Newtonian fluids have been obtained as particular cases of the solutions for Oldroyd-B fluids. Finally, by using dimensionless variables, some characteristics of the motion as well as the influence of the material parameters on the behavior of fluid are shown by graphical illustrations.

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 First Problem of Stokes for Generalized Burgers' Fluids

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Muhammad Jamil
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Velocity Field ◽  
Integral Transforms ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Second Grade ◽  
Material Parameters ◽  
Transient Solutions ◽  
Similar Solutions

The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Due to a Time-Dependent Couple

2011 ◽  
Vol 66 (1-2) ◽  
pp. 40-46 ◽  
Author(s):  
Corina Fetecau ◽  
Muhammad Imran ◽  
Constantin Fetecau
Keyword(s):  
Exact Solutions ◽  
Couette Flow ◽  
Bessel Functions ◽  
Time Dependent ◽  
Second Grade ◽  
Governing Equations ◽  
Material Parameters ◽  
Taylor Couette ◽  
Similar Solutions ◽  
Taylor Couette Flow

Taylor-Couette flow in an annulus due to a time-dependent torque suddenly applied to one of the cylinders is studied by means of finite Hankel transforms. The exact solutions, presented under series form in terms of usual Bessel functions, satisfy both the governing equations and all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for Maxwell, second grade, and Newtonian fluids performing the same motion. Finally, some characteristics of the motion, as well as the influence of the material parameters on the behaviour of the fluid, are emphasized by graphical illustrations.

EXACT SOLUTIONS FOR THE POISEUILLE FLOW OF A GENERALIZED MAXWELL FLUID INDUCED BY TIME-DEPENDENT SHEAR STRESS

2010 ◽  
Vol 51 (4) ◽  
pp. 416-429 ◽  
Author(s):  
W. AKHTAR ◽  
CORINA FETECAU ◽  
A. U. AWAN
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Poiseuille Flow ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Similar Solutions ◽  
Generalized Maxwell Fluid

AbstractThe Poiseuille flow of a generalized Maxwell fluid is discussed. The velocity field and shear stress corresponding to the flow in an infinite circular cylinder are obtained by means of the Laplace and Hankel transforms. The motion is caused by the infinite cylinder which is under the action of a longitudinal time-dependent shear stress. Both solutions are obtained in the form of infinite series. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases. Finally, the influence of the material and fractional parameters on the fluid motion is brought to light.

First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid

2014 ◽  
Vol 69 (5-6) ◽  
pp. 232-238 ◽  
Author(s):  
Corina Fetecau ◽  
Mehwish Rana ◽  
Niat Nigar ◽  
Constantin Fetecau
Keyword(s):  
Shear Stress ◽  
Circular Cylinder ◽  
Integral Transforms ◽  
Second Grade ◽  
Rotational Flow ◽  
Stress Distributions ◽  
Circular Duct ◽  
Material Parameters ◽  
Similar Solutions ◽  
Rate Type

Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.

General Solutions for the Unsteady Flow of Second-Grade Fluids over an Infinite Plate that Applies Arbitrary Shear to the Fluid

2011 ◽  
Vol 66 (12) ◽  
pp. 753-759 ◽  
Author(s):  
Constantin Fetecau ◽  
Corina Fetecau ◽  
Mehwish Rana
Keyword(s):  
Shear Stress ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Unsteady Motion ◽  
Newtonian Fluids ◽  
Second Grade ◽  
Moving Plate ◽  
General Solutions ◽  
Similar Solutions ◽  
Second Grade Fluids

General solutions corresponding to the unsteady motion of second-grade fluids induced by an infinite plate that applies a shear stress ƒ (t) to the fluid are established. These solutions can immediately be reduced to the similar solutions for Newtonian fluids. They can be used to obtain known solutions from the literature or any other solution of this type by specifying the function ƒ (.). Furthermore, in view of a simple remark, general solutions for the flow due to a moving plate can be developed.

Unsteady flow of a generalized Oldroyd-B fluid due to an infinite plate subject to a time-dependent shear stress

2010 ◽  
Vol 88 (9) ◽  
pp. 675-687 ◽  
Author(s):  
D. Vieru ◽  
Corina Fetecau ◽  
C. Fetecau
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Infinite Plate ◽  
Time Dependent ◽  
Fourier Cosine ◽  
Series Form ◽  
Maxwell Fluids ◽  
Similar Solutions

The unsteady flow of an incompressible generalized Oldroyd-B fluid induced by an infinite plate subject to a time-dependent shear-stress is studied by means of the Fourier cosine and Laplace transforms. The solutions that have been obtained, written under integral and series form in terms of the generalized Ga,b,c(·,t) functions, are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. They satisfy all imposed initial and boundary conditions, and for λ and λr → 0 reduce to the Newtonian solutions. Furthermore, the similar solutions for generalized Maxwell fluids as well as those for ordinary fluids are also obtained as limiting cases of general solutions. Finally, to reveal some relevant physical aspects of the obtained results, the diagrams of the velocity field v(y, t) have been depicted against y for different values of t and of the material and fractional parameters.

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.

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